Visit : www.EasyEngineeering.net
DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING SEVENTH SEMESTER IT 6005 DIGITAL IMAGE PROCESSING UNIT I PART B 1
What are the elements of image processing system? Describe its working. (May/June 2012), (Nov/Dec- 2012), (Nov/Dec-2008) Components of image processing: Different models of image processing systems available in market. It connected as peripheral to computer Software also developed for image processing Large scale IP systems used in different applications e.g Satellite image processing
IP COMPONENTS ARE Image sensors Specialized Image processing hardware CSomputer Software Mass storage capability Image display Hardcopy devices Imaging Sensors To acquire an image, two elements are needed Physical device –Is a device that is sensitive to the energy radiated by the object .
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
Digitizer-Is a device for converting the output of the physical sensing device into digital form. Specialized image processing hardware Also called front-end system.The main feature is speed.It has a digitizer and ALU.The ALU operations are parallel operations Computer May be PC to Supercomputer Used for off-line image processing tasks Software Consists of collection of modules that perform specific task User can also write code for their own algorithm implementation Mass storage capability Without compression an image need MB range memory for storage. We need mass stoarge Three categories Short term storage – computer memory On-line storage - for relatively fast recall (optical-media storage) Archival storage – infrequent recall – magnetic tape Display Color monitor Integral part of computer system Stereo display (two small display) used for some applications Hardcopy Laser Printer Digital media (CD-ROM disk) Networking
Default function of computer system large amount of date in image processing applications. Need more bandwidth In remote area – internet is not efficient Improve by optical fiber and broadband technologies
2 . What is a frame buffer? Write the categories of digital storage for image processing applications. (8) (Nov/Dec-2012) Frame buffer:A buffer that stores the contents of an image pixel by pixel. The three categories of difital storage are: Short term storage – computer memory On-line storage - for relatively fast recall (optical-media storage) Archival storage – infrequent recall – magnetic tape
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
3. Explain with neat diagram the elements of visual perception. (Nov/Dec-2008) Human intuition and analysis play a central role in the choice of one technique versus another ,and hence a basic human visual perception plays a vital role in image processing combined with DIP Algorithms which comprises of mathematical and probabilistic formulations Structure of the human eye (Horizontal cross section)
Sphere shape 3 membranes enclose the eye namely Cornea and sclera (outer) The choroid (netwand The retina
Cornea: It is tough and transparent tissue that covers anterior surface of the eye. Sclera : The sclera is continuation of cornea and also covers remain portion of the optic globe. Choroid: Choroid Contains network of blood vessels .The major source of nutrition to the eye is divided into ciliary body and iris diaphragm. The Iris diaphragm is used to control the amount of light enter into the eye Lens: The lens is made up of fibrous cells .It contains 60 to 70% water about 7% fat and more protein
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
Colored by slightly yellow pigmentation .The excessive clouding of lens caused by the affliction is commonly called as cataracts. Innermost membrane of lens is retina Retina: The retina consists of two types of light receptors- cones and rods Cones: There are 6 to 7 million numbers of cones in each eye.The cones are located at the central portion of the eye called fovea and is highly sensitive to color. Each cone connected to its nerve end .The Cone vision is called photopic or bright-light vision. Rods: There are 75 to 150 million distributed over retinal surface.The rods are connected to a single nerve, hence not involved in color vision.These are sensitive to low levels of illumination. Rod vision is called scotopic or dim-light vision.
Image Formation on the Eye The shape of the lens is controlled by the tension of the fibers of ciliary body. As the refractive power increases from minimum to maximum the distance from lens to retina varies from 17mm to 14mm. The eye focuses on an object from long distance where lens exhibits lower refractive and small distance where lens exhibits higher refractive.
The Retinal Image is reflected mainly on fovea. The perception takes place by receptors which transforms the radiant energy into electrical impulses and is decoded by brain. Brightness Adaptation and Discrimination Intensity is perceived by the human visual system. Subjective is a logarithmic function of the light intensity incident on the eye. Interpreting the impressive dynamic range is called Brightness Adaptation.
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
Brightness is not a simple function of intensity and Contrast is region’s perceived intensity. Example for simultaneous contrast
4. Explain any four basic relationships between pixels .
(8)
(Nov/Dec-2012)
1.Neighbors of a pixelA pixel p at coordinates (x,y) have 4 neighbors in horizontal and vertical directions. The 4 neighbor pixels have unit distance from pixel p, and coordinates of 4 neighboring pixels are 4 neighbors ,N4(p) (x-1,y) (x,y-1)
(x,y)
(x,y+1)
(x+1,y)
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
Diagonal neighbors ND(p) coordinates are given by (x+1,y+1), (x+1,y-1), (x-1,y+1), (x-1,y-1) (x-1,y-1)
(x-1,y+1) (x,y)
(x+1,y-1)
(x+1,y+1)
Combination of N4(p) and ND(p) are called 8-neighbors N8(p) Adjacency, Connectivity, Regions and Boundaries Pixel connectivity is the basis of regions and boundaries . If we want to connect two pixels then we need to check if i. They are neighbors and ii. They satisfy similarity condition Let V be the set of gray values used to define adjacency There are three types of adjacency i. 4 adjacency – 2 pixels p and q with values from V are 4 adjacent if q is in the set N4(p) ii. 8 adjacency - 2 pixels p and q with values from V are 4 adjacent if q is in the set ND(p) iii. m adjacency (mixed adjacency) - 2 pixels p and q with values from V are m adjacent if q is in the set N4(p) or q is in ND(p) and the set is not in V The ambiguities(difficult path) arise when we use 8 adjacency To eliminate that ambiguous we use m adjacency as shown in Fig: Pixel adjacency
A path from pixel p with coordinates (x,y) to pixel q with coordinates (s,t) is a sequence of distinct pixels with coordinates:
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
(x0,y0), (x1,y1), …., (xn,yn) (x0,y0) = (x,y) and (xn,yn) = (s,t) If (x0,y0) = (xn,yn) then the path is closed path.Here n is the length of the path. Let S is subset of pixels in an image S= {p,r,s,t,u,q} If two pixels p and q are connected by pixels r,s,t and u then S is called connected component (i.e Boundary). If two pixels p and q are connected by pixel r alone then S is called connected set (i.e Region).The R is a subset of pixels in an image and called as region if R is connected set.The boundary of a region R is set of pixels in the region that have one or more neighbors that are not in R.The boundary is called as global concept (closed path) and edge is called as local concept (gray level discontinuity). Distance Measures For pixels p,q, and z, with coordinates(x,y), (s,t), and (v,w), respectively, D is a distance function or metric if it satisfies the following conditions: D(p,q)>=0 (D(p,q)=0 iff p=q), D(p,q)=D5 R2Rr D(p,z)<=D(p,q)+D(q,z). The Euclidean distance between p and q 1is defined as De ( p, q) [( x s) 2 ( y t ) 2 ] 2 The D4 distance between p and q is defined as
D4 ( p, q) x s y t The D8 distance between p and q is defined as D8 ( p, q) max( x s , y t ) The pixels with D4 distance <=2 from (x,y) from the following contours of constant distance 2 2 1 2 2 1 0 1 2 2 1 2 2 The pixels with D8 distance <=2 from (x,y) from the following contours of constant distance:
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
2 2 2 2 2 2 1 1 1 2 2 1 0 1 2 2 1 1 1 2 2 2 2 2 2 The m adjacency is S p3 p4 p1
p2 p
5. How an RGB model is represented using HSI format? Describe the transformation. (May/June 2012) HSI color model RGB is useful for hardware implementations and is serendipitously related to the way in which the human visual system works.But, RGB is not a particularly intuitive way in which we describe colours rather when people describe colours they tend to use hue, saturation and brightness .RGB is great for colour generation, but HSI is great for colour description. The HSI model uses three measures to describe colours: Hue: A colour attribute that describes a pure colour (pure yellow, orange or red) Saturation: Gives a measure of how much a pure colour is diluted with white light Intensity: Brightness :Is nearly impossible to measure because it is so subjective. Instead we use intensity. Intensity is the same achromatic notion that we have seen in grey level images HSI, Intensity & RGB Intensity can be extracted from RGB images – which is not surprising if we stop to think about it Remember the diagonal on the RGB colour cube that we saw previously ran from black to white Now consider if we stand this cube on the black vertex and position the white vertex directly above it
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
Convertion of RGB to HSI model: Suppose R, G, and B are the red, green, and blue values of a color. The HSI intensity is given by the equation I = (R + G + B)/3. Now let m be the minimum value among R, G, and B. The HSI saturation value of a color is given by the equation S = 1 - m/I if I > 0, or S=0 if I = 0. To convert a color's overall hue, H, to an angle measure, use the following equations: H = cos-1[ (R - ½G - ½B)/√R² + G² + B² - RG - RB - GB ] if G ≥ B, or H = 360 - cos-1[ (R - ½G - ½B)/√R² + G² + B² - RG - RB - GB ] if B > G, where the inverse cosine output is in degrees.
