Abstract

We report the development of a wavelet multiresolution texture-based algorithm that uses the probability density functions (PDFs) of the subband of the wavelet decomposition of an image. The moments of these pdfs are used in a clustering algorithm to segment the targets from their background clutter. Using the tools of experimental methodology, we evaluate the performance of this algorithm on real infrared imagery under varying algorithm parameter sets as well as scene, image, and false-alarm conditions. We estimate a set of multidimensional predictive analytic performance models that relate the detection probabilities as functions of false alarm, algorithm internal parameter, target pixel number, target-to-background interference ratio, target-interference ratio, and Fechner-Weber and local entropy metrics in the scene. These models can be used to predict performance in regions were no data are available and to optimize performance by selection of the optimum parameter and constant false-alarm values in regions with known scene and metric conditions.

© 2004 Optical Society of America

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    [CrossRef]
  3. F. Sadjadi, “Experiments in the use of fractals in computer pattern recognition,” in Automatic Object Recognition III, F. A. Sadjadi, ed., Proc. SPIE1960, 214–222 (1993).
    [CrossRef]
  4. I. Daubechies, “Orthonormal bases of compactly supported wavelets,” Commun. Pure Appl. Math. 41, 909–991 (1988).
    [CrossRef]
  5. B. Julesz, “Texton: the elements of texture perception and their interactions,” Nature 290, 91–97 (1981).
    [CrossRef] [PubMed]
  6. S. G. Mallat, “A theory for multi-resolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 647–693 (1989).
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    [CrossRef]
  9. F. Sadjadi, “Automatic recognition of partially occluded objects,” in Automatic Object Recognition II, F. A. Sadjadi, ed., Proc. SPIE1700, 277–284 (1992).
    [CrossRef]
  10. F. Sadjadi, “Two-dimensional invariant object recognition by coding techniques,” Opt. Eng. 31(12), 2580–2583 (1992).
    [CrossRef]
  11. F. Sadjadi, “A sequential technique for 3-D object recognition,” in Intelligent Robots and Computer Vision, D. P. Casasent, ed., Proc. SPIE579, 265–267 (1985).
    [CrossRef]
  12. J. S. Walker, A Primer on Wavelets and their Scientific ApplicationsChapman & Hall/CRC, New York, 1999).
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  13. A. Laine, J. Fan, “Frame representation for texture segmentation,” IEEE Trans. Image Process. 5(5), 771–780 (1996).
    [CrossRef]
  14. G. Van de Wouwer, P. Scheunders, D. Van Dyck, “Statistical texture characterization from discrete wavelet representations,” IEEE Trans. Image Process. 8(4), 592–598 (1999).
    [CrossRef]
  15. A. Mojsilovic, V. Popovic, D. Rackov, “On the selection of optimal wavelet basis for texture characterization,” IEEE Trans. Image Process. 9(12), 2043–2050 (2000).
  16. T. Chang, C. C. K. Kuo, “Texture analysis and classification with tree-structured wavelet transform,” IEEE Trans. Image Process. 2(5), 429–441 (1993).
    [CrossRef]
  17. K. S. Thyaragajan, T. Nguyen, C. E. Persons, “A maximum likelihood approach to texture classification using wavelet transform,” in Proceedings of the IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1994), Vol. 2, pp. 640–644.
  18. M. Unser, “Texture classification and segmentation using wavelet frames,” IEEE Trans. Image Process. 4(11), 1549–1560 (1995).
    [CrossRef]
  19. J. Portilla, E. P. Simoncelli, “A parametric texture model based on joint statistics of complex wavelet coefficients,” Int. J. Comput. Vision 40(1), 49–71 (2000).
    [CrossRef]
  20. M. Proat, Y. Y. Zeevi, “Localized texture processing in vision: analysis and synthesis in Gaborian space,” IEEE Trans. Biomed. Eng. 36(1), 115–129 (1989).
    [CrossRef]
  21. E. Simoncelli, “Modeling the joint statistics of images in the wavelet domain,” in Wavelet Applications in Signal and Image Processing VII, M. A. Unser, A. Aldroubi, A. F. Laine, eds., Proc. SPIE3813, 188–195 (1999).
    [CrossRef]
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  26. D. Carevic, T. Caelli, “Application of partial modeling technique for texture segmentation,” J. Opt. Soc. Am. A 14(11), 2924–2937 (1997).
    [CrossRef]
  27. S. C. Zhu, Y. N. Wu, D. Mumford, “Prior learning and Gibbs reaction-diffusion,” IEEE Trans. Pattern Anal. Mach. Intell. 19(11), 1236–1250 (1997).
  28. J. Portilla, R. Navarro, O. Nestares, A. Tabernero, “Texture synthesis-by-analysis based on a multiscale early-vision model,” Opt. Eng. 35(8), 2403–2417 (1996).
    [CrossRef]
  29. S. C. Zhu, Y. N. Wu, D. Mumford, “Filters, random fields and maximum entropy {(FRAME)}—towards the unified theory for texture modeling,” in Proceedings of the IEEE Conference Computer Vision and Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 693–696.
  30. D. P. Casasent, J. S. Smokelin, A. Ye, “Wavelet and Gabor transforms for detection,” Opt. Eng. 31(9), 1893–1898 (1992).
    [CrossRef]
  31. D. Weber, D. Casasent, “Quadratic Gabor correlation filters for object detection,” IEEE Trans. Image Process. 10(2), 218–230 (2001).
    [CrossRef]
  32. S. Rong, “Modeling clutter and context for target detection in infrared images,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 106–113.
  33. L. Neiberg, D. Casasent, A. Talukder, “Feature space trajectory neural net classifier: confidences and thresholds for clutter and low contrast objects,” in Applications and Science of Artificial Neural Networks II, S. K. Rogers, D. W. Ruck, eds., Proc. SPIE2760, 435–446 (1996).
    [CrossRef]
  34. M. Cooper, I. Miller, “Information measures for object recognition accommodating signature variability,” IEEE Trans. Inf. Theory 46(5), 1869–1907 (2000).
  35. B. B. Chaudhuri, N. Sarkar, “Texture segmentation using fractal dimension,” IEEE Trans. Pattern Anal. Mach. Intell. 17(1), 72–77 (1995).
    [CrossRef]
  36. S. Chatterjee, R. Chellapa, “Maximum likelihood texture segmentation using Gaussian Markov random field models,” in Proceedings of IEEE Conference on Computer Vision and Graphics and Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 1987), pp. 298–303.

