V. Velisavljevic, B. Beferull-Lozano, M. Vetterli, and P. L. Dragotti, “Directionlets: anisotropic multidirectional representation with separable filtering,” IEEE Trans. Image Process. 15, 1916-1933 (2006).

[CrossRef]
[PubMed]

M. N. Do and M. Vetterli, “The contourlet transform: an efficient directional multiresolution image representation,” IEEE Trans. Image Process. 14, 2091-2106 (2005).

[CrossRef]
[PubMed]

D. Dragoman, “Applications of the Wigner distribution function in signal processing,” EURASIP J. Appl. Signal Process. 10, 1520-1534 (2005).

T. Maddess, Y. Nagai, A. C. James, and A. Ankiewcz, “Binary and ternary textures containing higher-order spatial correlations,” Vision Res. 44, 1093-1113 (2004).

[CrossRef]
[PubMed]

J. J. Wlodarz, “Entropy and Wigner distribution functions revisited,” Int. J. Theor. Phys. 42, 1075-1084 (2003).

[CrossRef]

J. L. Starck, E. Candes, and D. Donoho, “The curvelet transform for image denoising,” IEEE Trans. Image Process. 11, 670-684 (2002).

[CrossRef]

T. Maddess and Y. Nagai, “Discriminating isotrigon textures,” Vision Res. 41, 3837-3860 (2001).

[CrossRef]
[PubMed]

L. Stankovic, “A measure of some time-frequency distributions concentration,” Signal Process. 81, 623-631 (2001).

[CrossRef]

D. Donoho, “Wedgelets: nearly minimax estimation of edges,” Ann. Stat. 27, 859-867 (1999).

[CrossRef]

G. Süßmann, “Uncertainty relation: from inequality to equality,” Z. Naturforsch. 52, 49-52 (1997).

K. P. Purpura, J. D. Victor, and E. Katz, “Striate cortex extracts higher-order spatial correlations from visual textures,” Proc. Natl. Acad. Sci. U.S.A. 91, 8482-8486 (1994).

[CrossRef]
[PubMed]

W. J. Williams, M. L. Brown, and A. O. Hero, “Uncertainty, information and time-frequency distributions,” Proc. SPIE 1566, 144-156 (1991).

[CrossRef]

A. Cumani, “Edge detection in multispectral images,” Comput. Vis. Graph. Image Process. 53, 40-51 (1991).

L. D. Jacobson and H. Wechsler, “Joint spatial/spatial-frequency representation,” Signal Process. 14, 37-68 (1988).

[CrossRef]

T. A. C. M. Claasen and W. F. G. Mecklenbräuker, “The Wigner distribution--a tool for time-frequency analysis. Part I. Continuous-time signals,” Philips J. Res. 35, 237-250 (1980).

T. A. C. M. Claasen and W. F. G. Mecklenbräuker, “The Wigner distribution--a tool for time-frequency analysis. Part II. Discrete-time signals,” Philips J. Res. 35, 276-300 (1980).

T. A. C. M. Claasen and W. F. G. Mecklenbräuker, “The Wigner distribution--a tool for time-frequency analysis. Part III. Relations with other time-frequency transformations,” Philips J. Res. 35, 372-389 (1980).

R. Schumer and L. Ganz, “Independent stereoscopic channels for different extents of spatial pooling,” Vision Res. 19, 1303-1314 (1979).

[CrossRef]
[PubMed]

B. Julesz, E. N. Gilbert, and J. D. Victor, “Visual discrimination of textures with identical third-order statistics,” Biol. Cybern. 31, 137-140 (1978).

[CrossRef]
[PubMed]

C. W. Tyler, “Stereoscopic tilt and size effects,” Perception 4, 287-192 (1975).

[CrossRef]

L. Cohen, “Generalized phase-space distribution functions,” J. Math. Phys. 7, 781-786 (1966).

[CrossRef]

D. W. Allan, “Statistics of atomic frequency standard,” Proc. IEEE 54, 223-231 (1966).

[CrossRef]

J. Ville, “Théorie and applications de la Notion de Signal Analytique,” Cables Transm. 2A, 61-74 (1948).

E. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40, 749-759 (1932).