Conversion of HSI to RGB model R = I + 2IS G = I - IS B = I - IS. If 0 < H < 120, then R = I + IS*cos(H)/cos(60-H) G = I + IS*[1 - cos(H)/cos(60-H)] B = I - IS. If H = 120, then the red, green, and blue values are R = I - IS G = I + 2IS B = I - IS. If 120 < H < 240, then R = I - IS G = I + IS*cos(H-120)/cos(180-H) B = I + IS*[1 - cos(H-120)/cos(180-H)]. If H = 240 then
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
R = I - IS G = I - IS B = I + 2IS. And if 240 < H < 360, we have R = I + IS*[1 - cos(H-240)/cos(300-H)] G = I - IS B = I + IS*cos(H-240)/cos(300-H).
6. Write a short notes on RGB colour model. Two very popular models used in colour image processing:
(Nov/Dec-2011)
RGB (Red Green Blue) HSI (Hue Saturation Intensity)
In the RGB model each colour appears in its primary spectral components of red, green and blue The model is based on a Cartesian coordinate system RGB values are at 3 corners Cyan magenta and yellow are at three other corners Black is at the origin White is the corner furthest from the origin Different colours are points on or inside the cube represented by RGB vectors
Images represented in the RGB colour model consist of three component images – one for each primary colour The number of bits used to represent each pixel is referred to as the colour depth A 24-bit image is often referred to as a full-colour image as it allows (2^8)^3 = 16,777,216 colours
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
RGB Color Cube
R = 8 bits G = 8 bits B = 8 bits Color depth 24 bits = 16777216 colors
Hidden faces of the cube
When fed into a monitor these images are combined to create a composite colour image.
The RGB Cube is divided into 6 intervals on each axis to achieve the total 63 = 216 common colors.However, for 8 bit color representation, there are the total 256 colors. Therefore, the remaining 40 colors are left to OS 7. Explain the principle of sampling and quantization. Discuss the effect of increasing the a) Sampling frequency b) Quantization levels, on image (May/June 2012), (Nov/Dec-2009) Image Sampling and Quantization
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
There are number of ways to acquire an image. Most of sensors output is continuous voltage.But the output required is a digital output. Hence sampling and quantization process are used.Image is continuous in co-ordinates as well as amplitude.Hence we need to sample both coordinates and amplitude.
In first figure the scan line A-B is in continuous manner and is illustrated in second figure (one dimensional) Uniform intervals in co-ordinates give sampling (Digitizing coordinates) In third figure continuous amplitude is there, by using quantization(using eight gray levels Black to white) we can convert it into discrete values (Digitizing amplitude) The fourth figure represents digital image, Repeat the scan line, we will get 2-D image. But some sensors give digitized image.
The image can be represented as
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
MXN digital image can be expressed as
f (0,0) f (0,1)........................... f (0, N 1) f (1,0) f (1,1)........................... f (1, N 1) f(x,y)= f ( M 1,0) f ( M 1,1).......... f ( M 1, N 1) Each element of this matrix array is called an image element, picture element, pixel or pel Function ‘f ’ represents grey level intensity value at coordinates (x,y).The requirement for M and N is that it should be an positive integers. If sampling frequency is increased => the resultant output image having pleasing effect. 8. Explain how an analog image is converted into digital image.
(Nov./Dec.2015)
An image on film can be understood by a two dimensional light intensity function f(x,y) where (1) x and y are spatial coordinates (2) the value of f at any point (x,y) is proportional to brightness or Gray value of the image at that point. It cannot be stored as such on digital computer. A digitized image is one in which spatial and gray scale values have been made discrete. Intensities measured across regular spaced grid in x and y directions which are sampled to 8 bits per point for black and white, 3x8 bits per pixel for color images. They are stored as a two dimensional arrays of gray scale values. The array elements are called pixels and identified as x,y coordinates. Matrices are perfect tools for mapping, representation of analog images into digital images. For example an image that is 800 pixels wide and 600 pixels high can be represented as 600x800 matrix. Each element of the matrix, pixel is used to represent intensity. Given a 17” computer screen with resolution of a higher quality image. a. 600x 800 b. 1024x 76800000110111101111011 digitize. The range of colors or shades of grey that can be represented in an image depend on the amount of space allotted. The process of analog to digital signal conversion is completed by encoding the quantized values into binary spectrum.
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
9. What is meant by image sensing? Explain the construction and operation of various image acquisition devices. (Nov./Dec.2015) The types of images are generated by the combination of an “illumination” source and the reflection or absorption of energy from that source by the elements of the “scene” being imaged. For example, the illumination may originate from a source of electromagnetic energy such as radar, infrared, or X-ray energy. But, as noted earlier, it could originate from less traditional sources, such as ultrasound or even a computer-generated illumination pattern. Similarly, the scene elements could be familiar objects, but they can just as easily be molecules, buried rock formations, or a human brain. We could even image a source, such as acquiring images of the sun. Depending on the nature of the source, illumination energy is reflected from, or transmitted through, objects. An example in the first category is light reflected from a planar surface. An example in the second category is when X-rays pass through a patient’s body for the purpose of generating a diagnostic X-ray film. Image Acquisition using a Single Sensor The components of a single sensor. The most common sensor of this type is the photodiode, which is constructed of silicon materials and whose output voltage waveform is proportional to light. The use of a filter in front of a sensor improves selectivity. The single sensor is mounted on a lead screw that provides motion in the perpendicular direction. Since mechanical motion can be controlled with high precision, this method is an inexpensive (but slow) way to obtain high-resolution images. Other similar mechanical arrangements use a flat bed, with the sensor moving in two linear directions. These types of mechanical digitizers sometimes are referred to as microdensitometers. Image Acquisition using Sensor Strips A geometry that is used much more frequently than single sensors consists of an in-line arrangement of sensors in the form of a sensor strip. The strip provides imaging elements in one direction. Motion perpendicular to the strip provides imaging in the other direction This is the type of arrangement used in most flat bed scanners. Sensing devices with 4000 or more inline sensors are possible. In-line sensors are used routinely in airborne imaging applications, in which the imaging system is mounted on an aircraft that flies at a constant altitude and speed over the geographical area to be imaged. Image Acquisition using Sensor Arrays Individual sensors can be arranged in the form of a 2-D array. Numerous electromagnetic and some ultrasonic sensing devices are arranged frequently in an array format. This is also the predominant arrangement found in digital cameras. A typical sensor for these cameras is a CCD array, which can be manufactured with a broad range of sensing properties and can be packaged in rugged arrays of 4000 * 4000 elements or more. CCD sensors are used widely in digital cameras and other light sensing instruments.
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
PART A 1. Define – Brightness (May/June 2012) Brightness of an object is the perceived luminance of the surround. Two objects with different surroundings would have identical luminance but different brightness. 2. Define sampling and quantization. (Nov/Dec.2008) Sampling means digitizing the co-ordinate value (x, y). Quantization means digitizing the amplitude value. 3. Specify the properties of 2D fourier transform.( Nov/Dec 2008) The properties are 1. Separability 2. Translation 3. Periodicity and conjugate symmetry 4. Rotation 5. Distributivity and scaling 6. Average value 7. Laplacian 8. Convolution and correlation 9. sampling 4.
What is Machband effect? (Nov./Dec.2013)
Mach bands is an optical illusion named after the physicist Ernst Mach. It exaggerates the contrast between edges of the slightly differing shades of gray, as soon as they contact one another, by triggering edge-detection in the human visual system.
5.
Define – Checker Board effect (Nov./Dec.2015)(May/June 2013)
This effect is observed by leaving unchanged the number of grey levels and varying the spatial resolution while keeping the display area unchanged. The checkerboard effect is caused by pixel replication, that is, lower resolution images were duplicated in order to fill the display area. 6.
Compare RGB and HSI model (April/May 2014) It directly reflects the physical properties of "Truecolor" displays. The HSV, or HSB, model describes colors in terms of hue, saturation, and value (brightness). Note that the range of values for each attribute is arbitrarily defined by various tools or standards. Be sure to determine the value ranges before attempting to interpret a value.
7.
What is brightness and contrast? (Nov./Dec.2012) (Nov./Dec.2013) Brightness refers to the overall lightness or darkness of the image. Contrast is the difference in brightness between objects or regions.
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
8.
Define optical illusion and machband. (May/June 2013)(April/May 2015) An optical illusion (also called a visual illusion) is an illusion caused by the visual system and characterized by visually perceived images that differ from objective reality. Mach bands is an optical illusion named after the physicist Ernst Mach. It exaggerates the contrast between edges of the slightly differing shades of gray, as soon as they contact one another, by triggering edge-detection in the human visual system.