2001

D. Weber, D. Casasent, “Quadratic Gabor correlation filters for object detection,” IEEE Trans. Image Process. 10(2), 218–230 (2001).
[CrossRef]

2000

M. Cooper, I. Miller, “Information measures for object recognition accommodating signature variability,” IEEE Trans. Inf. Theory 46(5), 1869–1907 (2000).

J. Portilla, E. P. Simoncelli, “A parametric texture model based on joint statistics of complex wavelet coefficients,” Int. J. Comput. Vision 40(1), 49–71 (2000).
[CrossRef]

A. Mojsilovic, V. Popovic, D. Rackov, “On the selection of optimal wavelet basis for texture characterization,” IEEE Trans. Image Process. 9(12), 2043–2050 (2000).

1999

G. Van de Wouwer, P. Scheunders, D. Van Dyck, “Statistical texture characterization from discrete wavelet representations,” IEEE Trans. Image Process. 8(4), 592–598 (1999).
[CrossRef]

1997

S. C. Zhu, Y. N. Wu, D. Mumford, “Prior learning and Gibbs reaction-diffusion,” IEEE Trans. Pattern Anal. Mach. Intell. 19(11), 1236–1250 (1997).

D. Carevic, T. Caelli, “Application of partial modeling technique for texture segmentation,” J. Opt. Soc. Am. A 14(11), 2924–2937 (1997).
[CrossRef]

1996

J. Portilla, R. Navarro, O. Nestares, A. Tabernero, “Texture synthesis-by-analysis based on a multiscale early-vision model,” Opt. Eng. 35(8), 2403–2417 (1996).
[CrossRef]

A. Laine, J. Fan, “Frame representation for texture segmentation,” IEEE Trans. Image Process. 5(5), 771–780 (1996).
[CrossRef]

1995

B. B. Chaudhuri, N. Sarkar, “Texture segmentation using fractal dimension,” IEEE Trans. Pattern Anal. Mach. Intell. 17(1), 72–77 (1995).
[CrossRef]

M. Unser, “Texture classification and segmentation using wavelet frames,” IEEE Trans. Image Process. 4(11), 1549–1560 (1995).
[CrossRef]

1993

T. Chang, C. C. K. Kuo, “Texture analysis and classification with tree-structured wavelet transform,” IEEE Trans. Image Process. 2(5), 429–441 (1993).
[CrossRef]