[CrossRef]

D. W. Allan, “Statistics of atomic frequency standard,” Proc. IEEE 54, 223-231 (1966).

[CrossRef]

T. Maddess, Y. Nagai, A. C. James, and A. Ankiewcz, “Binary and ternary textures containing higher-order spatial correlations,” Vision Res. 44, 1093-1113 (2004).

[CrossRef]
[PubMed]

P. Flandrin, R. G. Baraniuk, and O. Michel, “Time-frequency complexity and information,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 1994), Vol. 3, pp. 329-332.

M. E. Barilla, M. G. Forero, and M. Spann, “Color-based texture segmentation,” in Information Optics, 5th International Workshop, G.Cristóbal, B.Javidi, and S.Vallmitjana, eds. (AIP, 2006), pp. 401-409.

V. Velisavljevic, B. Beferull-Lozano, M. Vetterli, and P. L. Dragotti, “Directionlets: anisotropic multidirectional representation with separable filtering,” IEEE Trans. Image Process. 15, 1916-1933 (2006).

[CrossRef]
[PubMed]

K. H. Brenner, “A discrete version of the Wigner distribution function,” EURASIP J. Appl. Signal Process. 2005, 307-309.

W. J. Williams, M. L. Brown, and A. O. Hero, “Uncertainty, information and time-frequency distributions,” Proc. SPIE 1566, 144-156 (1991).

[CrossRef]

G. Smith and I. Burns, “MeasTex image texture database and test suite” (1997). Available online at http://www.texturesynthesis.com/meastex/meastex.html.

J. L. Starck, E. Candes, and D. Donoho, “The curvelet transform for image denoising,” IEEE Trans. Image Process. 11, 670-684 (2002).

[CrossRef]

T. A. C. M. Claasen and W. F. G. Mecklenbräuker, “The Wigner distribution--a tool for time-frequency analysis. Part II. Discrete-time signals,” Philips J. Res. 35, 276-300 (1980).

T. A. C. M. Claasen and W. F. G. Mecklenbräuker, “The Wigner distribution--a tool for time-frequency analysis. Part III. Relations with other time-frequency transformations,” Philips J. Res. 35, 372-389 (1980).

T. A. C. M. Claasen and W. F. G. Mecklenbräuker, “The Wigner distribution--a tool for time-frequency analysis. Part I. Continuous-time signals,” Philips J. Res. 35, 237-250 (1980).

L. Cohen, “Generalized phase-space distribution functions,” J. Math. Phys. 7, 781-786 (1966).

[CrossRef]

A. Cumani, “Edge detection in multispectral images,” Comput. Vis. Graph. Image Process. 53, 40-51 (1991).

B. Yegnanarayana, P. Pavan Kumar, and S. Das, “One-dimensional Gabor filtering for texture edge detection,” Proceedings of Indian Conference on Computer Vision, Graphics and Image Processing (IEEE, 1998), pp. 231-237.

P. de Rivaz and N. Kingsbury, “Complex wavelet features for fast texture image retrieval,” Proceedings of IEEE Conference on Image Processing (IEEE, 1999), pp. 25-28.

M. N. Do and M. Vetterli, “The contourlet transform: an efficient directional multiresolution image representation,” IEEE Trans. Image Process. 14, 2091-2106 (2005).

[CrossRef]
[PubMed]

J. L. Starck, E. Candes, and D. Donoho, “The curvelet transform for image denoising,” IEEE Trans. Image Process. 11, 670-684 (2002).

[CrossRef]

D. Donoho, “Wedgelets: nearly minimax estimation of edges,” Ann. Stat. 27, 859-867 (1999).

[CrossRef]

D. Dragoman, “Applications of the Wigner distribution function in signal processing,” EURASIP J. Appl. Signal Process. 10, 1520-1534 (2005).