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
UNIT
II IMAGE ENHANCEMENT PART A
1. Give the PDF of uniform noise and sketch it.(April/May 2015)(Nov./Dec.2013) The probability density function of the continuous uniform distribution is:
2. Define and give the transfer function of Mean and Geometric Mean filter. (April/May 2015) Mean filtering is a simple, intuitive and easy to implement method of smoothing images, i.e. reducing the amount of intensity variation between one pixel and the next. It is often used to reduce noise in images
The geometric mean filter is member of a set of nonlinear mean filters which are better at removing Gaussian type noise and preserving edge features than the arithmetic mean filter. The geometric mean filter is very susceptible to negative outliers. The definition of geometric mean filter is
fˆ ( x, y ) g ( s, t ) ( s ,t )S xy
1 mn
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
where the coordinate (x, y) is defined over the image f and the coordinate (s,t) is defined over the sub image g. 3. State the principle of directional smoothing.(Nov./Dec. 2011) Directional smoothing is the process used to protect the edges from distortion in the form of blurring while smoothing the images. 4. What are the types of Image enhancement available? (Nov./Dec.2012) The types of Image enhancement are: Frequency domain methods. Spatial domain methods 5.
Mention the procedure in Marker selection. .(Nov./Dec.2012)
'Major genes' that are responsible for economically important characteristics are frequent in the plant kingdom. Such characteristics include disease resistance, male sterility, [7] self-incompatibility, and others related to shape, color, and architecture of whole plants and are often of mono- or oligogenic in nature. The marker loci that are tightly linked to major genes can be used for selection and are sometimes more efficient than direct selection for the target gene. 6. Define and give the transfer function of contraharmonic filters. (April/May 2013) The contraharmonic mean of a set of positive numbers is defined as the arithmetic mean of the squares of the numbers divided by the arithmetic mean of the numbers:
7. What is meant by bit plane slicing? (Nov./Dec.2016) Separating a digital image into its bit planes and analyzing the relative importance played by each bit of the image, implying, it determines the adequacy of numbers of bits used to quantize each pixel , useful for image compression. 8. What is unsharp masking? (Nov./Dec.2016)
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
Unsharp masking (USM) is an image sharpening technique, often available in digital image processing software. The "unsharp" of the name derives from the fact that the technique uses a blurred, or "unsharp", negative image to create a mask of the original image. 9. List out the categories of image enhancement. (Nov./Dec.2012) The 2 categories of image enhancement are: Spatial domain enhancement Frequency domain enhancement. Spatial domain refers to image plane itself & approaches in this category are based on direct manipulation of picture image.Frequency domain methods based on modifying the image by Fourier transform. 10. What is a multimodal histogram? (May/June 2012) A multimodal histogram is the histogram which has two or more dominant modes, i.e probability distribution with two or more modes.
11. State the principle of directional smoothing. (Nov./Dec. 2011) Directional smoothing is the process used to protect the edges from distortion in the form of blurring while smoothing the images. 12. Define – Histogram (Nov./Dec.2009) (Nov./Dec.2012) The histogram of a digital image with gray levels in the range [0, L-1] is a discrete function h(rk) = nk, where rk is the kth gray level and nk is the number of pixels in the image having gray level rk .
PART B 1. What is Histogram equalization?Discuss in detail procedure involved in histogram equalization.(Nov./Dec.2012)(Nov./Dec.2016)(April/May2015).(May/June2014)(Nov./Dec.2014) Histogram equalization is used to enhance contrast. It is not necessary that contrast will always be increase in this. There may be some cases were histogram equalization can be worse. In that cases the contrast is decreased. Consider for a moment continuous functions, and let the variable r represent the gray levels of the image to be enhanced. We assume that r has been normalized to the interval [0, 1], with r=0 representing black and r=1 representing white. Later, we consider a discrete formulation and allow pixel values to be in
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
the interval [0, L-1]. For any r satisfying the aforementioned conditions, we focus attention on transformations of the form that produce a level s for every pixel value r in the original image. For reasons that will become obvious shortly, we assume that the transformation function T(r) satisfies the following conditions: (a) T(r) is single-valued and monotonically increasing in the interval 0 ≤ r ≤ 1; and (b) (b) 0 ≤ T(r) ≤ 1 for 0 ≤ r ≤ 1. The requirement in (a) that T(r) be single valued is needed to guarantee that the inverse transformation will exist, and the monotonicity condition preserves the increasing order from black to white in the output image.A transformation function that is not monotonically increasing could result in at least a section of the intensity range being inverted, thus producing some inverted gray levels in the output image. Finally, condition (b) guarantees that the output gray levels will be in the same range as the input levels. .The inverse transformation from s (a) back to r is denoted (b) It can be shown by example that even if T(r) satisfies conditions (a) and (b), it is possible that the (a) corresponding inverse T-1 (s) may fail to be single valued.
A gray-level transformation function that is both single valued and monotonically increasing. The gray levels in an image may be viewed as random variables in the interval [0, 1].One of the most fundamental descriptors of a random variable is its probability density function (PDF). Let pr(r) and ps(s) denote the probability density functions of random variables r and s,respectively,where the subscripts on p are used to denote that pr and ps are different functions.A basic result from an elementary probability theory is that, if pr(r) and T(r) are known and T-1 (s) satisfies condition (a), then the probability density function ps(s) of the transformed variable s can be obtained using a rather simple formula:
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
Thus, the probability density function of the transformed variable, s, is determined by the graylevel PDF of the input image and by the chosen transformation function. A transformation function of particular importance in image processing has the form
Given transformation function T(r),we find ps(s) by applying Eq. We know from basic calculus (Leibniz’s rule) that the derivative of a definite integral with respect to its upper limit is simply the integrand evaluated at that limit. In other words,
Substituting this result for dr/ds, and keeping in mind that all probability values are positive,Yields
The probability of occurrence of gray level r in an image is approximated by
where, as noted at the beginning of this section, n is the total number of pixels in the image, nk is the number of pixels that have gray level rk, and L is the total number of possible gray levels in the image.The discrete version of the transformation function given in Eq. is
Thus, a processed (output) image is obtained by mapping each pixel with level rk in the input image into a corresponding pixel with level sk in the output image. As indicated earlier, a plot of pr (rk) versus rk is called a histogram. The transformation (mapping) is called histogram equalization or histogram linearization. It is not difficult to show that the transformation in Eq.satisfies conditions (a) and (b) stated previously. Unlike its continuos counterpart, it cannot be proved in general that this discrete transformation will produce the discrete equivalent of a uniform probability density function, which would be a uniform histogram
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
(a) Images (b) Results of histogram equalization. (c) Corresponding histograms.
2. Specify the expression for (Nov./Dec.2012)(May/June 2013) 1.Mean filter 2.Harmonic filter 3. Contra harmonic filter Mean filter This is the simplest of the mean filters. Let Sxv represent the set of coordinates in a rectangular subimage window of size m X n, centered at point (x, y).The arithmetic mean filtering process computes the average value of the corrupted image g(x, y) in the area defined by Sxy.The value of the restored
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
image at any point (x, y) is simply the arithmetic mean computed using the pixels in the region defined by S. In other words.
Harmonic filter The harmonic mean filtering operation is given by the expression
Contraharmonic filter The contraharmonic mean filtering operation yields a restored image based on the expression
3. Write notes on Homomorphic filtering. (Nov./Dec.2012)(April/May 2015) Homomorphic filtering is a generalized technique for signal and image processing, involving a nonlinear mapping to a different domain in which linear filter techniques are applied, followed by mapping back to the original domain. Homomorphic Filtering can be used for improving the appearance of a grayscale image by simultaneous intensity range compression (illustration) and contrast enhancement (reflection).
Where, m = image, i = illumination, r = reflectance We have to transform the equation into frequency domain in order to apply high pass filter. However, it's very difficult to do calculation after applying Fourier transformation to this equation because it's not a product equation anymore. Therefore, we use 'log' to help solving this problem. Then, applying Fourier transformation
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
Or Next, applying high-pass filter to the image. To make the illumination of an image more even, the highfrequency components are increased and low-frequency components are decrease.
Where H = any high-pass filter N = filtered image in frequency domain Afterward, returning frequency domain back to the spatial domain by using inverse Fourier transform.
Finally, using exponential function to eliminate the log we used at the beginning to get the enhanced image
4. Explain in detail the method for smoothening the image in frequency domain.(Nov./Dec.2016) (May/June 2013) In inverse filtering - there is no clear provision for handling noise. Wiener filtering - incorporates both degradation function and random noise factor. The objective of this method is the difference between an estimate and uncorrupted image f is minimized. The difference is known as error and is given by e2 E ( f f )2
Where ‘E’ represents the mean value The assumptions are:
The noise and image are uncorrelated. Either noise or image has zero mean value Gray levels in the estimate are a linear function of the levels in the degraded image.
Based on these assumptions, the minimum of the error function in frequency domain
H (u, v) S f (u, v) G(u, v) F (u, v) 2 S f (u, v) H (u, v) S (u, v) H (u, v) G(u, v) F (u, v) 2 H (u, v) S (u, v) / S f (u, v) Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
1 H (u, v) 2 G(u, v) F (u, v) 2 H (u, v) H (u, v) S (u, v) / S f (u, v)
where H(u,v) is the transform of the degraded function G(u,v) is the transform of the degraded image. H (u, v)is complex conjugate of H(u,v) 2 H (u, v) H (u, v) H (u, v) S (u, v) N (u, v)
2
is power spectrum of the noise
S f (u, v) F (u, v)
2
is power spectrum of undegraded image.
