The 6th International Conference on Ubiquitous Robots and Ambient Intelligence (URAI 2009)

Diff RGB: A Novel Constant Intensity Color Space Sunglok Choi and Wonpil Yu Robot Research Department, ETRI, Daejeon, Republic of Korea {sunglok, ywp}@etri.re.kr

Abstract— A novel color space, Diff RGB, is compared with popular normalized RGB. It keeps similar intensity in spite of intensity variation as like the normalized RGB. However, its transformation is much faster than the normalization, and it does not have any exceptional case in its transformation. Two applications of Diff RGB, landmark detection and skin color detection, are briefly explained. Keywords— Color Space, Normalized RGB, Diff RGB

(a) Normalized RGB Fig. 1.

(b) Diff RGB

Two Constant Intensity Planes in 3D RGB Space

1. Introduction A camera observes single color as various colors because of light and shading, which cause difficulty in image processing such as segmentation. One major approach is to transform an image into another color space which is robust in variation of light intensity and shading [1]. HSI, YUV, and YCbCr are utilized without its intensity (I) or luminance (Y) component. The unused component is highly related with brightness and darkness, while other components are related with color tone and saturation. Normalized RGB is also popular color space, which projects raw RGB into a constant intensity space. Many applications have utilized it because its transformation requires much simpler calculation than others. A novel color space, Diff RGB, is analyzed in this paper, which was proposed in the author’s previous paper [2], [3]. It keeps the same constant intensity property. However, its transformation is much faster than the normalized RGB and it does not have the invalid point. Section 2 provides basic explanation and comparison between the normalized RGB and Diff RGB. Section 3 introduces two examples which the Diff RGB had been utilized. Finally, Section 4 contains summary and further works. 2. Normalized RGB vs. Diff RGB The normalized RGB and Diff RGB transform 3D RGB space into 2D constant intensity plane. Intensity is defined in HSI color space as follows: R+G+B , (1) 3 where R, G, and B is each color value. Each component is represented as an integer between 0 and 255 in usual digital images. I=

This work was supported partly by the R&D program of the Korea Ministry of Knowledge and Economy (MKE) and the Korea Evaluation Institute of Industrial Technology (KEIT). (2008-S-031-01, Hybrid u-Robot Service System Technology Development for Ubiquitous City)

Table 1. C OMPARISON BETWEEN N ORMALIZED RGB AND D IFF RGB

The normalized RGB is to divide each RGB channel by their sum as follows: R G B r= , g= , b= . (2) R+G+B R+G+B R+G+B The transformed components become real number between 0 and 1. The color space satisfies r + g + b = 1 (Figure 1(a)), which means that each components are linearly dependent. In other words, the color space lose one dimension, the intensity component (1). It preserves hue and saturation slightly different with the original, but it sustains similar color in change of intensity from 80 to 170 (Figure 2). It is impossible to transform the original RGB to its normalized color when a pixel is black (R = G = B = 0). The invalid point is also observed in Figure 2(b). The Diff RGB is to subtract each RGB component from one of others as follows: r0 = R − G ,

g0 = G − B ,

b0 = B − R .

(3)

The transformed components become integer between −255 and +255. The Diff RGB also satisfies the constant intensity property, r0 + g0 + b0 = 0 (Figure 1(b)). It keeps similar color in spite of intensity variation while it represents similar hue and saturation (Figure 2). Two extrema, white and black, have the same color because the color space makes the constant intensity. It is more intrinsic property, which the normalized RGB does not have. Besides, it does not have invalid point.

The 6th International Conference on Ubiquitous Robots and Ambient Intelligence (URAI 2009)

(a) Hue-Saturation Variation Fig. 2.

Transformed Results in Various Color

(a) Landmark Detection Fig. 3.

(b) Intensity Variation

(b) Skin Detection

Two Applications

The normalized RGB needs almost 26 times longer computation since it requires floating point operations and conditional branch due to its invalid point (Table 1). Computation time for 10 million pixels is measured using clock() function in standard C library. The Diff RGB has 0.5 times larger projection area, which is the area of projected plane (Figure 1) by each color space when its minima and maxima is scaled to 0 and 1, respectively. The bigger area causes more distinguishable hue and saturation (Figure 2(a)).

Fig. 4.

Three Representative Images in the Fingertip Mouse

4. Conclusion 3. Applications Diff RGB was applied to landmark detection in localization (Figure 3(a) [3]) and skin detection in a fingertip mouse (Figure 3(b) [2]). Color landmarks and hands had single color, but they showed similar but various color due to curvature of objects and variation of illumination. It caused a trouble, but it was relaxed by the normalized RGB and Diff RGB. Figure 4 shows several images in the fingertip mouse. The Diff RGB was performed as following C code, which maps the original RGB [0, 255] into the Diff RGB [0, 255] without complex scaling. rr = (R >> 1) + ((255 - G) >> 1); gg = (G >> 1) + ((255 - B) >> 1); bb = (B >> 1) + ((255 - R) >> 1); Shading on hands and light variation did not change skin color significantly in two color spaces. Diff RGB also performed almost 20 times faster than the normalized RGB. Both color space did not recognize white, gray, and black color (achromatic color). The problem can restricts their application, but it is simply solved by including the intensity component (1) instead of one of three components.

The Diff RGB was examined with the normalized RGB. Both color space transform the original RGB into the constant intensity plane, but the Diff RGB is much faster and does not contain the invalid point. Moreover, it keeps similar hue and saturation with the original RGB due to larger projection area. Conversion by intensity variation (Figure 2(b)) is symmetric, which is more intrinsic than the normalized RGB. The Diff RGB needs to be utilized to many practical applications. Embedded systems such as cellular phones are promising applications due to its low computational burden. The lookup table can accelerate its transform significantly. References [1] V. Vezhnevets, V. Sazonov, and A. Andreeva, “A survey on pixel-based skin color detection techniques,” in Proceedings of the International Conference on Computer Graphics and Vision (GrapiCon), September 2003, pp. 85–92. [2] S. Choi, “Three new algorithms for vision-based mouse in embedded system,” Master’s thesis, Seoul National University, 2004. [3] N. S. Kuppuswamy, S.-H. Cho, D. Stonier, S.-L. Choi, and J.-H. Kim, “Design of an omnidirectional robot for fira robosot,” in Proceedings of the FIRA Robot World Congress, June 2006.