V. Velisavljevic, B. Beferull-Lozano, M. Vetterli, and P. L. Dragotti, “Directionlets: anisotropic multidirectional representation with separable filtering,” IEEE Trans. Image Process. 15, 1916-1933 (2006).

[CrossRef]
[PubMed]

R. Eisberg and R. Resnick, Quantum Physics (Wiley, 1974).

P. Flandrin, R. G. Baraniuk, and O. Michel, “Time-frequency complexity and information,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 1994), Vol. 3, pp. 329-332.

M. E. Barilla, M. G. Forero, and M. Spann, “Color-based texture segmentation,” in Information Optics, 5th International Workshop, G.Cristóbal, B.Javidi, and S.Vallmitjana, eds. (AIP, 2006), pp. 401-409.

R. Schumer and L. Ganz, “Independent stereoscopic channels for different extents of spatial pooling,” Vision Res. 19, 1303-1314 (1979).

[CrossRef]
[PubMed]

B. Julesz, E. N. Gilbert, and J. D. Victor, “Visual discrimination of textures with identical third-order statistics,” Biol. Cybern. 31, 137-140 (1978).

[CrossRef]
[PubMed]

W. J. Williams, M. L. Brown, and A. O. Hero, “Uncertainty, information and time-frequency distributions,” Proc. SPIE 1566, 144-156 (1991).

[CrossRef]

L. D. Jacobson and H. Wechsler, “Joint spatial/spatial-frequency representation,” Signal Process. 14, 37-68 (1988).

[CrossRef]

T. Maddess, Y. Nagai, A. C. James, and A. Ankiewcz, “Binary and ternary textures containing higher-order spatial correlations,” Vision Res. 44, 1093-1113 (2004).

[CrossRef]
[PubMed]

R. A. Johnson and D. W. Wichern, Applied Multivariate Statistical Analysis (Prentice Hall, 1992).

B. Julesz, E. N. Gilbert, and J. D. Victor, “Visual discrimination of textures with identical third-order statistics,” Biol. Cybern. 31, 137-140 (1978).

[CrossRef]
[PubMed]

K. P. Purpura, J. D. Victor, and E. Katz, “Striate cortex extracts higher-order spatial correlations from visual textures,” Proc. Natl. Acad. Sci. U.S.A. 91, 8482-8486 (1994).

[CrossRef]
[PubMed]

P. de Rivaz and N. Kingsbury, “Complex wavelet features for fast texture image retrieval,” Proceedings of IEEE Conference on Image Processing (IEEE, 1999), pp. 25-28.

T. Maddess, Y. Nagai, A. C. James, and A. Ankiewcz, “Binary and ternary textures containing higher-order spatial correlations,” Vision Res. 44, 1093-1113 (2004).

[CrossRef]
[PubMed]

T. Maddess and Y. Nagai, “Discriminating isotrigon textures,” Vision Res. 41, 3837-3860 (2001).

[CrossRef]
[PubMed]

T. Maddess and Y. Nagai, “Lessons from biological processing of image texture,” in International Congress Series (Elsevier, 2004), Vol. 1269, pp. 26-29.

[CrossRef]

T. A. C. M. Claasen and W. F. G. Mecklenbräuker, “The Wigner distribution--a tool for time-frequency analysis. Part II. Discrete-time signals,” Philips J. Res. 35, 276-300 (1980).

T. A. C. M. Claasen and W. F. G. Mecklenbräuker, “The Wigner distribution--a tool for time-frequency analysis. Part I. Continuous-time signals,” Philips J. Res. 35, 237-250 (1980).

T. A. C. M. Claasen and W. F. G. Mecklenbräuker, “The Wigner distribution--a tool for time-frequency analysis. Part III. Relations with other time-frequency transformations,” Philips J. Res. 35, 372-389 (1980).

P. Flandrin, R. G. Baraniuk, and O. Michel, “Time-frequency complexity and information,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 1994), Vol. 3, pp. 329-332.