This result is known as Wiener filter. The filter, which consists of the terms inside the bracket, is referred as minimum mean square error filter or the least square error filter. Wiener filter overcome the problem as inverse filter with zeros in the degradation function. Note that if the noise is zero, then the noise power spectrum vanishes and the Wiener filter reduces to the inverse filter. If the noise is white noise, then we know that the spectrum of white noise is constant. Now the estimate expression becomes 1 H (u, v) 2 G (u, v) F (u, v) 2 H (u, v) H (u, v) K Inverse filtering The inverse filtering is one of the restoration techniques of images degraded by a degradation function H. Also inverse filtering is simplest method. Already we know that the objective of image restoration is to estimate the original image from the degrade image. In this inverse filtering technique, an estimate F (u, v) , of the transform of the original image simply by dividing the transform of the degraded image G(u,v), by the degradation function. G(u, v) …………. F (u, v) H (u, v)
we know that.
(1)
G(u, v) H (u, v) F (u, v) N (u, v), substitute in Eq.1, we get N (u, v) F (u, v) F (u, v) H (u, v)
………….
(2)
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
From Eq.2, we observed that even we known about the degradation function H, we cannot recover the original image. Because noise is a random function whose Fourier transform is not known. Also if the degraded function value is zero or small value then the second term dominate the estimation. 5. Explain Gradient operators for Image Enhancement.(May/June 2013) The gradient of the picture function can be estimated by applying the masks to the 8- neighborhood N8[x; y] of pixel [x; y] as given in Equations. These masks dene the Prewitt operator credited to Dr Judith Prewitt who used them in detecting boundaries in biomedical images.
The operation M 0 N is defined formally in the next section: operationally, mask M is overlaid on image neighborhood N so that each intensity Nij can be multiplied by weight Mij ; finally all these products are summed.
the two analogous Sobel masks; their derivation and interpretation is the same as for the Prewitt masks except that the assumption is that the center estimate should be weighted twice as much as the estimate to either side. The Roberts masks are only 2x2; hence they are both more efficient to use and more locally applied. Often referred to as the Roberts cross operator, these masks actually compute a gradient estimate at the center of a 4-neighborhood and not at a center pixel. Moreover, the actual coordinate system in which
the
operator
is
defined
is
rotated
45degree
off
the standard row direction. It is common to avoid computing a square root in order to compute gradient magnitude; alternatives are max( j @f @x j ; j @f @y j ), j @f @x j + j @f @y j , or ( @f @x 2 + @f @y 2 )=2. With these estimates, one must be careful when trying to interpret the actual gradient or gradient direction.
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
6. How Mean filters are used for image enhancement? (May/June 2013) Mean
filtering
is
a
simple,
intuitive
and
easy
to
implement
method
of
smoothing images, i.e. reducing the amount of intensity variation between one pixel and the next. It is often used to reduce noise in images. The idea of mean filtering is simply to replace each pixel value in an image with the mean (`average') value of its neighbors, including itself. This has the effect of eliminating pixel values which are unrepresentative of their surroundings. Mean filtering is usually thought of as a convolution filter. Like other convolutions it is based around a kernel, which represents the shape and size of the neighborhood to be sampled when calculating the mean. Often a 3×3 square kernel is used, as shown in Figure 1, although larger kernels (e.g. 5×5 squares) can be used for more severe smoothing. (Note that a small kernel can be applied more than once in order to produce a similar but not identical effect as a single pass with a large kernel.)
Computing the straightforward convolution of an image with this kernel carries out the mean filtering process.
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
IMAGE RESTORATION AND SEGMENTATION PART A 1. Why is image subjected to wiener filtering?(Nov./Dec.2012) The Wiener filtering executes an optimal tradeoff between inverse filtering and noise smoothing. It removes the additive noise and inverts the blurring simultaneously. 2. What is Bit plane slicing?(Nov./Dec.2012)(Nov./Dec.2016) Instead of highlighting gray level ranges, highlighting the contribution made tototal image appearance by specific bits might be desired. Suppose that each pixel inan image is represented by 8 bits. Imagine that the image is composed of eight 1-bitplanes, ranging from bit plane 0 for LSB to bit plane-7 for MSB. 3. Define image degradation model and sketch it.(May/June 2013)(April/May 2015) A system operator H, which together with an additive white noise term _(x,y) a operates on an input image f(x,y) to produce a degraded image g(x,y).
4. Define rubber sheet transformation..(May/June 2013) The geometric transformation applied to the image to modify the spatial relationship between the pixels and to restore the image is called rubber sheet transform.This process is viewed as the process of printing an image on a sheet of rubber and then strtching this sheet to a predefined set of rules. 5. What is geometric transformation?(April/May 2015) A geometric transformation is any bijection of a set having some geometric structure to itself or another such set. Specifically, "A geometric transformation is a function whose domain and range are sets of points. 6. Why geometric transformation are called so?( May/June 2012) In mathematics, a transformation could be any function mapping a set X on to another set or on to itself. The set X has some additional algebraic or geometric structure and hence the term geometric transformation. 7 .What is inverse filtering? (Nov./Dec. 2011)
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
Inverse filter restores a blurred image perfectly from an output of a noiseless linear system. 8. Define averaging filters. (Nov./Dec. 2009) The averaging filters calculates the average value of pixels. 9 .State the condition to be met by the partitions in region based segmentation.(Nov./Dec.2011) 1. indicates that the segmentation must be complete; that is, every pixel must be in a region. 2.requires that points in a region must be connected. 3 indicates that the regions must be disjoint. 4. deals with the properties that must be satisfied by the pixels in a segmented region – for example = TRUE if all pixels in have the same gray level. 5. indicates that regions and are different in the sense of predicate P. 10. What is inverse filtering? (Nov.Dec.2011) The simplest approach to restoration is direct inverse filtering, an estimate F^(u,v) of the transform of the original image simply by dividing the transform of the degraded image G^(u,v) by the degradation function. F^ (u,v) = G^(u,v)/H(u,v) 11. What is meant by Image Restoration? (May/June 2012) Restoration attempts to reconstruct or recover an image that has been degraded by using a clear knowledge of the degrading phenomenon. 12. Give the difference between Enhancement and Restoration? (Nov./Dec.2009) Enhancement technique is based primarily on the pleasing aspects it might present to the viewer. For example: Contrast Stretching. Where as Removal of image blur by applying a deblurrings function is considered a restoration technique. 13.State the causes of degradation in an image.(Nov./Dec.2016) Improper opening and closing of the shutter of camera b)Mis-focus of Lensc) Atmospheric Turbulenced)Relative motion between camera and object which causes motion Blur. 14.First order derivative and second order derivative.(Nov./Dec.2016) First order derivative It is positive at the points of transition into and out of ramp (move left to right). It is zero at constant gray level Second order derivative
It is positive at transition with the dark side of edge It is negative at transition with the light side of edge
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
It is zero along the ramp and at constant gray level
PART B 1. What is gray level interpolation?Explain the schemes involved in it.(Nov./Dec.2012)(May/June 2013) Spatial Transformation => non integer coordinates value => no gray levels are present in g, Inferring what gray level at these location The technique used to accomplish this called gray-level interpolation. Simplest method- nearest neighborhood approach(zero-order interpolation)
From figure The mapping of integer (x,y) coordinates into fractional coordinates (x’,y’) The selection of closest integer coordinate neighbor to (x’,y’) and Assignment of the gray level of this nearest neighborhood to the pixel located at (x,y) Drawback of nearest neighborhood – undesirable artifacts (distortion of straight edges)Non integer coordinates (x’.y’) are known, gray level at these location is v( x, y ' ) ax ' by ' cx ' y ' d
Four coefficients are determined – four eqns formed using four known neighbors of (x’,y’). v(x’,y’) is computed and this value is assigned to the location in f(x,y) => spatial mapping. Fits surface of the sin(z)/z type through a more number of neighbors=>smooth estimate of gray level
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
Application: 3-D graphics and medical imaging Drawback: computational burden For general purpose applications: Bilinear interpolation is optimum one. 2.Differentiate constrained and unconstrained restoration.(Nov./Dec.2012) In the absence of any knowledge about the noise n, a meaningful criterion function is to seek f^such that Hf^ approximates of in a least square sense by assuming the noise term is as small as possible. It is also known as least square error approach. n=g-Hf To estimate original image f^ , noise n has to be minimized and f^=g/H where, H=system operator f^=estimated input image g=degraded image
Constrained Restoration It is also known as maximum square error approach n=g-Hf.To estimate the original image f^,noise n has to be maximized and f^=g/H. 3.Write notes on (Nov./Dec.2012)(May/June 2013) (i) Inverse filtering (ii) Weiner filtering Inverse filtering The inverse filtering is one of the restoration techniques of images degraded by a degradation function H. Also inverse filtering is simplest method. Already we know that the objective of image restoration is to estimate the original image from the degrade image. In this inverse filtering technique, an estimate F (u, v) , of the transform of the original image simply by dividing the transform of the degraded image G(u,v), by the degradation function.
