Threshold Superposition in Morphological Image Analysis Systems

It is shown that four composite morphological systems, namely morphological edge detection, peak/valley extraction, skeletonization, and shape-size distributions obey a weak linear superposition, called threshold-linear superposition. The output image signal or measurement from each system is shown to be the sum of outputs due to input binary images that result from thresholding the input gray-level image at all levels. These results are generalized to a vector space formulation, e.g. to any finite linear combination of simple morphological systems. Thus many such systems processing gray-level images are reduced to corresponding binary image processing systems, which are easier to analyze and implement. >

[1]  Petros Maragos,et al.  Morphological skeleton representation and coding of binary images , 1984, IEEE Trans. Acoust. Speech Signal Process..

[2]  Azriel Rosenfeld,et al.  A Note on the Use of Local MIN and MAX Operations in Digital Picture Processing , 1977 .

[3]  I. Herstein,et al.  Topics in algebra , 1964 .

[4]  J. Fitch,et al.  Median filtering by threshold decomposition , 1984 .

[5]  Raghu Krishnapuram,et al.  Morphologic edge detection in range images , 1991, Optics & Photonics.

[6]  Anastasios N. Venetsanopoulos,et al.  Multidimensional shape description and recognition using mathematical morphology , 1988, J. Intell. Robotic Syst..

[7]  G. Neudeck,et al.  VLSI Implementation of a fast rank order filtering algorithm , 1985, ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[8]  Frank Y. Shih,et al.  Threshold Decomposition of Gray-Scale Morphology into Binary Morphology , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[9]  Petros Maragos,et al.  Morphological filters-Part II: Their relations to median, order-statistic, and stack filters , 1987, IEEE Trans. Acoust. Speech Signal Process..

[10]  Thomas S. Huang,et al.  A generalization of median filtering using linear combinations of order statistics , 1983 .

[11]  Jean Serra,et al.  Image Analysis and Mathematical Morphology , 1983 .

[12]  J P Allebach,et al.  Optical median filtering using threshold decomposition. , 1987, Applied optics.

[13]  G. Matheron.  Éléments pour une théorie des milieux poreux , 1967 .

[14]  Lucas J. van Vliet,et al.  A nonlinear laplace operator as edge detector in noisy images , 1989, Comput. Vis. Graph. Image Process..

[15]  F. Meyer.  Iterative image transformations for an automatic screening of cervical smears. , 1979, The journal of histochemistry and cytochemistry : official journal of the Histochemistry Society.

[16]  Xinhua Zhuang,et al.  Image Analysis Using Mathematical Morphology , 1987, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[17]  Vartkes Goetcherian,et al.  From binary to grey tone image processing using fuzzy logic concepts , 1980, Pattern Recognit..

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

[19]  Petros Maragos,et al.  Morphological filters-Part I: Their set-theoretic analysis and relations to linear shift-invariant filters , 1987, IEEE Trans. Acoust. Speech Signal Process..

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

[21]  William T. Rhodes,et al.  Nonlinear Optical Image Filtering By Time-Sequential Threshold Decomposition , 1988 .

[22]  Azriel Rosenfeld,et al.  A Min-Max Medial Axis Transformation , 1981, IEEE Transactions on Pattern Analysis and Machine Intelligence.

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

[24]  Peter Edwin Miller.  An investigation of Boolean image neighborhood transformations , 1978 .

[25]  Edward J. Coyle,et al.  Stack filters , 1986, IEEE Trans. Acoust. Speech Signal Process..