Abstract

We describe a novel method for skeletonization of gray-scale electronic speckle pattern interferometry (ESPI) fringe patterns. Our method is based on the gradient vector field (GVF). We propose a new partial differential equation model for calculating the GVF of ESPI fringe patterns. Further, we propose rules used to measure the possibility of each pixel on the skeleton based on the topological analysis of the GVF. The final skeletons are traced, which mimics the behavior of edge detection based on these rules. The proposed method works directly on the gray-scale images.

© 2008 Optical Society of America

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References

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  1. M. Aslan, 'Toward the development of high-speed microscpoic ESPI system for monitoring laser heating/drilling of alumina (Al2O3) substrates,' Ph.D. dissertation (Pennsylvania State University, 2000).
  2. C. Tang, F. Zhang, B. Li, and H. Yan, Appl. Opt. 45, 7392 (2006).
    [CrossRef] [PubMed]
  3. C. Quan, C. J. Tay, F. Yang, and X. He, Appl. Opt. 44, 4814 (2005).
    [CrossRef] [PubMed]
  4. S. Tari, J. Shah, and H. Pien, Comput. Vis. Graph. Image Understand. 66, 133 (1997).
    [CrossRef]
  5. J. H. Jang and K. S. Hong, in Proceedings Eighth IEEE International Conference on Computer Vision (IEEE, 2001), pp. 18-23.
  6. Z. Yu and C. Bajaj, in Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2004), Vol. 1, pp. 415-420.
  7. D. Chen and A. A. Farag, in ICGST International Conference on Graphics, Vision, and Image Processing (GVIP '05) (ICGST, 2005), pp. 113-118.
  8. C. Xu and J. L. Prince, IEEE Trans. Image Process. 7, 359 (1998).
  9. P. Perona and J. Malik, IEEE Trans. Pattern Anal. Mach. Intell. 12, 629 (1990).
    [CrossRef]
  10. Y. Chen, C. A. Z. Barcelos, and B. A. Mairz, Comput. Vis. Graph. Image Understand. 82, 85 (2001).
    [CrossRef]
  11. Y. Chen, B. C. Vemuri, and L. Wang, Comput. Math. Appl. 39, 131 (2000).
    [CrossRef]

2006 (1)

2005 (1)

2001 (1)

Y. Chen, C. A. Z. Barcelos, and B. A. Mairz, Comput. Vis. Graph. Image Understand. 82, 85 (2001).
[CrossRef]

2000 (1)

Y. Chen, B. C. Vemuri, and L. Wang, Comput. Math. Appl. 39, 131 (2000).
[CrossRef]

1998 (1)

C. Xu and J. L. Prince, IEEE Trans. Image Process. 7, 359 (1998).

1997 (1)

S. Tari, J. Shah, and H. Pien, Comput. Vis. Graph. Image Understand. 66, 133 (1997).
[CrossRef]

1990 (1)

P. Perona and J. Malik, IEEE Trans. Pattern Anal. Mach. Intell. 12, 629 (1990).
[CrossRef]

Appl. Opt. (2)

Comput. Math. Appl. (1)

Y. Chen, B. C. Vemuri, and L. Wang, Comput. Math. Appl. 39, 131 (2000).
[CrossRef]

Comput. Vis. Graph. Image Understand. (2)

S. Tari, J. Shah, and H. Pien, Comput. Vis. Graph. Image Understand. 66, 133 (1997).
[CrossRef]

Y. Chen, C. A. Z. Barcelos, and B. A. Mairz, Comput. Vis. Graph. Image Understand. 82, 85 (2001).
[CrossRef]

IEEE Trans. Image Process. (1)

C. Xu and J. L. Prince, IEEE Trans. Image Process. 7, 359 (1998).

IEEE Trans. Pattern Anal. Mach. Intell. (1)

P. Perona and J. Malik, IEEE Trans. Pattern Anal. Mach. Intell. 12, 629 (1990).
[CrossRef]

Other (4)

M. Aslan, 'Toward the development of high-speed microscpoic ESPI system for monitoring laser heating/drilling of alumina (Al2O3) substrates,' Ph.D. dissertation (Pennsylvania State University, 2000).

J. H. Jang and K. S. Hong, in Proceedings Eighth IEEE International Conference on Computer Vision (IEEE, 2001), pp. 18-23.

Z. Yu and C. Bajaj, in Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2004), Vol. 1, pp. 415-420.

D. Chen and A. A. Farag, in ICGST International Conference on Graphics, Vision, and Image Processing (GVIP '05) (ICGST, 2005), pp. 113-118.

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Figures (2)

Fig. 1
Fig. 1

Computer-simulated fringe pattern and its skeletons obtained by our method: (a) initial image, (b) black fringe skeletons of (a), (c) white fringe skeletons of (a), (d) filtered image of (a) using a 3 × 3 window mean filtering only once, (e) black fringe skeletons of (d), (f) superimposition of the white fringe skeletons of (d) onto (d).

Fig. 2
Fig. 2

Experimentally obtained ESPI fringe pattern and its skeletons obtained by our method: (a) initial image, (b) black fringe skeletons of (a), (c) white fringe skeletons of (a), (d) filtered image of (a) using a 3 × 3 window mean filtering only once, (e) black fringe skeletons of (d), (f) superimposition of the white fringe skeletons of (d) onto (d).

Equations (14)

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E = Ω ( μ ( u x 2 + u y 2 + v x 2 + v y 2 ) + F 2 V F 2 ) d x d y ,
E 1 = Ω { [ α g ( V ) V + β ( V I ) 2 ] + γ f ( V ) } d x d y .
E 2 = Ω [ a V + ( b 2 ) V V 2 ] d x d y ,
u t = α g ( u ) u div ( u u ) + α ( g ( u ) ) u β ( u I x ) u + γ div ( g ( u ) u ) ,
u t = a ( t ) div ( u u ) b ( u u ) ,
v t = α g ( v ) v div ( v v ) + α ( g ( v ) ) v β ( v I y ) v + γ div ( g ( v ) v ) ,
v t = a ( t ) div ( v v ) b ( v v ) ,
V 0 = V 0 = ( I x , I y ) .
u N = u u 2 + v 2 , v N = v u 2 + v 2 .
S x , y = ( u x , y N x ) 2 + ( v x , y N y ) 2 max ( ( u x , y N x ) 2 + ( v x , y N y ) 2 ) .
( u N x u N y v N x v N y ) ( x , y ) .
JM x , y = ( u x , y N x + v x , y N y ) real ( u x , y N x ) 2 2 ( u x , y N x ) ( v x , y N y ) + ( v x , y N y ) 2 + 4 ( u x , y N y ) ( v x , y N x ) λ ,
f W ( x , y ) = { 1 , skeleton pixel if S x , y > T ¯ , JM x , y < 0 0 , nonskeleton pixel otherwise ,
f B ( x , y ) = { 1 , skeleton pixel if S x , y > T ¯ , JM x , y > 0 0 , nonskeleton pixel otherwise ,

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