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
G(u, v) …………. F (u, v) H (u, v) we know that. G(u, v) H (u, v) F (u, v) N (u, v)
N (u, v) F (u, v) F (u, v) H (u, v)
(1)
, substitute in Eq.1, we get ………….
(2)
From Eq.2, we observed that even we known about the degradation function H, we cannot recover the original image. Because noise is a random function whose Fourier transform is not known. Also if the degraded function value is zero or small value then the second term dominate the estimation. Weiner filtering In inverse filtering - there is no clear provision for handling noise. Wiener filtering - incorporates both degradation function and random noise factor. The objective of this method is the difference between an estimate and uncorrupted image f is minimized. The difference is known as error and is given by e2 E ( f f )2
Where ‘E’ represents the mean value The assumptions are: The noise and image are uncorrelated. Either noise or image has zero mean value Gray levels in the estimate are a linear function of the levels in the degraded image. Based on these assumptions, the minimum of the error function in frequency domain H (u, v) S f (u, v) G(u, v) F (u, v) 2 S f (u, v) H (u, v) S (u, v)
H (u, v) G(u, v) F (u, v) 2 H (u, v) S (u, v) / S f (u, v) 1 H (u, v) 2 G(u, v) F (u, v) 2 H (u, v) H (u, v) S (u, v) / S f (u, v)
where H(u,v) is the transform of the degraded function
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
G(u,v) is the transform of the degraded image. H (u, v) is complex conjugate of H(u,v) H (u, v)
S (u, v) N (u, v)
2
2
H (u, v) H (u, v)
is power spectrum of the noise
S f (u, v) F (u, v) is power spectrum of undegraded image. 2
This result is known as Wiener filter. The filter, which consists of the terms inside the bracket, is referred as minimum mean square error filter or the least square error filter. Wiener filter overcome the problem as inverse filter with zeros in the degradation function. Note that if the noise is zero, then the noise power spectrum vanishes and the Wiener filter reduces to the inverse filter. If the noise is white noise, then we know that the spectrum of white noise is constant. Now the estimate expression becomes 1 H (u, v) 2 G (u, v) F (u, v) 2 H (u, v) H (u, v) K
4.Explain the process of dam construction with watershed algorithm?.(Nov./Dec.2012)(May/june 2013)(Nov./Dec.2016)(May/June 2012)(April/May 2015) Segmentation based on Detection of discontinuities Thresholding and Region Processing Advantages: Simple to implement and Speed Drawback: - Need post processing (edge linking) Watershed algorithm Stable segmentation results Continuous segmentation boundaries and Knowledge based constraints Basic Concepts
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
The concept of watersheds is based on visualizing an image in three dimensions: two spatial coordinates versus gray levels. • In such a topographic interpretation, we consider three types of points: – (a) points belonging to a regional minimum – (b) points at which a drop of water would fall with certainty to a single minimum – (c) points at which water would be equally likely to fall to more than one such minimum • The principal objective of segmentation algorithms based on these concepts is to find the watershed lines. Basic Idea : •
The hole is punched in each regional minimum and the entire topography is flooded from below by letting water rise through the holes at a uniform rate. Dam is built to prevent, when the rising water in different catchment basins is about to merge. Flooding level stop when only the tops of the dams are visible above the water line. Dam boundaries = watershed lines. This idea is represented in the following example.
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
Segmentation by Morphological Watersheds – Dam Construction
Dam construction is based on binary images. Dams – used to separate sets of binary points. Simplest way to construct dam - morphological dilation Dam construction illustrated in the following figure.
Figure (a) –portion of two catchment basins at flooding step n-1 Figure (b) – flooding level at next step n Dam – to prevent water spilled from one basin to next M1, M2 – sets of coordinates of points in two regional minima. Cn-1(M1), Cn-1 (M2) –sets of coordinates of points in flooding step n-1 Union of these two is C[n-1]
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
Two connected components in figure (a) and only one connected component in figure (b) and let this conneted component be denoted as q. Because at flooding step n, two catchment basins are merged. Two components extracted from q –
q C[ N 1]
Dilation We need to keep in mind that dilation is based on set operations and therefore is a nonlinear operation, while the convolution is linear. Dilation “grows” or “thickens” objects in a binary image The manner and extend of this growth is controlled by the structuring element. Figure (c)_ structuring element •
Each of the connected components (Figure a) is dilated by structuring element, subject to two conditions.
The dilation has to be constrained to q and The dilation cannot be performed on points that would cause the sets being dilated to merge (Single connected component) From Figure (d)
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
Light gray level – first dilation – satisfy condition (i) and not (ii)
Medium gray levels – 2nd dilation – satisfy (ii) not (i) which means it stops the further dilation process. Crossed hatch lines satisfy two conditions –this path - separating dam at stage n flooding. Dam gray level =1+ maximum gray level in image
This method
Produce connected boundaries (no need – post processing) Eliminates the problems of broken segmentation lines
5. Describe the constrained least square filtering for image restoration.(May/june 2013) To know about the degraded function is the common problem to all the methods. The difficulty in Wiener filtering is, the power spectra of the undegraded image and noise must be known. By using Eq (1.5.5.), we can get better estimation, but a constant ‘K’ is not always a suitable solution. This Constrained Least Squares Filtering approach requires only knowing about mean and variance of the noise. Already we discussed that how to calculate mean and variance of noise. Hence this is important advantage of this method. The Wiener filter is based on minimizing a statistical criterion. This algorithm gives optimal result for each image. We can write the Eq.1.1 in vector –matrix form as follows, g Hf …………… (1)
It consider about the sensitivity of H to noise. One way to alleviate the noise sensitivity problem is to base optimality of restoration on a measure of smoothness, such as the second derivative of an image. To be meaningful, the restoration must be constrained by the parameters of the problems. The minimum of the criterion function C is given by M 1 N 1
C 2 f ( x, y)
2
…………….(2)
x 0 y 0
Subject to the constraint
g Hf
2
2
…………………(3)
The frequency domain solution of this optimization problem is given by the expression
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
H (u, v) G(u, v) F (u, v) 2 2 H (u, v) P(u, v)
…..(4)
Constraint in Eq.4 obtained by adjusted the parameter . P(u,v) is the Fourier Transform of the function
0 1 p( x, y ) 1 4 0 1
0 1 0
……………(1.6.5)
When =0 then this Constrained Least Squares Filter reduces to inverse filter. Residual vector ‘r’ is defined as r g Hf
………..(1.6.6)
F (u, v) is a function of and is given by
( ) r T r r 2
…………. (1.6.7)
Eq (1.6.7) is a monotonically increasing function of . We want to adjust gamma so that, r2 2 a
…………… (1.6.8)
Where ‘a’ is an accuracy factor. The steps involved for finding the desired value of is Specify an initial value of Compute r
2
Stop if Eq.(1.6.8) is satisfied, otherwise return to step2 after increasing if r
if r
2
2
a or decreasing a . Use the new value of in Eq (1.6.4) to recompute the optimum estimate F (u, v) . 2
2
Newton-Raphson algorithm can be used to improve the speed of convergence. This algorithm proceeded 2
as follows. To compute r , From Eq (1.6.6) R(u, v) G(u, v) H (u, v) F (u, v)
…………… (1.6.9)
By taking inverse transform of R(u,v) we can get r(x,y) and
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
M 1 N 1
r
2
r 2 ( x, y )
…………..(1.6.10)
x 0 y 0
The variance of the noise over the entire image is estimated by the sample-average method
2 Where
1 MN
( x, y) m
M 1 N 1
2
………………… (1.6.11)
x 0 y 0
m
1 MN
M 1 N 1
( x, y)
……………….. (1.6.12)
x 0 y 0
is the sample mean value. We can write Eq (1.6.11) as
2 MN 2 m 2 ……………….(1.6.13) By having knowledge of this mean and variance we can implement optimum restoration algorithm. Here assuming that the noise and image gray-level values are not correlated which is basic assumption for all the methods. 6. Explain edge linking using Hough transform.(Nov./Dec.2016)(Nov./Dec.2012)(Nov./Dec.2013)(April/May2015) The Hough transform is a technique which can be used to isolate features of a particular shape within an image. Because it requires that the desired features be specified in some parametric form, the classicalHough transform is most commonly used for the detection of regular curves such as lines, circles, ellipses, etc. A generalized Hough transform can be employed in applications where a simple analytic description of a feature(s) is not possible. Due to the computational complexity of the generalized Hough algorithm, we restrict the main focus of this discussion to the classical Hough transform. Despite its domain restrictions, the classical Hough transform (hereafter referred to without the classical prefix) retains many applications, as most manufactured parts (and many anatomical parts investigated in medical imagery) contain feature boundaries which can be described by regular curves. The main advantage of the Hough transform technique is that it is tolerant of gaps in feature boundary descriptions and is relatively unaffected by image noise. The Hough technique is particularly useful for computing a global description of a feature(s) (where the number of solution classes need not be known a priori), given (possibly noisy) local measurements. The motivating idea behind the Hough technique for line detection is that each input measurement (e.g. coordinate point) indicates its contribution to a globally consistent solution (e.g. the physical line which gave rise to that image point). As a simple example, consider the common problem of fitting a set of line segments to a set of discrete image points (e.g. pixel locations output from an edge detector). Figure 1 shows some possible solutions to
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
this problem. Here the lack of a priori knowledge about the number of desired line segments (and the ambiguity about what constitutes a line segment) render this problem under-constrained.
a line segment in a number of forms. However, a convenient equation for describing a set of lines uses parametric or normal notion:
where r is the length of a normal from the origin to this line and Ɵ is the orientation of r with respect to the X-axis. (See Figure 2.) For any point
on this line, r and Ɵ are constant.
