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Image Edge Detection Algorithm with a Single Grid System of Coupled - - PowerPoint PPT Presentation

Dec 26, 2023 142 likes •309 views

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

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SLIDE 1

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

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SLIDE 2

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

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SLIDE 3

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

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SLIDE 4

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

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1D pulse propagating in space 2D spiral waves

  • 0.4

0.0 0.4 0.8 1.2 100 200 300 400 500

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SLIDE 5

Background: Definition of Image Edge

  • Point having rapid brightness change

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space (x,y) Edge position Image brightness Inflection point:

2 

 I

I(x,y)

Image brightness distribution

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SLIDE 6

Background: Previous Edge Detection Algorithms

  • Algorithms by Marr and Hildreth (1980)

– LoG: Laplacian-of-the-Gaussian

  • Gaussian: noise reduction
  • Laplacian operator: detection of inflection points

– DoG: Difference-of-two-Gaussians

  • Ge: excitation (blurred)
  • Gi: inhibition (more blurred)

– Detecting zero-crossing points

  • Algorithm by Canny (1986)

– Gaussian smoothing + gradient operator + threshold – assumption: continuity of edges

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Ge - Gi

Inflection point

Ge Gi

Zero-crossing point

I(x,y)

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SLIDE 7

Our Previous Edge Detection Algorithm: FitzHugh-Nagumo (FHN) Model

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 

bv u t v v u a u u t u       d d ) 1 )( ( ε 1 d d

(a) Uni-stable element (b) Bi-stable element

Phase plot

FHN model

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SLIDE 8

Our Previous Edge Detection Algorithm: Single Grid System of Coupled FHN (cFHN)

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  • Uni-stable elements placed at image grid points

– Nomura et al., J. Phys. Soc. Jpn., 2003 – Kurata et al., Phys. Rev. E, 2009

  • The initial conditions:

ui,j=Ii,j, vi,j=0

  • Strong inhibition: Cu<<Cv

 Stationary pulses at edge positions

  • Weak inhibition: Cu>Cv

 Propagating pulses

 

 

 

j i j i j i j i v j i j i j i j i j i j i j i u j i

bv u v v C t v v u a u u u u C t u

, , , , , , , , , , , ,

4 d d ) 1 )( ( ε 1 4 d d          

u and v (Cu>Cv)

u and v (Cu << Cv)

ui,j, ui,j : averages in the nearest four points.

Spatial coupling

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SLIDE 9

Our Previous Algorithm for Edge Detection: Example of Edge Detection with cFHN

  • Example:
  • Threshold for the initial condition u0 & Self-organized pulse

=> Previous algorithm does not work for gray level images

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Initial condition of ui,j Result of edge detection (a=0.1)

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SLIDE 10

0.00 0.05 0.10 0.15 0.0 0.5 1.0

Proposed Algorithm: cFHN & Initial Conditions

  • Coupled FHN elements: delaying computation of ui,j
  • The initial conditions

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 

 

 

              t bv u v v C t v v u f t v u a u u u u C t u

j i j i j i j i v j i j i j i j i j i j i j i j i j i u j i

, 4 d d ) , ( , ) 1 )( ( ε 1 4 d d

, , , , , , , , , , , , , ,

, ) (

, ,

  t I t u

j i j i

) , ( ) (

, , j i j i

I f t v    

u v

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SLIDE 11

Experimental Results: Artificial Noiseless Image

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The Image

500500 pixels 256 brightness levels

Proposed Algorithm

Cu=4,Cv=12, a=0.1, b=4.5, e=1.010-3, =5.0 10-4 dt=1.0  10-4

Canny Algorithm

s=0.40, ql0.10, qh0.20

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SLIDE 12

Experimental Results: Artificial Noisy Image

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Proposed Algorithm

Cu=4,Cv=12, a=0.1, b=4.5, e=1.010-3, =0.1 dt=1.0  10-4

Canny Algorithm

s=1.20 ql0.40, qh0.70

The Image

500500 pixels 256 brightness levels S.D. of noise=10

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SLIDE 13

Experimental Results: Quantitative Results with P, R and F measures

  • Algorithms:

– Our Previous Algorithm (Nomura et al., 2011) – Proposed Algorithm – Canny Algorithm (Canny, 1986)

  • Evaluation measures:

Mo: obtained edge map Mt: true edge map

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R P PR F M M M R M M M P

t

  • t
  • t

      2 , ,

Algorithm Image P R F Our Previous Algorithm (a) (b) 0.989 0.747 0.906 0.908 0.946 0.819 Proposed Algorithm (a) (b) 0.999 0.825 0.979 0.945 0.989 0.881 Canny Algorithm (a) (b) 1.000 0.999 0.975 0.965 0.987 0.982 Image: (a) Noiseless image (b) Noisy image (s.d.=10.0) red is the best performance

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SLIDE 14

Experimental Results: Real Image (1/2)

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The image 659409 pixels, 256 brightness levels

http://marathon.csee.usf.edu/edge/edgecompare_main.html

Proposed Algorithm Canny Algorithm

http://marathon.csee.usf.edu/edge/edgecompare_main.html

Cu=4 Cv=12 a=0.1 b=4.5 e=1.010-3 =0.1 dt=1.0  10-4 s=0.6 ql0.5 qh0.9

Proposed Algorithm Canny Algorithm

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SLIDE 15

Experimental Results: Real Image (2/2)

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The image 461665 pixels 256 brightness levels

http://marathon.csee.usf.edu/edge/edgecompare_main.html

Canny Algorithm s=1.2, ql0.3, qh0.8

http://marathon.csee.usf.edu/edge/edgecompare_main.html

Proposed Algorithm Cu=4,Cv=12, a=0.1, b=4.5 e=1.010-3, =0.1 dt=1.0  10-4

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SLIDE 16

Conclusion

  • Grid system of coupled FitzHugh-Nagumo elments for image

edge detection

– Reconsidering initial conditions for ui,j and vi,j – Delaying computation of ui,j

  • Experiments for artificial and real gray level images
  • The proposed algorithm achieved better performance than
  • ur previous algorithm.
  • Future topics:

– Noise robustness – Detection of blurred edges and edge strength evaluation

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