1992

F. Sadjadi, “Two-dimensional invariant object recognition by coding techniques,” Opt. Eng. 31(12), 2580–2583 (1992).
[CrossRef]

D. P. Casasent, J. S. Smokelin, A. Ye, “Wavelet and Gabor transforms for detection,” Opt. Eng. 31(9), 1893–1898 (1992).
[CrossRef]

1990

1989

M. Proat, Y. Y. Zeevi, “Localized texture processing in vision: analysis and synthesis in Gaborian space,” IEEE Trans. Biomed. Eng. 36(1), 115–129 (1989).
[CrossRef]

S. G. Mallat, “A theory for multi-resolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 647–693 (1989).
[CrossRef]

1988

I. Daubechies, “Orthonormal bases of compactly supported wavelets,” Commun. Pure Appl. Math. 41, 909–991 (1988).
[CrossRef]

1981

B. Julesz, “Texton: the elements of texture perception and their interactions,” Nature 290, 91–97 (1981).
[CrossRef] [PubMed]

B. Chaudhuri, B.

B. B. Chaudhuri, N. Sarkar, “Texture segmentation using fractal dimension,” IEEE Trans. Pattern Anal. Mach. Intell. 17(1), 72–77 (1995).
[CrossRef]

Belongie, S.

J. Puzicha, S. Belongie, “Model-based halftoning for color image segmentation,” in Proceedings of the International Conference on Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 2000), Vol. 3, pp. 629–32.

Brodatz, P.

P. Brodatz, Textures (Dover, New York, 1966).

Caelli, T.

Carevic, D.

Casasent, D.

D. Weber, D. Casasent, “Quadratic Gabor correlation filters for object detection,” IEEE Trans. Image Process. 10(2), 218–230 (2001).
[CrossRef]

L. Neiberg, D. Casasent, A. Talukder, “Feature space trajectory neural net classifier: confidences and thresholds for clutter and low contrast objects,” in Applications and Science of Artificial Neural Networks II, S. K. Rogers, D. W. Ruck, eds., Proc. SPIE2760, 435–446 (1996).
[CrossRef]

Casasent, D. P.

D. P. Casasent, J. S. Smokelin, A. Ye, “Wavelet and Gabor transforms for detection,” Opt. Eng. 31(9), 1893–1898 (1992).
[CrossRef]

Chang, T.

T. Chang, C. C. K. Kuo, “Texture analysis and classification with tree-structured wavelet transform,” IEEE Trans. Image Process. 2(5), 429–441 (1993).
[CrossRef]

Chatterjee, S.

S. Chatterjee, R. Chellapa, “Maximum likelihood texture segmentation using Gaussian Markov random field models,” in Proceedings of IEEE Conference on Computer Vision and Graphics and Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 1987), pp. 298–303.

Chee, J.

J. Chee, T. N. Pappas, A. Mojsilovic, B. Rogowitz, “Adaptive image segmentation,” in Proceedings of the IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 2002), pp. 777–780.

Chellapa, R.

S. Chatterjee, R. Chellapa, “Maximum likelihood texture segmentation using Gaussian Markov random field models,” in Proceedings of IEEE Conference on Computer Vision and Graphics and Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 1987), pp. 298–303.

Cooper, M.

M. Cooper, I. Miller, “Information measures for object recognition accommodating signature variability,” IEEE Trans. Inf. Theory 46(5), 1869–1907 (2000).

Daubechies, I.

I. Daubechies, “Orthonormal bases of compactly supported wavelets,” Commun. Pure Appl. Math. 41, 909–991 (1988).
[CrossRef]

Do, M. N.

M. N. Do, M. Vetterli, “Texture similarity measurement using Kullback-Leibler distance on wavelet subbands,” in Proceedings of the IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 2000), pp. 730–733.

Fan, J.

A. Laine, J. Fan, “Frame representation for texture segmentation,” IEEE Trans. Image Process. 5(5), 771–780 (1996).
[CrossRef]

Julesz, B.

B. Julesz, “Texton: the elements of texture perception and their interactions,” Nature 290, 91–97 (1981).
[CrossRef] [PubMed]

Kuo, C. C. K.

T. Chang, C. C. K. Kuo, “Texture analysis and classification with tree-structured wavelet transform,” IEEE Trans. Image Process. 2(5), 429–441 (1993).
[CrossRef]

Laine, A.