In an image analysis context, the coordinates of the point(s) of edge segments (i.e. are known and therefore serve as constants in the parametric line equation, while
) in the image and
are the
unknown variables we seek. If we plot the possible values defined by each , points in cartesian image space map to curves (i.e. sinusoids) in the polar Hough parameter space. This point-tocurvetransformation is the Hough transformation for straight lines. When viewed in Hough parameter space, points which are collinear in the cartesian image space become readily apparent as they yield curves which intersect at a common
point.
7.Explain region based segmentation with an example.(Nov./Dec.2016)(Apri/May 2015) Region-Based Segmentation
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
• •
• • •
Edges and thresholds sometimes do not give good results for segmentation. Region-based segmentation is based on the connectivity of similar pixels in a region. – Each region must be uniform. – Connectivity of the pixels within the region is very important. There are two main approaches to region-based segmentation: region growing and region splitting. Let R represent the entire image region. Segmentation is a process that partitions R into subregions, R1,R2,…,Rn, such that n
(a) Ri R i 1
(b) Ri is a connected region, i 1,2,..., n (c) Ri R j for all i and j, i j (d) P( Ri ) TRUE for i 1,2,..., n (e) P( Ri R j ) FALSE for any adjacent regions Ri and R j whereP(Rk): a logical predicate defined over the points in set Rk For example: P(Rk)=TRUE if all pixels in Rkhave the same gray level.
After region growing -> descriptors are used Problems:
Descriptors can yield misleading results
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
UNIT IV WAVELETS AND IMAGE COMPRESSION PART A 1.What is the need for Compression?( Nov./Dec.2011)( April/May 2013)( April/May2015) In terms of storage, the capacity of a storage device can be effectively increased with methods that compress a body of data on its way to a storage device and decompresses it when it is retrieved. In terms of communications, the bandwidth of a digital communication link can be effectively increased by compressing data at the sending end and decompressing data at the receiving end. At any given time, the ability of the Internet to transfer data is fixed. Thus, if data can effectively be compressed wherever possible, significant improvements of data throughput can be achieved. Many files can be combined into one compressed document making sending easier. 2.Define compression ratio. (Nov.Dec 2009) Compression Ratio is defined as original size / compressed size: 1 3. What are the coding systems in JPEG? (Nov./Dec.2012) 1. A lossy baseline coding system, which is based on the DCT and is adequate for most compression application. 2. An extended coding system for greater compression, higher precision or progressive reconstruction applications. 3. a lossless independent coding system for reversible compression. 4.What is JPEG? (Nov./Dec.2011) The acronym is expanded as "Joint Photographic Expert Group". It is an international standard in 1992. It perfectly Works with color and grayscale images, Many applications e.g., satellite, medical,... 5. What are the basic steps in JPEG? (Nov/Dec.2009) The Major Steps in JPEG Coding involve: _ DCT (Discrete Cosine Transformation) _ Quantization _ Zigzag Scan _ DPCM on DC component _ RLE on AC Components _ Entropy Coding 6.What is MPEG? (Nov./Dec.2011) The acronym is expanded as "Moving Picture Expert Group". It is an international standard in 1992. It perfectly Works with video and also used in teleconferencing Input image
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
PART B 1. How an image is compressed using JPEG Image compression standard? (May/June 2013) ( April/May2015) The acronym is expanded as "Joint Photographic Expert Group". It is an international standard in 1992. It perfectly Works with color and grayscale images, Many applications e.g., satellite, medical. The Major Steps in JPEG Coding involve: DCT (Discrete Cosine Transformation) Quantization Zigzag Scan DPCM on DC component RLE on AC Components Entropy Coding ENCODER
DECODER
JPEG is a transform coding approach using DCT. Consider 8*8 block of the image as shown in table Table : an 8*8 block of an image 124 121 125 124 127
125 122 120 122 119 117 118 121 120 119 119 120 120 118 124 123 122 121 121 120 120 124 125 125 126 125 124 124 127 128 129 130 128 127 125
143 142 143 142 140 139 139 139
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
150 148 152 152 152 152 150 151 156 159 158 155 158 158 157 156 The Transform The transform used in the Jpeg scheme is the DCT .The input image is first “level shifted by 2p-1 ie) subtract 2p-1 from each pixel value. Then the image is divided into blockes of size 8*8 , which are transformed using an 8*8 forward DCT .The table show the DCT coefficient. Table: The DCT coefficient 39.88 6.56 -2.24 1.22 -0.37 -1.08 0.79 1.13 -102.43 4.56 2.26 1.12 0.35 -0.63 -1.05 -0.48 37.77 1.31 1.77 0.25 -1.50 -2.21 -0.10 0.23 -5.67 2.24 -1.32 -0.81
1.41 0.22 -0.13 0.17
-3.37 -0.74 -1.75 0.77 -0.62 -2.65 -1.30 0.76 5.98 -0.13 -0.45 -0.77 1.99 -0.26 1.46 0.00 3.97 5.52
2.39 -0.55 -0.051-0.84 -0.52 -0.13
-3.43 0.51 -1.07 0.87 0.96 0.09 0.33 0.01 Quantization The JPEG algorithm uses uniform midthread quantization to quantize the various coefficient. The quantizer step sizes are organized in a table called the quantization table as shown in table Table: Sample Quantization table 16 11 10 16 24 40 51 61 12 12 14 19 26 58 60 55 14 13 16 24 40 57 69 56 14 17 22 29 51 87 80 62 18 22 37 56 68 109103 77 24 35 55 64 81 104 113 92 49 64 78 87 103 121 120 101
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
72 92 95 98 12 100 103 99 The lable corresponding to the quantized value of the transform coefficient θij is obtained as Lij=θij/Qij+0.5 Where Qij is the (i,j)th element of the quantization table. The reconstructed value is obtained by multiplying the lable with corresponding entry in the quantization table Table: The quantizer lable 21 0 0 0 0 0 0 -9 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Coding In this approach the lable for the DC and AC coefficient are coded differently using Huffman codes. The DC coefficient values partitioned into categories. The categories are then Huffman coded. The AC coefficient is generated in slightly different manner. There are two special codes: End-of-block(EOF) and ZRL Table: Coding of the differences of the DC labels
0 1 2 3
-3 -7
…………………….
-1
0 1
-2
2
-4
4
3 ……… 7
Table: sample table for obtaining the Huffman code for a given label value and run length
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
Z/C
Codeword
0/0
1010
0/1
00
Z/c
Codeword
…..
Z/C F/0
1/1
1100
Codeword 11111111001
F/1 111111111111110101
To encode the AC coefficient First using Zigzag scan. We obtain -9 3 0 0 0 0 0 ……… 0 The first value belong to category 1. transmit the code corresponding to 0/1 follow by a single bit 1 to indicate that the value being transmitted is 1 and not -1 .Simillarly other AC coefficient code are transmited. To obtain the reconstruction of the original block Dequantization is performed and taking inverse transform of the coefficient we get the reconstructed block. 2. Describe run length encoding with an example . ( April/May2015) Run Length Encoding Consider a matrix A with 15 elements, A= [10 10 9 9 9 9 4 0 0 0 0 0 10 10 10] In the given example, 10 has occurred 2 times, 9 has occurred 4 times, 4 has occurred once, 0 has occurred 5 times and 10 has occurred 3 times. After Run length encoding, we obtain the matrix without any repetition in the adjacent elements, [10 9 4 0 10]. And the occurrences of each element [2 4 1 5 3] Thus the matrix is reduced to 10 elements from 15 elements.
1. 2. 3. 4.
5.
Reduction method. Consider the above matrix A, Find the difference between adjacent elements. Use the function ‘diff(A)’ to find the difference. [0 -1 0 0 0 -5 -4 0 0 0 0 10 0 0] Convert it to logical format. The elements without repetition are denoted with one and the repeated elements with zero. [0 1 0 0 0 1 1 0 0 0 0 1 0 0 1] Find the position of the elements that has the value one in the above step. [2 6 7 12 15]. Find the unique element values using the positions obtained from the above step. In the matrix A, the element at the position 2 is 10, the element at the position 6 is 9, the element at the position 7 is 4, the element at the position 12 is 0 and the element at the position 15 is 10. [10 9 4 0 10] The first element in the matrix is 10, it has occurred 2 times. We obtained the occurrence of the first element alone from the matrix in the step 3. For the remaining elements, find the difference of the matrix in the step 3.
