Image Edge Detection Algorithm with a Single Grid System of Coupled FitzHugh-Nagumo Elements A. Nomura, M. Ichikawa, K. Okada, T. Sakurai & Y. Mizukami Yamaguchi Univ. & Chiba Univ. Japan Key words: image processing, edge detection application of nonlinear elements, FitzHugh-Nagumo model initial conditions for FHN model
Outline • Introduction: Motivation and Approach • Background: – Nonlinear phenomena and pattern formation in nature – Image edge detection and previous algorithms in image processing • Our Previous Edge Detection Algorithm with cFHN – FitzHugh-Nagumo (FHN) model – Grid system of coupled FHN (cFHN) and the initial conditions • Proposed Edge Detection Algorithm with cFHN – The initial conditions • Experimental Results – Artificial images with/without noise – Real images • Conclusion 2
Introduction: Motivation and Approach • Motivation – Biological visual system – Bio-inspired image processing • edge detection, segmentation and stereo disparity detection • Approach – Coupled FitzHugh-Nagumo (cFHN) elements on a grid system – Reaction-diffusion system (diffusively coupled elements) • Our previous edge detection algorithm – does not work for gray level image – noise vulnerability or not robust to noise 3
Background: Nonlinear Phenomena & Pattern Formation • Nonlinear elements in nature – Biological response to external stimuli: FitzHuhg-Nagumo model – Nonlinear oscillation or excitation in chemical reaction system • Reaction-diffusion system – System of diffusively coupled nonlinear elements in space – Patterns: traveling pulses in 1D space and spiral waves in 2D space – Information transmission & information processing 1.2 0.8 0.4 0.0 -0.4 2D spiral waves 0 100 200 300 400 500 1D pulse propagating in space 4
Background: Definition of Image Edge • Point having rapid brightness change Image brightness distribution I ( x , y ) 2 Image brightness I 0 Inflection point: space ( x , y ) Edge position 5
Background: Previous Edge Detection Algorithms • Algorithms by Marr and Hildreth (1980) G e I ( x , y ) – LoG: Laplacian-of-the-Gaussian • Gaussian: noise reduction Inflection • Laplacian operator: detection of inflection points G i point – DoG: Difference-of-two-Gaussians • G e : excitation (blurred) G e - G i • G i : inhibition (more blurred) – Detecting zero-crossing points • Algorithm by Canny (1986) Zero-crossing – Gaussian smoothing + gradient operator + threshold point – assumption: continuity of edges 6
Our Previous Edge Detection Algorithm: FitzHugh-Nagumo (FHN) Model (a) Uni-stable element FHN model d u 1 u ( u a )( 1 u ) v ε d t Phase plot d v u bv d t (b) Bi-stable element 7
Our Previous Edge Detection Algorithm: Single Grid System of Coupled FHN (cFHN) • Uni-stable elements placed at image grid points – Nomura et al., J. Phys. Soc. Jpn. , 2003 – Kurata et al., Phys. Rev. E , 2009 d u 1 i , j C u 4 u u ( u a )( 1 u ) v u i , j i , j i , j i , j i , j i , j ε d t d v i , j C v 4 v u bv v i , j i , j i , j i , j d t Spatial coupling u i , j , u i , j : averages in the nearest four points. • The initial conditions: u i,j = I i,j , v i,j =0 u and v ( C u << C v ) • Strong inhibition: C u << C v Stationary pulses at edge positions • Weak inhibition: C u > C v u and v Propagating pulses ( C u > C v ) 8
Our Previous Algorithm for Edge Detection: Example of Edge Detection with cFHN • Example: Initial condition of u i,j Result of edge detection ( a =0.1) • Threshold for the initial condition u 0 & Self-organized pulse => Previous algorithm does not work for gray level images 9
Proposed Algorithm: cFHN & Initial Conditions • Coupled FHN elements: delaying computation of u i , j d u 1 i , j C u 4 u u ( u a )( 1 u ) v , t 0 u i , j i , j i , j i , j i , j i , j ε d t f ( u , v ) i , j i , j d v i , j C v 4 v u bv , t v i , j i , j i , j i , j d t v 0.15 • The initial conditions 0.10 v ( t ) f ( I , 0 ) i , j i , j 0.05 u 0.00 0.0 0.5 1.0 u ( t ) I , t 0 10 i , j i , j
Experimental Results: Artificial Noiseless Image The Image Proposed Algorithm Canny Algorithm 500 500 pixels s =0.40, q l 0.10, q h 0.20 C u =4, C v =12, a =0.1, b =4.5, e =1.0 10 -3 , =5.0 10 -4 256 brightness levels d t =1.0 10 -4 11
Experimental Results: Artificial Noisy Image The Image Proposed Algorithm Canny Algorithm 500 500 pixels s =1.20 C u =4, C v =12, a =0.1, b =4.5, e =1.0 10 -3 , =0.1 q l 0.40, q h 0.70 256 brightness levels d t =1.0 10 -4 S.D. of noise=10 12
Experimental Results: Quantitative Results with P, R and F measures Algorithm Image P R F Image: (a) Noiseless image Our Previous (a) 0.989 0.906 0.946 (b) Noisy image Algorithm (b) 0.747 0.908 0.819 (s.d.=10.0) Proposed (a) 0.999 0.979 0.989 Algorithm (b) 0.825 0.945 0.881 red is the best performance Canny (a) 1.000 0.975 0.987 Algorithm (b) 0.999 0.965 0.982 • Algorithms: – Our Previous Algorithm (Nomura et al., 2011) – Proposed Algorithm – Canny Algorithm (Canny, 1986) • Evaluation measures: M M M M 2 PR t o t o M o : obtained edge map P , R , F M M P R M t : true edge map o t 13
Experimental Results: Real Image (1/2) C u =4 C v =12 a =0.1 b =4.5 e =1.0 10 -3 =0.1 d t =1.0 10 -4 The image Proposed Algorithm 659 409 pixels, 256 brightness levels http://marathon.csee.usf.edu/edge/edgecompare_main.html Proposed Algorithm s =0.6 q l 0.5 q h 0.9 Canny Algorithm Canny Algorithm 14 http://marathon.csee.usf.edu/edge/edgecompare_main.html
Experimental Results: Real Image (2/2) The image Proposed Algorithm Canny Algorithm 461 665 pixels s =1.2, q l 0.3, q h 0.8 C u =4, C v =12, a =0.1, b =4.5 e =1.0 10 -3 , =0.1 http://marathon.csee.usf.edu/edge/edgecompare_main.html 256 brightness levels d t =1.0 10 -4 http://marathon.csee.usf.edu/edge/edgecompare_main.html 15
Conclusion • Grid system of coupled FitzHugh-Nagumo elments for image edge detection – Reconsidering initial conditions for u i , j and v i , j – Delaying computation of u i , j • Experiments for artificial and real gray level images • The proposed algorithm achieved better performance than our previous algorithm. • Future topics: – Noise robustness – Detection of blurred edges and edge strength evaluation 16
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