Perceptual organization in image analysis : a mathematical approach based on scale, orientation and curvature

• A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers.

[1]  Mads Nielsen,et al.  Feature-Based Image Analysis , 2003, International Journal of Computer Vision.

[2]  Lance R. Williams,et al.  Euclidean Group Invariant Computation of Stochastic Completion Fields Using Shiftable-Twistable Functions , 2000, Journal of Mathematical Imaging and Vision.

[3]  J. C. van der Meer,et al.  A note on local Morse theory in state-scale space and Gaussian deformations , 2005 .

[4]  Tony Lindeberg,et al.  Scale-Space Theory in Computer Vision , 1993, Lecture Notes in Computer Science.

[5]  J. Koenderink The structure of images , 2004, Biological Cybernetics.

[6]  Luc Florack,et al.  On Image Reconstruction from Multiscale Top Points , 2005, Scale-Space.

[7]  D. Ts'o,et al.  Functional organization of primate visual cortex revealed by high resolution optical imaging. , 1990, Science.

[8]  F. Olver Asymptotics and Special Functions , 1974 .

[9]  Andreas Rieder,et al.  Wavelets: Theory and Applications , 1997 .

[10]  Tony Lindeberg,et al.  Scale-Space for Discrete Signals , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[11]  N. Temme Special Functions: An Introduction to the Classical Functions of Mathematical Physics , 1996 .

[12]  van Ma Markus Almsick,et al.  Context models of lines and contours , 2007 .

[13]  S. Twareque Ali,et al.  A general theorem on square-integrability: Vector coherent states , 1998 .

[14]  K. S. Pedersen,et al.  On α Kernels , Lévy Processes , and Natural Image Statistics , 2022 .

[15]  Luc Van Gool,et al.  An Extended Class of Scale-Invariant and Recursive Scale Space Filters , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[16]  Luc Florack,et al.  A Linear Image Reconstruction Framework Based on Sobolev Type Inner Products , 2005, International Journal of Computer Vision.

[17]  Tai Sing Lee,et al.  Image Representation Using 2D Gabor Wavelets , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[18]  J. R. Higgins An Interpolation Series Associated with the Bessel–Hankel Transform , 1972 .

[19]  R. W. van der Put Methods for 3D orientation analysis and their application to the study of arterial remodeling , 2005 .

[20]  Christopher Isham,et al.  Coherent states for n‐dimensional Euclidean groups E(n) and their application , 1991 .

[21]  L. Milne‐Thomson A Treatise on the Theory of Bessel Functions , 1945, Nature.

[22]  C. Chitti Babu,et al.  On feature extraction in pattern recognition , 1972, Inf. Sci..

[23]  R. Walde,et al.  Introduction to Lie groups and Lie algebras , 1973 .

[24]  Waldemar Hebisch,et al.  Estimates on the semigroups generated by left invariant operators on Lie groups. , 1992 .

[25]  Luc Florack,et al.  Multiscale hierarchical segmentation , 2003 .

[26]  Joachim Weickert,et al.  Scale-Space Theories in Computer Vision , 1999, Lecture Notes in Computer Science.

[27]  Max A. Viergever,et al.  Invertible Apertured Orientation Filters in Image Analysis , 1999, International Journal of Computer Vision.

[28]  Luc Florack,et al.  Hierarchical Pre-Segmentation without Prior Knowledge , 2001, ICCV.

[29]  Lance R. Williams,et al.  Analytic solution of stochastic completion fields , 1995, Biological Cybernetics.

[30]  M. Wertheimer Untersuchungen zur Lehre von der Gestalt. II , 1923 .

[31]  Luc Florack,et al.  Using multiscale top points in image matching , 2004, 2004 International Conference on Image Processing, 2004. ICIP '04..

[32]  Luc Florack,et al.  Image Reconstruction from Multiscale Critical Points , 2003, Scale-Space.

[33]  Michael Kerckhove,et al.  Scale-Space and Morphology in Computer Vision , 2001, Lecture Notes in Computer Science 2106.

[34]  Fjl Frans Martens Spaces of analytic functions on inductive/projective limits of Hilbert spaces , 1988 .

[35]  Derek W. Robinson,et al.  Elliptic Operators and Lie Groups , 1991 .

[36]  D. Mumford Elastica and Computer Vision , 1994 .