Scale-space from nonlinear filters

Decomposition by extrema is put into the context of linear vision systems and scale-space. One dimensional discrete M- and N-sieves neither introduce new edges as the scale increases nor create new extrema. They share this property with diffusion based filters. Furthermore M- and N-sieve algorithms are extremely fast with order complexity n. Used to decompose an image, the resulting granularity is appropriate for pattern recognition.<<ETX>>

[1]  Andrew P. Witkin,et al.  Scale-space filtering: A new approach to multi-scale description , 1984, ICASSP.

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

[3]  G. Matheron.  Random Sets and Integral Geometry , 1976 .

[4]  Alan L. Yuille,et al.  Scaling Theorems for Zero Crossings , 1987, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[5]  Paul Jackway.  Morphological scale-space , 1992 .

[6]  Stanley R Sternberg,et al.  Grayscale morphology , 1986 .

[7]  Andrew P. Witkin,et al.  Scale-Space Filtering , 1983, IJCAI.

[8]  Ioannis Pitas,et al.  Morphological Shape Decomposition , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[9]  J. Andrew Bangham,et al.  Multiscale median and morphological filters for 2D pattern recognition , 1994, Signal Process..

[10]  Andrew P. Witkin,et al.  Uniqueness of the Gaussian Kernel for Scale-Space Filtering , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[11]  Pierre Chardaire,et al.  Properties of multiscale morphological filters, namely, the morphology decomposition theorem , 1994, Electronic Imaging.

[12]  G. Wise,et al.  A theoretical analysis of the properties of median filters , 1981 .

[13]  H. Blum.  Biological shape and visual science (part I) , 1973 .

[14]  Edward R. Dougherty,et al.  Gray-scale granulometries compatible with spatial scalings , 1993, Signal Process..

[15]  G. A. Watson.  A treatise on the theory of Bessel functions , 1944 .

[16]  M.-H. Chen,et al.  A Multiscanning Approach Based on Morphological Filtering , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[17]  Petros Maragos,et al.  Pattern Spectrum and Multiscale Shape Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[18]  J. Andrew Bangham,et al.  Properties of a Series of Nested Median Filters, Namely the Data Sieve , 1993, IEEE Trans. Signal Process..

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

[20]  Peter F. M. Nacken.  Openings Can Introduce Zero Crossings in Boundary Curvature , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[21]  Jitendra Malik,et al.  Scale-Space and Edge Detection Using Anisotropic Diffusion , 1990, IEEE Trans. Pattern Anal. Mach. Intell..