A. Laine, J. Fan, “Frame representation for texture segmentation,” IEEE Trans. Image Process. 5(5), 771–780 (1996).
[CrossRef]

Malik, J.

Mallat, S. G.

S. G. Mallat, “A theory for multi-resolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 647–693 (1989).
[CrossRef]

Miller, I.

M. Cooper, I. Miller, “Information measures for object recognition accommodating signature variability,” IEEE Trans. Inf. Theory 46(5), 1869–1907 (2000).

Mojsilovic, A.

A. Mojsilovic, V. Popovic, D. Rackov, “On the selection of optimal wavelet basis for texture characterization,” IEEE Trans. Image Process. 9(12), 2043–2050 (2000).

J. Chee, T. N. Pappas, A. Mojsilovic, B. Rogowitz, “Adaptive image segmentation,” in Proceedings of the IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 2002), pp. 777–780.

Mumford, D.

S. C. Zhu, Y. N. Wu, D. Mumford, “Prior learning and Gibbs reaction-diffusion,” IEEE Trans. Pattern Anal. Mach. Intell. 19(11), 1236–1250 (1997).

S. C. Zhu, Y. N. Wu, D. Mumford, “Filters, random fields and maximum entropy {(FRAME)}—towards the unified theory for texture modeling,” in Proceedings of the IEEE Conference Computer Vision and Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 693–696.

Navarro, R.

J. Portilla, R. Navarro, O. Nestares, A. Tabernero, “Texture synthesis-by-analysis based on a multiscale early-vision model,” Opt. Eng. 35(8), 2403–2417 (1996).
[CrossRef]

Neiberg, L.

L. Neiberg, D. Casasent, A. Talukder, “Feature space trajectory neural net classifier: confidences and thresholds for clutter and low contrast objects,” in Applications and Science of Artificial Neural Networks II, S. K. Rogers, D. W. Ruck, eds., Proc. SPIE2760, 435–446 (1996).
[CrossRef]

Nestares, O.

J. Portilla, R. Navarro, O. Nestares, A. Tabernero, “Texture synthesis-by-analysis based on a multiscale early-vision model,” Opt. Eng. 35(8), 2403–2417 (1996).
[CrossRef]

Nguyen, T.

K. S. Thyaragajan, T. Nguyen, C. E. Persons, “A maximum likelihood approach to texture classification using wavelet transform,” in Proceedings of the IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1994), Vol. 2, pp. 640–644.

Pappas, T. N.

J. Chee, T. N. Pappas, A. Mojsilovic, B. Rogowitz, “Adaptive image segmentation,” in Proceedings of the IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 2002), pp. 777–780.

Perona, P.

Persons, C. E.

K. S. Thyaragajan, T. Nguyen, C. E. Persons, “A maximum likelihood approach to texture classification using wavelet transform,” in Proceedings of the IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1994), Vol. 2, pp. 640–644.

Popovic, V.

A. Mojsilovic, V. Popovic, D. Rackov, “On the selection of optimal wavelet basis for texture characterization,” IEEE Trans. Image Process. 9(12), 2043–2050 (2000).

Portilla, J.

J. Portilla, E. P. Simoncelli, “A parametric texture model based on joint statistics of complex wavelet coefficients,” Int. J. Comput. Vision 40(1), 49–71 (2000).
[CrossRef]

J. Portilla, R. Navarro, O. Nestares, A. Tabernero, “Texture synthesis-by-analysis based on a multiscale early-vision model,” Opt. Eng. 35(8), 2403–2417 (1996).
[CrossRef]

Proat, M.

M. Proat, Y. Y. Zeevi, “Localized texture processing in vision: analysis and synthesis in Gaborian space,” IEEE Trans. Biomed. Eng. 36(1), 115–129 (1989).
[CrossRef]

Puzicha, J.

J. Puzicha, S. Belongie, “Model-based halftoning for color image segmentation,” in Proceedings of the International Conference on Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 2000), Vol. 3, pp. 629–32.

Rackov, D.

A. Mojsilovic, V. Popovic, D. Rackov, “On the selection of optimal wavelet basis for texture characterization,” IEEE Trans. Image Process. 9(12), 2043–2050 (2000).

Rao, K.

K. Rao, “Combinatorics reduction for target recognition in ATR applications,” in Automatic Object Recognition II, F. A. Sadjadi, ed., Proc. SPIE1700, 285–295 (1992).
[CrossRef]

Rogowitz, B.