T. Maddess, Y. Nagai, A. C. James, and A. Ankiewcz, “Binary and ternary textures containing higher-order spatial correlations,” Vision Res. 44, 1093-1113 (2004).

[CrossRef]
[PubMed]

T. Maddess and Y. Nagai, “Discriminating isotrigon textures,” Vision Res. 41, 3837-3860 (2001).

[CrossRef]
[PubMed]

T. Maddess and Y. Nagai, “Lessons from biological processing of image texture,” in International Congress Series (Elsevier, 2004), Vol. 1269, pp. 26-29.

[CrossRef]

B. Yegnanarayana, P. Pavan Kumar, and S. Das, “One-dimensional Gabor filtering for texture edge detection,” Proceedings of Indian Conference on Computer Vision, Graphics and Image Processing (IEEE, 1998), pp. 231-237.

K. P. Purpura, J. D. Victor, and E. Katz, “Striate cortex extracts higher-order spatial correlations from visual textures,” Proc. Natl. Acad. Sci. U.S.A. 91, 8482-8486 (1994).

[CrossRef]
[PubMed]

A. Rényi, “Some fundamental questions of information theory,” in Selected Papers of Alfréd Rényi, P.Turán, ed. (Akadémiai Kiadó, 1976), pp. 526-552 (1976). [Originally published in Magy. Tud. Akad. Mat. Fiz Tud. Oszt. Kozl., 10, 251-282 (1960)].

R. Eisberg and R. Resnick, Quantum Physics (Wiley, 1974).

T. H. Sang and W. J. Williams, “Rényi information and signal dependent optimal kernel design.” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 1995), Vol. 2, pp. 997-1000.

R. Schumer and L. Ganz, “Independent stereoscopic channels for different extents of spatial pooling,” Vision Res. 19, 1303-1314 (1979).

[CrossRef]
[PubMed]

C. E. Shannon and W. Weaver, The Mathematical Theory of Communication (University of Illinois Press, 1949).

G. Smith and I. Burns, “MeasTex image texture database and test suite” (1997). Available online at http://www.texturesynthesis.com/meastex/meastex.html.

M. E. Barilla, M. G. Forero, and M. Spann, “Color-based texture segmentation,” in Information Optics, 5th International Workshop, G.Cristóbal, B.Javidi, and S.Vallmitjana, eds. (AIP, 2006), pp. 401-409.

L. Stankovic, “A measure of some time-frequency distributions concentration,” Signal Process. 81, 623-631 (2001).

[CrossRef]

J. L. Starck, E. Candes, and D. Donoho, “The curvelet transform for image denoising,” IEEE Trans. Image Process. 11, 670-684 (2002).

[CrossRef]

G. Süßmann, “Uncertainty relation: from inequality to equality,” Z. Naturforsch. 52, 49-52 (1997).

C. W. Tyler, “Stereoscopic tilt and size effects,” Perception 4, 287-192 (1975).

[CrossRef]

V. Velisavljevic, B. Beferull-Lozano, M. Vetterli, and P. L. Dragotti, “Directionlets: anisotropic multidirectional representation with separable filtering,” IEEE Trans. Image Process. 15, 1916-1933 (2006).

[CrossRef]
[PubMed]

V. Velisavljevic, B. Beferull-Lozano, M. Vetterli, and P. L. Dragotti, “Directionlets: anisotropic multidirectional representation with separable filtering,” IEEE Trans. Image Process. 15, 1916-1933 (2006).

[CrossRef]
[PubMed]

M. N. Do and M. Vetterli, “The contourlet transform: an efficient directional multiresolution image representation,” IEEE Trans. Image Process. 14, 2091-2106 (2005).

[CrossRef]
[PubMed]

K. P. Purpura, J. D. Victor, and E. Katz, “Striate cortex extracts higher-order spatial correlations from visual textures,” Proc. Natl. Acad. Sci. U.S.A. 91, 8482-8486 (1994).

[CrossRef]
[PubMed]

B. Julesz, E. N. Gilbert, and J. D. Victor, “Visual discrimination of textures with identical third-order statistics,” Biol. Cybern. 31, 137-140 (1978).

