0

Line Extraction via Phase Congruency with a Novel Adaptive Scale Selection for Poisson Noisy Images Vladimir A. Krylov 1 and James D. B. Nelson 2 1 Dept. 2 Dept.

of Engineering DITEN, University of Genoa

of Statistical Science, University College London

19 October 2015

Introduction ● Methodology ● Experimental study ● Conclusions ●

1

Outline • Introduction Line extraction and Poisson noise.

• Methodology Adaptive scale selection and phase congruency.

• Experimental validation Mammographic images and comparisons.

• Conclusions And perspectives.

Line Extraction via Phase Congruency and Adaptive Scales

Vladimir Krylov and James Nelson

Introduction ● Methodology ● Experimental study ● Conclusions ●

2

Line extraction Curvilinear structures (CLS) are key to understanding and analysis of the image structure Instrumental in medical applications:  Assistance for diagnosis;  Quality enhancement;  Image co-registration;  Specific pattern extraction.

Spiculated cancerous mass

Eye vessel pattern

Line Extraction via Phase Congruency and Adaptive Scales

Vladimir Krylov and James Nelson

Introduction ● Methodology ● Experimental study ● Conclusions ●

3

Poisson noise Poisson noise has a discrete distribution with intensity

:

It is data dependent: Input Gaussian

Poisson-noise pattern is typical of: Poisson  low-quality, low-contrast data;  numerous medical imaging modalities: mammography, X-ray, nuclear imaging (PET, SPECT), fluorescent confocal microscopy imaging, etc.

Line Extraction via Phase Congruency and Adaptive Scales

Vladimir Krylov and James Nelson

Introduction ● Methodology ● Experimental study ● Conclusions ●

4

Processing pipeline Step I. Adaptive scale selection based on Poisson homogeneity

Step II. CLS extraction using phase congruency

Line Extraction via Phase Congruency and Adaptive Scales

Vladimir Krylov and James Nelson

Introduction ● Methodology ● Experimental study ● Conclusions ●

5

Phase congruency Is a tool to detect line- and edge-like features in the frequency domain

PC is calculated as For improved localization we define

Local frequency extracted via banks of Gabor filters at different scales.

Line Extraction via Phase Congruency and Adaptive Scales

Vladimir Krylov and James Nelson

Introduction ● Methodology ● Experimental study ● Conclusions ●

6

Multiscale filtering Gabor filters impulse response is equal to a Gaussian modulated by a sinusoidal wave W

With

and - standard deviations in time domain. Gabor filters are employed for:  Optimal scale identification  Calculation of phase congruency;

Line Extraction via Phase Congruency and Adaptive Scales

Vladimir Krylov and James Nelson

Introduction ● Methodology ● Experimental study ● Conclusions ●

7

Adaptive scale I We propose to select the optimal scale adaptively according to homogeneity w.r.t. Poisson distribution (with parameter ). Consider N scales, and test the hypothesis

Testing based on the dispersion index

Goodness-of-fit statistic

Line Extraction via Phase Congruency and Adaptive Scales

Vladimir Krylov and James Nelson

Introduction ● Methodology ● Experimental study ● Conclusions ●

8

Adaptive scale II Dispersion index-based test statistic Consider

scales and

orientations

Alternative procedure to estimate the optimal scale due to dependencies:

Line Extraction via Phase Congruency and Adaptive Scales

Vladimir Krylov and James Nelson

Introduction ● Methodology ● Experimental study ● Conclusions ●

9

Line extraction The phase congruency is multiplied by

to suppress non-desirable line features.

PC is evaluated over the adaptive range of scales

Global PC

Adaptive PC

Line Extraction via Phase Congruency and Adaptive Scales

Vladimir Krylov and James Nelson

Introduction ● Methodology ● Experimental study ● Conclusions ●

10

Outline of the method

Line Extraction via Phase Congruency and Adaptive Scales

Vladimir Krylov and James Nelson

Introduction ● Methodology ● Experimental study ● Conclusions ●

11

Experiments Mammographic imagery: MLO views (50 µ) with malformations:  Spicules patterns;  Architectural distortions.

Employed settings: Scales Scale range Orientations Mean thresholding, No morphology.

Mammographic ROI

Line Extraction via Phase Congruency and Adaptive Scales

Optimal scales

Extracted lines

Vladimir Krylov and James Nelson

Introduction ● Methodology ● Experimental study ● Conclusions ●

12

Comparisons Considered benchmarks: line enhancement and primitive-based.

Mammographic ROI

Extracted lines

Line Extraction via Phase Congruency and Adaptive Scales

Radon enhancement after thresholding (Sampat, 2008)

Primitive-based stochastic geometry (Krylov, 2014)

Vladimir Krylov and James Nelson

Introduction ● Methodology ● Experimental study ● Conclusions ●

13

Conclusion An automatic approach of adaptive multi-scale line extraction from Poisson-noisy images is proposed.

Advantages:  Application independent and Poisson-noise specific;  Adaptive scale selection approach;  Low computational complexity (+parallelizable). Limitations:  Pixel-based formulation;  Intra-sample dependence.

Line Extraction via Phase Congruency and Adaptive Scales

Vladimir Krylov and James Nelson