J. Chee, T. N. Pappas, A. Mojsilovic, B. Rogowitz, “Adaptive image segmentation,” in Proceedings of the IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 2002), pp. 777–780.

Rong, S.

S. Rong, “Modeling clutter and context for target detection in infrared images,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 106–113.

Sadjadi, F.

F. Sadjadi, “Two-dimensional invariant object recognition by coding techniques,” Opt. Eng. 31(12), 2580–2583 (1992).
[CrossRef]

F. Sadjadi, “Experiments in the use of fractals in computer pattern recognition,” in Automatic Object Recognition III, F. A. Sadjadi, ed., Proc. SPIE1960, 214–222 (1993).
[CrossRef]

F. Sadjadi, “Performance evaluation of a texture-based segmentation algorithm,” in Signal and Image Processing Systems Performance Evaluation, Simulation, and Modeling, H. N. Nasr, M. E. Bazakos, eds., Proc. SPIE1483, 185–195 (1991).
[CrossRef]

F. Sadjadi, “Automatic recognition of partially occluded objects,” in Automatic Object Recognition II, F. A. Sadjadi, ed., Proc. SPIE1700, 277–284 (1992).
[CrossRef]

F. Sadjadi, “A sequential technique for 3-D object recognition,” in Intelligent Robots and Computer Vision, D. P. Casasent, ed., Proc. SPIE579, 265–267 (1985).
[CrossRef]

Sarkar, N.

B. B. Chaudhuri, N. Sarkar, “Texture segmentation using fractal dimension,” IEEE Trans. Pattern Anal. Mach. Intell. 17(1), 72–77 (1995).
[CrossRef]

Scheunders, P.

G. Van de Wouwer, P. Scheunders, D. Van Dyck, “Statistical texture characterization from discrete wavelet representations,” IEEE Trans. Image Process. 8(4), 592–598 (1999).
[CrossRef]

Simoncelli, E.

E. Simoncelli, “Modeling the joint statistics of images in the wavelet domain,” in Wavelet Applications in Signal and Image Processing VII, M. A. Unser, A. Aldroubi, A. F. Laine, eds., Proc. SPIE3813, 188–195 (1999).
[CrossRef]

Simoncelli, E. P.

J. Portilla, E. P. Simoncelli, “A parametric texture model based on joint statistics of complex wavelet coefficients,” Int. J. Comput. Vision 40(1), 49–71 (2000).
[CrossRef]

Smokelin, J. S.

D. P. Casasent, J. S. Smokelin, A. Ye, “Wavelet and Gabor transforms for detection,” Opt. Eng. 31(9), 1893–1898 (1992).
[CrossRef]

Tabernero, A.

J. Portilla, R. Navarro, O. Nestares, A. Tabernero, “Texture synthesis-by-analysis based on a multiscale early-vision model,” Opt. Eng. 35(8), 2403–2417 (1996).
[CrossRef]

Talukder, A.

L. Neiberg, D. Casasent, A. Talukder, “Feature space trajectory neural net classifier: confidences and thresholds for clutter and low contrast objects,” in Applications and Science of Artificial Neural Networks II, S. K. Rogers, D. W. Ruck, eds., Proc. SPIE2760, 435–446 (1996).
[CrossRef]

Thyaragajan, K. S.

K. S. Thyaragajan, T. Nguyen, C. E. Persons, “A maximum likelihood approach to texture classification using wavelet transform,” in Proceedings of the IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1994), Vol. 2, pp. 640–644.

Unser, M.

M. Unser, “Texture classification and segmentation using wavelet frames,” IEEE Trans. Image Process. 4(11), 1549–1560 (1995).
[CrossRef]

Van de Wouwer, G.

G. Van de Wouwer, P. Scheunders, D. Van Dyck, “Statistical texture characterization from discrete wavelet representations,” IEEE Trans. Image Process. 8(4), 592–598 (1999).
[CrossRef]

Van Dyck, D.

G. Van de Wouwer, P. Scheunders, D. Van Dyck, “Statistical texture characterization from discrete wavelet representations,” IEEE Trans. Image Process. 8(4), 592–598 (1999).
[CrossRef]

Vetterli, M.

M. N. Do, M. Vetterli, “Texture similarity measurement using Kullback-Leibler distance on wavelet subbands,” in Proceedings of the IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 2000), pp. 730–733.