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
i.e. diff([2 6 7 12 15]); The result after concatenating the first element of the matrix obtained in step 3 with difference for the matrix in the step 3 is [2 4 1 5 3] 6. Thus in the step 4 we obtain the elements without repetition, [10 9 4 0 10] and the occurrences in step 5, [2 4 1 5 3]. 3. What is the need for image compression? Explain image compression in detail.(Nov./Dec.2016) In terms of storage, the capacity of a storage device can be effectively increased with methods that compress a body of data on its way to a storage device and decompresses it when it is retrieved. In terms of communications, the bandwidth of a digital communication link can be effectively increased by compressing data at the sending end and decompressing data at the receiving end. Compression: It is the process of reducing the size of the given data or an image. It will help us to reduce the storage space required to store an image or File. Image Compression Model: There are two Structural model and they are broadly Classified as follows An Encoder A Decoder.
Encoder
Channel
Decoder
An Input image f(x,y) is fed in to encoder and create a set of symbols and after transmission over the channel ,the encoded representation is fed in to the decoder. A General Compression system model: The General system model consist of the following components,They are broadly classified as Source Encoder Channel Encoder Channel Channel Decoder Source Decoder
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
Source Encoder
Channel Encoder
Channel
Channel Decoder
Source Decoder
The Source Encoder Will removes the input redundancies. The channel encoder will increase the noise immunity of the source encoder’s output. If the channel between encoder and decoder is noise free then the channel encoder and decoder can be omitted.
Mapper
Symbol Encoder
Quantizer
MAPPER: It transforms the input data in to a format designed to reduce the interpixel redundancy in the input image. QUANTIZER: It reduce the accuracy of the mapper’s output. SYMBOL ENCODER: It creates a fixed or variable length code to represent the quantizer’s output and maps the output in accordance with the code.
Symbol decoder
Inverse mapper
SYMBOL DECODER: The inverse operation of the source encoder’s symbol will be performed and maps the blocks.
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
4. Draw and explain the block diagram of MPEG ENCODER. (NOV/DEC 2012). MPEG: Moving Pictures Experts Group, established in 1988 for the development of digital video. • It is appropriately recognized that proprietary interests need to be maintained within the family of MPEG standards: – Accomplished by defining only a compressed bitstream that implicitly defines the decoder. – The compression algorithms, and thus the encoders, are completely up to the manufacturers.
MPEG-1 adopts the CCIR601 digital TV format also known as SIF (Source Input Format). • MPEG-1 supports only non-interlaced video. Normally, its picture resolution is: – 352 × 240 for NTSC video at 30 fps – 352 × 288 for PAL video at 25 fps – It uses 4:2:0 chroma subsampling • The MPEG-1 standard is also referred to as ISO/IEC 11172. It has five parts: 11172-1 Systems, 11172-2 Video, 11172-3 Audio, 11172-4 Conformance, and 11172-5 Software. Motion Compensation (MC) based video encoding in H.261 works as follows: – In Motion Estimation (ME), each macroblock (MB) of the Target P-frame is assigned a best matching MB from the previously coded I or P frame - prediction. – prediction error: The difference between the MB and its matching MB, sent to DCT and its subsequent encoding steps. – The prediction is from a previous frame — forward prediction.. The MB containing part of a ball in the Target frame cannot find a good matching MB in the previous frame because half of the ball was occluded by another object. A match however can readily be obtained from the next frame. MPEG introduces a third frame type — B-frames, and its accompanying bi-directional motion compensation. • The MC-based B-frame coding idea is illustrated in Fig. 11.2: – Each MB from a Bframe will have up to two motion vectors (MVs) (one from the forward and one from the backward prediction). – If matching in both directions is successful, then two MVs will be sent and the two corresponding matching MBs are averaged (indicated by ‘%’ in the figure) before comparing to the
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
Target MB for generating the prediction error. – If an acceptable match can be found in only one of the reference frames, then only one MV and its corresponding MB will be used from either the forward or backward prediction Source formats supported: – H.261 only supports CIF (352 × 288) and QCIF (176 × 144) source formats, MPEG-1 supports SIF (352 × 240 for NTSC, 352 × 288 for PAL). – MPEG-1 also allows specification of other formats as long as the Constrained Parameter Set (CPS) as shown in Table 11.1 is satisfied: Table 11.1: The MPEG-1 Constrained Parameter Set Parameter Value Horizontal size of picture ≤ 768 Vertical size of picture ≤ 576 No. of MBs / picture ≤ 396 No. of MBs / second ≤ 9, 900 Frame rate ≤ 30 fps Bit-rate ≤ 1, 856 kbps Source formats supported: – H.261 only supports CIF (352 × 288) and QCIF (176 × 144) source formats, MPEG-1 supports SIF (352 × 240 for NTSC, 352 × 288 for PAL). – MPEG-1 also allows specification of other formats as long as the Constrained Parameter Set (CPS) as shown in Table 11.1 is satisfied: Table 11.1: The MPEG-1 Constrained Parameter Set Parameter Value Horizontal size of picture ≤ 768 Vertical size of picture ≤ 576 No. of MBs / picture ≤ 396 No. of MBs / second ≤ 9, 900 Frame rate ≤ 30 fps Bit-rate ≤ 1, 856 kbps. Quantization: – MPEG-1 quantization uses different quantization tables for its Intra and Inter coding For DCT coefficients in Intra mode: QDCT[i, j] = round !8 × DCT[i, j] step size[i, j] " = round ! 8 × DCT[i, j] Q1[i, j] ∗ scale" (11.1) DCT coefficients in Inter mode, QDCT[i, j] = # 8 × DCT[i, j] step size[i, j] $ = # 8 × DCT[i, j] Q2[i, j] ∗ scale MPEG-1 allows motion vectors to be of sub-pixel precision (1/2 pixel). The technique of “bilinear interpolation” for H.263 can be used to generate the needed values at halfpixel locations. • Compared to the maximum range of ±15 pixels for motion vectors in H.261, MPEG-1 supports a range of [−512, 511.5] for half-pixel precision and [−1, 024, 1, 023] for full-pixel precision motion vectors • The MPEG-1 bitstream allows random access — accomplished by GOP layer in which each GOP is time coded. • The typical size of compressed P-frames is significantly smaller than that of I-frames — because temporal redundancy is exploited in inter-frame compression. • B-frames are even smaller than Pframes — because of (a) the advantage of bi-directional prediction and (b) the lowest priority given to B-frames. MPEG-2: For higher quality video at a bit-rate of more than 4 Mbps. • Defined seven profiles aimed at different applications: – Simple, Main, SNR scalable, Spatially scalable, High, 4:2:2, Multiview. – Within each profile, up to four levels are defined (Table 11.5). – The DVD video specification allows only four
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
display resolutions: 720 × 480, 704 × 480, 352 × 480, and 352 × 240 — a restricted form of the MPEG2 Main profile at the Main and Low levels.
Supporting Interlaced Video • MPEG-2 must support interlaced video as well since this is one of the options for digital broadcast TV and HDTV. In interlaced video each frame consists of two fields, referred to as the top-field and the bottom-field. – In a Frame-picture, all scanlines from both fields are interleaved to form a single frame, then divided into 16×16 macroblocks and coded using MC. – If each field is treated as a separate picture, then it is called Field-picture. MPEG-2 defines Frame Prediction and Field Prediction as well as five prediction modes: 1. Frame Prediction for Frame-pictures: Identical to MPEG- 1 MC-based prediction methods in both Pframes and Bframes. 2. Field Prediction for Field-pictures: A macroblock size of 16 × 16 from Field-pictures is used. 3.Field Prediction for Frame-pictures: The top-field and bottom-field of a Frame-picture are treated separately. Each 16 × 16 macroblock (MB) from the target Framepicture is split into two . 4. 16 × 8 parts, each coming from one field. Field prediction is carried out for these 16 × 8 parts in a manner similar to that shown in Fig. 11.6(b). 4. 16 × 8 MC for Field-pictures: Each 16 × 16 macroblock (MB) from the target Field-picture is split into top and bottom 16 × 8 halves. Field prediction is performed on each half. This generates two motion vectors for each 16 × 16 MB in the P-Field-picture, and up to four motion vectors for each MB in the B-Field-picture. This mode is good for a finer MC when motion is rapid and irregular. 5. Dual-Prime for P-pictures: First, Field prediction from each previous field with the same parity (top or bottom) is made. Each motion vector mv is then used to derive a calculated motion vector cv in the field with the opposite parity taking into account the temporal scaling and vertical shift between lines in the top and bottom fields. For each MB the pair mv and cv yields two preliminary predictions. Their prediction errors are averaged and used as the final prediction error. This mode mimics B-picture
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
prediction for P-pictures without adopting backward prediction (and hence with less encoding delay). This is the only mode that can be used for either Framepictures or Field-pictures. 5. Discus the method of constructing the masking function based on maximum variance and maximum magnitude . (NOV/DEC 2012) A mask Processing Methods -A pixel’s value is computed from its old value and the values of pixels in its vicinity. - More costly operations than simple point processes, but more powerful. A mask is a small matrix whose values are called weights. Each mask has an origin, which is usually one of its positions. The origins of symmetric masks are usually their center pixel position. -For nonsymmetric masks, any pixel location may be chosen as the origin (depending on the intended use). Applying Masks to Images (filtering) – application of a mask to an input image produces an output image of the same size as the input. Convolution (1) For each pixel in the input image, the mask is conceptually placed on top of the image with its origin lying on that pixel. (2) The values of each input image pixel under the mask are multiplied by the values of the corresponding mask weights. (3) The results are summed together to yield a single output value that is placed in the output image at the location of the pixel being processed on the input. Cross Correlation - Correlation translates the mask directly to the image without flipping it. - It is often used in applications where it is necessary to measure the similarity between images or parts of images. - If the mask is symmetric (i.e., the flipped mask is the same as the original one) then the results of convolution and correlation are the same. Normalization of mask weights - The sum of weights in the convolution mask affect the overall intensity of the resulting image. - Many convolution masks have coefficients that sum to 1 (the convolved image will have the same average intensity as the original one) Some masks have negative weights and sum to 0. - Pixels with negative values may be generated using masks with negative weights. - Negative values are mapped to the positive range through appropriate normalization. Sharpening (or High-pass) - It is used to emphasize the fine details of an image (has the opposite effect of smoothing). - Points of high contrast can be detected by computing intensity differences in local image
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
regions. - The weights of the mask are both positive and negative. When the mask is over an area of constant or slowly varying gray level, the result of convolution will be close to zero. When gray level is varying rapidly within the neighborhood, the result of convolution will be a large number. Typically, such points form the border between different objects or scene parts (i.e., sharpening is a precursor step to edge detection).