[CrossRef]
[PubMed]

J. Ville, “Théorie and applications de la Notion de Signal Analytique,” Cables Transm. 2A, 61-74 (1948).

C. E. Shannon and W. Weaver, The Mathematical Theory of Communication (University of Illinois Press, 1949).

L. D. Jacobson and H. Wechsler, “Joint spatial/spatial-frequency representation,” Signal Process. 14, 37-68 (1988).

[CrossRef]

R. A. Johnson and D. W. Wichern, Applied Multivariate Statistical Analysis (Prentice Hall, 1992).

N. Wiener, Cybernetics (Wiley, 1948).

E. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40, 749-759 (1932).

[CrossRef]

W. J. Williams, M. L. Brown, and A. O. Hero, “Uncertainty, information and time-frequency distributions,” Proc. SPIE 1566, 144-156 (1991).

[CrossRef]

T. H. Sang and W. J. Williams, “Rényi information and signal dependent optimal kernel design.” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 1995), Vol. 2, pp. 997-1000.

J. J. Wlodarz, “Entropy and Wigner distribution functions revisited,” Int. J. Theor. Phys. 42, 1075-1084 (2003).

[CrossRef]

B. Yegnanarayana, P. Pavan Kumar, and S. Das, “One-dimensional Gabor filtering for texture edge detection,” Proceedings of Indian Conference on Computer Vision, Graphics and Image Processing (IEEE, 1998), pp. 231-237.

D. Donoho, “Wedgelets: nearly minimax estimation of edges,” Ann. Stat. 27, 859-867 (1999).

[CrossRef]

B. Julesz, E. N. Gilbert, and J. D. Victor, “Visual discrimination of textures with identical third-order statistics,” Biol. Cybern. 31, 137-140 (1978).

[CrossRef]
[PubMed]

J. Ville, “Théorie and applications de la Notion de Signal Analytique,” Cables Transm. 2A, 61-74 (1948).

A. Cumani, “Edge detection in multispectral images,” Comput. Vis. Graph. Image Process. 53, 40-51 (1991).

D. Dragoman, “Applications of the Wigner distribution function in signal processing,” EURASIP J. Appl. Signal Process. 10, 1520-1534 (2005).

K. H. Brenner, “A discrete version of the Wigner distribution function,” EURASIP J. Appl. Signal Process. 2005, 307-309.

V. Velisavljevic, B. Beferull-Lozano, M. Vetterli, and P. L. Dragotti, “Directionlets: anisotropic multidirectional representation with separable filtering,” IEEE Trans. Image Process. 15, 1916-1933 (2006).

[CrossRef]
[PubMed]

J. L. Starck, E. Candes, and D. Donoho, “The curvelet transform for image denoising,” IEEE Trans. Image Process. 11, 670-684 (2002).

[CrossRef]

M. N. Do and M. Vetterli, “The contourlet transform: an efficient directional multiresolution image representation,” IEEE Trans. Image Process. 14, 2091-2106 (2005).

[CrossRef]
[PubMed]

J. J. Wlodarz, “Entropy and Wigner distribution functions revisited,” Int. J. Theor. Phys. 42, 1075-1084 (2003).

[CrossRef]

L. Cohen, “Generalized phase-space distribution functions,” J. Math. Phys. 7, 781-786 (1966).

[CrossRef]

C. W. Tyler, “Stereoscopic tilt and size effects,” Perception 4, 287-192 (1975).

[CrossRef]

T. A. C. M. Claasen and W. F. G. Mecklenbräuker, “The Wigner distribution--a tool for time-frequency analysis. Part I. Continuous-time signals,” Philips J. Res. 35, 237-250 (1980).

T. A. C. M. Claasen and W. F. G. Mecklenbräuker, “The Wigner distribution--a tool for time-frequency analysis. Part II. Discrete-time signals,” Philips J. Res. 35, 276-300 (1980).