Walker, J. S.

J. S. Walker, A Primer on Wavelets and their Scientific ApplicationsChapman & Hall/CRC, New York, 1999).
[CrossRef]

Weber, D.

D. Weber, D. Casasent, “Quadratic Gabor correlation filters for object detection,” IEEE Trans. Image Process. 10(2), 218–230 (2001).
[CrossRef]

Wu, Y. N.

S. C. Zhu, Y. N. Wu, D. Mumford, “Prior learning and Gibbs reaction-diffusion,” IEEE Trans. Pattern Anal. Mach. Intell. 19(11), 1236–1250 (1997).

S. C. Zhu, Y. N. Wu, D. Mumford, “Filters, random fields and maximum entropy {(FRAME)}—towards the unified theory for texture modeling,” in Proceedings of the IEEE Conference Computer Vision and Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 693–696.

Ye, A.

D. P. Casasent, J. S. Smokelin, A. Ye, “Wavelet and Gabor transforms for detection,” Opt. Eng. 31(9), 1893–1898 (1992).
[CrossRef]

Zeevi, Y. Y.

M. Proat, Y. Y. Zeevi, “Localized texture processing in vision: analysis and synthesis in Gaborian space,” IEEE Trans. Biomed. Eng. 36(1), 115–129 (1989).
[CrossRef]

Zhu, S. C.

S. C. Zhu, Y. N. Wu, D. Mumford, “Prior learning and Gibbs reaction-diffusion,” IEEE Trans. Pattern Anal. Mach. Intell. 19(11), 1236–1250 (1997).

S. C. Zhu, Y. N. Wu, D. Mumford, “Filters, random fields and maximum entropy {(FRAME)}—towards the unified theory for texture modeling,” in Proceedings of the IEEE Conference Computer Vision and Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 693–696.

Commun. Pure Appl. Math.

I. Daubechies, “Orthonormal bases of compactly supported wavelets,” Commun. Pure Appl. Math. 41, 909–991 (1988).
[CrossRef]

IEEE Trans. Biomed. Eng.

M. Proat, Y. Y. Zeevi, “Localized texture processing in vision: analysis and synthesis in Gaborian space,” IEEE Trans. Biomed. Eng. 36(1), 115–129 (1989).
[CrossRef]

IEEE Trans. Image Process.

D. Weber, D. Casasent, “Quadratic Gabor correlation filters for object detection,” IEEE Trans. Image Process. 10(2), 218–230 (2001).
[CrossRef]

A. Laine, J. Fan, “Frame representation for texture segmentation,” IEEE Trans. Image Process. 5(5), 771–780 (1996).
[CrossRef]

G. Van de Wouwer, P. Scheunders, D. Van Dyck, “Statistical texture characterization from discrete wavelet representations,” IEEE Trans. Image Process. 8(4), 592–598 (1999).
[CrossRef]

A. Mojsilovic, V. Popovic, D. Rackov, “On the selection of optimal wavelet basis for texture characterization,” IEEE Trans. Image Process. 9(12), 2043–2050 (2000).

T. Chang, C. C. K. Kuo, “Texture analysis and classification with tree-structured wavelet transform,” IEEE Trans. Image Process. 2(5), 429–441 (1993).
[CrossRef]

M. Unser, “Texture classification and segmentation using wavelet frames,” IEEE Trans. Image Process. 4(11), 1549–1560 (1995).
[CrossRef]

IEEE Trans. Inf. Theory

M. Cooper, I. Miller, “Information measures for object recognition accommodating signature variability,” IEEE Trans. Inf. Theory 46(5), 1869–1907 (2000).

IEEE Trans. Pattern Anal. Mach. Intell.

B. B. Chaudhuri, N. Sarkar, “Texture segmentation using fractal dimension,” IEEE Trans. Pattern Anal. Mach. Intell. 17(1), 72–77 (1995).
[CrossRef]

S. C. Zhu, Y. N. Wu, D. Mumford, “Prior learning and Gibbs reaction-diffusion,” IEEE Trans. Pattern Anal. Mach. Intell. 19(11), 1236–1250 (1997).

S. G. Mallat, “A theory for multi-resolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 647–693 (1989).
[CrossRef]

Int. J. Comput. Vision

J. Portilla, E. P. Simoncelli, “A parametric texture model based on joint statistics of complex wavelet coefficients,” Int. J. Comput. Vision 40(1), 49–71 (2000).
[CrossRef]

J. Opt. Soc. Am. A

Nature

B. Julesz, “Texton: the elements of texture perception and their interactions,” Nature 290, 91–97 (1981).
[CrossRef] [PubMed]

Opt. Eng.