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
UNIT V
IMAGE REPRESENTATION AND RECOGNITION
Boundary representation – Chain Code – Polygonal approximation, signature, boundary segments – Boundary description – Shape number – Fourier Descriptor, moments- Regional Descriptors –Topological feature, Texture – Patterns and Pattern classes – Recognition based on matching. PART A 1. What is skeletonizing?(Nov./Dec.2016)
In digital image processing, morphological skeleton is a skeleton (or medial axis) representation of a shape or binary image, computed by means of morphological operators.
Examples of skeleton extraction of figures in the binary image Morphological skeletons are of two kinds: Those defined by means of morphological openings, from which the original shape can be reconstructed, Those computed by means of the hit-or-miss transform, which preserve the shape's topology. 2.Define texture. .(Nov./Dec.2016) An image texture is a set of metrics calculated in image processing designed to quantify the perceived texture of an image. Image texture gives us information about the spatial arrangement of color or intensities in an image or selected region of an image. 3.Does the use of chain code compress the description information of an object contour? Chain codes are the most size-efficient representations of rasterised binary shapes and contours. A chain code is a lossless compression algorithm for monochrome images. The basic principle of chain codes is to separately encode each connected component, or "blob", in the image. For each such region, a point on the boundary is selected and its coordinates are transmitted. The encoder then moves along the boundary of the region and, at each step, transmits a symbol representing the direction of this movement. This continues until the encoder returns to the starting position, at which point the blob has been completely described, and encoding continues with the next blob in the image. This encoding method is particularly effective for images consisting of a reasonably small number of large connected components.
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
4. What is meant by pattern classes? A pattern classes are family of patterns that share some common properties.Pattern classes are denoted by w1, w2,….., wN where N is the number of classes.
PART B 1. Explain in detail any two boundary representation schemes .(Nov./Dec.2016) After image segmentation the resulting collection of regions is usually represented and described in a form suitable for higher level processing. Most important representations are based on shape or texture. Desirable property: descriptors should be insensitive to changes in size, translation or rotation. Actual measurement of features in digital images makes use of many of the techniques discussed earlier, such as linear or morphological image operators.
Put boundary points of a binary region R (or its boundary) in a clockwise-sorted order. Needed for computation of boundary descriptors. Chain Codes
Freeman chain codes: strings of integers representing a boundary by a connected sequence of straight-line segments of specified length and direction. The direction of each line segment is coded using a numbering scheme adapted to the connectivity. The accuracy of the straight-line representation depends on the spacing of the sampling grid. Chain codes
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
Chain codes: first difference First difference of a chain code: count number of direction changes (e.g., counterclockwise) that separate two adjacent code elements. chain code: 10103322 (start lower left) first difference: 33133030 (circular sequence)
Polygon representation A digital boundary can also be approximated by a polygon, possibly with minimum length (MPP: minimumperimeter polygon). Such rubber band approximations directly within the grey value image are known as active contour models, or snakes.
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
Minimum-perimeter polygon (MPP)
(a) Light grey: region containing the boundary curve. (b) Convex (white) and concave (black) corner vertices. (c) Concave vertices moved to diagonal mirror locations. The MPP is indicated. Signatures 1-D representation of a boundary Example: distance r(θ) of centroid to boundary as a function of angle θ. Often the boundary is first smoothed
2. Explain image recognition based on matching.(Nov./Dec.2016) (Apr./May.2017) Template Matching is a high-level machine vision method that distinguishes the parts on an image that match a predefined layout. The algorithm is: An image having texts (might be in degraded form) or objects is taken as input and converted into gray scale image. It is passed through Gaussian filter in order to smoothen the broken edges and noise.
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
It is passed through other pre-processing filters like dilation, noise pixel removal step, thresholding, etc. (texts or objects in white). All the separate white regions are marked as different objects and counted, cropped to its minimum size. A bounding box is created around each object. After that, the object region is resized to the size of templates and then each object is compared to all the templates pre-saved in a matrix.corr2 (template {1, n}, char) is a function that calculates the correlation in the template image and the test object image. The template image which has the highest correlation coefficient is marked as identified object or text. Similarly all the texts or objects are compared and the results are stored in a text file which is displayed at the end of the program. Template Matching methods are relied upon to address the prerequisite of distinguishing all input picture areas at which the template image article is available. Contingent upon the particular issue close by, the client may (or may not) have any desire to recognize the pivoted or scaled events Let the template T(xt , yt ), where (xt , yt ) represent thecoordinates of each pixel in the template.
Then simply move the center (or the origin) of the template T(xt , yt ) over each (x, y) point in the search image and calculate the sum of products between the coefficients in S(x, y) and T(xt , yt ) over the whole area spanned by the template. As all possible positions of the template with respect to the search image are considered, the position with the highest score is the best position. This method is sometimes referred to as 'Linear Spatial Filtering’ and the template is called a filter mask. Above Figure shows an example with a real optical image. The first image shows a cup in a simple background. The second image shows the estimated position of the template with proper application of geometric parameters. It is seen here that the algorithm settled into this estimate after 42 iterations and that it is an accurate estimate. Improvements can be made to the matching method by using more than one template, these other templates can have different scales and rotations. Template matching has various different applications and is used in such fields as face recognition and medical image processing. Systems have been developed and used in the past to count the number of faces that walk across part of a bridge within a certain amount of time. Other systems include automated calcified nodule detection within digital chest X-rays. Template matching is a Hierarchical process, the required number of comparisons can be significantly reduced by clustering .
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
3. Explain the various boundary descriptors in detail with a neat diagram. (Apr./May.2017) There are many features that depend on boundary descriptors of objects such as bending energy, curvature etc. For an irregularly shaped object, the boundary direction is a better representation although it is not directly used for shape descriptors like centroid, orientation, area. Consecutive points on the boundary of a shape give relative position or direction. A 4- or 8-connected chain code is used to represent the boundary of an object by a connected sequence of straight line segments. 8 connected number schemes are used to represent the direction in this case. It starts with a beginning location and a list of numbers representing directions such as ddd N ,,, 21 ⋅⋅⋅⋅ . Each direction provides a compact representation of all the information in a boundary. The directions also represent the slope of the boundary. In Fig. below an 8 connectivity chain code is displayed where the boundary description for the boxes with red arrows will be 2-1-0-7-7-0-1-1.
Curvature : The rate of change of a slope is called the curvature. As the digital boundary is generally jagged, getting a true measure of curvature is difficult. The curvature at a single point in the boundary can be defined by its adjacent line segments. The difference between slopes of two adjacent (straight) line segments is a good measure of the curvature at that point of intersection . The curvature of the boundary at can be estimated from the change in the slope is given by,
Curvature (κ) is a local attribute of a shape. The object boundary is traversed clockwise for finding the curvature. A vertex point is in a convex segment when the change of slope at that point is positive;
Visit : www.EasyEngineeering.net
Visit : www.EasyEngineeering.net
Bending Energy The descriptor called bending energy is obtained by integrating the squared curvature p through the boundary length L . It s a robust shape descriptor and can be used for matching shapes.
The value 2π / R will be obtained as its minimum for a perfect circle with radius R and the value will be higher for an irregular object. Total Absolute Curvature Total absolute curvature is the curvatures added along the boundary points and divided by the boundary length.
As the convex object will have the minimum value, a rough object will have a higher value.
Visit : www.EasyEngineeering.net