T. A. C. M. Claasen and W. F. G. Mecklenbräuker, “The Wigner distribution--a tool for time-frequency analysis. Part III. Relations with other time-frequency transformations,” Philips J. Res. 35, 372-389 (1980).

E. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40, 749-759 (1932).

[CrossRef]

D. W. Allan, “Statistics of atomic frequency standard,” Proc. IEEE 54, 223-231 (1966).

[CrossRef]

K. P. Purpura, J. D. Victor, and E. Katz, “Striate cortex extracts higher-order spatial correlations from visual textures,” Proc. Natl. Acad. Sci. U.S.A. 91, 8482-8486 (1994).

[CrossRef]
[PubMed]

W. J. Williams, M. L. Brown, and A. O. Hero, “Uncertainty, information and time-frequency distributions,” Proc. SPIE 1566, 144-156 (1991).

[CrossRef]

L. Stankovic, “A measure of some time-frequency distributions concentration,” Signal Process. 81, 623-631 (2001).

[CrossRef]

L. D. Jacobson and H. Wechsler, “Joint spatial/spatial-frequency representation,” Signal Process. 14, 37-68 (1988).

[CrossRef]

T. Maddess and Y. Nagai, “Discriminating isotrigon textures,” Vision Res. 41, 3837-3860 (2001).

[CrossRef]
[PubMed]

T. Maddess, Y. Nagai, A. C. James, and A. Ankiewcz, “Binary and ternary textures containing higher-order spatial correlations,” Vision Res. 44, 1093-1113 (2004).

[CrossRef]
[PubMed]

R. Schumer and L. Ganz, “Independent stereoscopic channels for different extents of spatial pooling,” Vision Res. 19, 1303-1314 (1979).

[CrossRef]
[PubMed]

G. Süßmann, “Uncertainty relation: from inequality to equality,” Z. Naturforsch. 52, 49-52 (1997).

T. Maddess and Y. Nagai, “Lessons from biological processing of image texture,” in International Congress Series (Elsevier, 2004), Vol. 1269, pp. 26-29.

[CrossRef]

B. Yegnanarayana, P. Pavan Kumar, and S. Das, “One-dimensional Gabor filtering for texture edge detection,” Proceedings of Indian Conference on Computer Vision, Graphics and Image Processing (IEEE, 1998), pp. 231-237.

MATLAB code for segmentation and classification of multitexture images is available from http://www.cse.iitk.ac.in/~amit/courses/768/00/rajrup/.

P. de Rivaz and N. Kingsbury, “Complex wavelet features for fast texture image retrieval,” Proceedings of IEEE Conference on Image Processing (IEEE, 1999), pp. 25-28.

M. E. Barilla, M. G. Forero, and M. Spann, “Color-based texture segmentation,” in Information Optics, 5th International Workshop, G.Cristóbal, B.Javidi, and S.Vallmitjana, eds. (AIP, 2006), pp. 401-409.

G. Smith and I. Burns, “MeasTex image texture database and test suite” (1997). Available online at http://www.texturesynthesis.com/meastex/meastex.html.

C. E. Shannon and W. Weaver, The Mathematical Theory of Communication (University of Illinois Press, 1949).

N. Wiener, Cybernetics (Wiley, 1948).

A. Rényi, “Some fundamental questions of information theory,” in Selected Papers of Alfréd Rényi, P.Turán, ed. (Akadémiai Kiadó, 1976), pp. 526-552 (1976). [Originally published in Magy. Tud. Akad. Mat. Fiz Tud. Oszt. Kozl., 10, 251-282 (1960)].

T. H. Sang and W. J. Williams, “Rényi information and signal dependent optimal kernel design.” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 1995), Vol. 2, pp. 997-1000.

P. Flandrin, R. G. Baraniuk, and O. Michel, “Time-frequency complexity and information,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 1994), Vol. 3, pp. 329-332.

R. Eisberg and R. Resnick, Quantum Physics (Wiley, 1974).

R. A. Johnson and D. W. Wichern, Applied Multivariate Statistical Analysis (Prentice Hall, 1992).