F. Sadjadi, “Two-dimensional invariant object recognition by coding techniques,” Opt. Eng. 31(12), 2580–2583 (1992).
[CrossRef]

D. P. Casasent, J. S. Smokelin, A. Ye, “Wavelet and Gabor transforms for detection,” Opt. Eng. 31(9), 1893–1898 (1992).
[CrossRef]

J. Portilla, R. Navarro, O. Nestares, A. Tabernero, “Texture synthesis-by-analysis based on a multiscale early-vision model,” Opt. Eng. 35(8), 2403–2417 (1996).
[CrossRef]

Other

S. C. Zhu, Y. N. Wu, D. Mumford, “Filters, random fields and maximum entropy {(FRAME)}—towards the unified theory for texture modeling,” in Proceedings of the IEEE Conference Computer Vision and Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 693–696.

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Figures (9)

Fig. 1
Fig. 1

Normalized empirical PDF versus model PDF for the diagonal wavelet transform subband for the image shown in Fig. 3(c).

Fig. 2
Fig. 2

Wavelet-based target detection.

Fig. 3
Fig. 3

Samples from IR imagery sequence: (a) very long-range image of a target, (b) long-range image of a target, (c) short-range image of a target.

Fig. 4
Fig. 4

Segmentation results for the sequence shown in Fig. 3.

Fig. 5
Fig. 5

ROC curve for the case of POT = 25 and W = 4.

Fig. 6
Fig. 6

Variation of segmentation accuracy as a function of the number of pixels on a target.

Fig. 7
Fig. 7

Variation of optimum PD versus TIR, TBIR, FW, and entropy.

Fig. 8
Fig. 8

Variation of FA versus TIR, TBIR, FW, and entropy.

Fig. 9
Fig. 9

Variation of PD versus W and FA for POT = 1386.

Equations (22)

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Wsa, b= stgabtdt,gabt=gt-b/aa,
g(·)=exp-t/t°2/2expj2πf°t.
fh1|d1a1|v1
f · g=f11g11+f12g12++fNMgNM
PDFx=K exp-|x|αβ,
K=β2αΓ1/β, where Γx=0exp-ttx-1dt,
α=meanΓ1/βΓ2/β,
β=F-1mean2variance, where Fx=Γ2/xΓ3/xΓ1/x.
TIR2=1/N0i=1N0xTi-1/N0i=1N0xbi21/N0i=1N0xbi2-1/N0i=1N0xbi2=x¯T-x¯b2σb2,
TBIR2=x¯T-x¯b2σbσT,
Entropy=-P logp,
FW=logx¯Tx¯B-x¯T
PD=Number of ground-truth targets detectedNumber of ground truth targets.
Modified PD=Number of ground-truth target pixels detectedNumber of ground-truth target pixels.
FA=Total number of clutter regions of declared targetTotal number of frames.
SA=Number of pixels ofsegmented regionground-truth regionNumber of pixels ofground truthsegmented region.
PD=a0+a1x1+a2x2+a3x3+a12x1x2+a13x1x3+a23x2x3+a11x12+a22x22+a33x32,
PD=0.8958+0.0071x1-0.0745x2+3.4056x3+0.0001x1x2-0.0003x1x3+0.0126x2x3-0.0000x12+0.0025x22-3.0974x32; residual=1.6902.
PD=0.9101+0.6710x1-0.1872x2+3.2187x3+0.0525x1x2-0.2737x1x3+0.0536x2x3-0.2732x12+0.0008x22-2.7602x32; residual=1.8152.
PD=0.1968x1+0.1056x2+10.5736x3-0.0724x1x2-2.6009x1x3+0.1708x2x3+0.0487x12+0.0063x22-1.1865x32; residual=2.0507.
PD=-1.5991+2.2918x1+0.0891x2+2.3795x3-0.0796x1x2-0.2549x1x3+0.0378x2x3-0.4579x12-0.000x22-2.8866x32; residual=1.7731.
PD=-21.5001+11.0160x1-0.5371x2+5.7786x3+0.0993x1x2-0.7126x1x3+0.0610x2x3-1.3283x12+0.0017x22-2.7030x32; residual=1.8328.

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