Differential morphology and image processing Export

@article{citeulike:2289607, abstract = {Image processing via mathematical morphology has traditionally used geometry to intuitively understand morphological signal operators and set or lattice algebra to analyze them in the space domain. We provide a unified view and analytic tools for morphological image processing that is based on ideas from differential calculus and dynamical systems. This includes ideas on using partial differential or difference equations (PDEs) to model distance propagation or nonlinear multiscale processes in images. We briefly review some nonlinear difference equations that implement discrete distance transforms and relate them to numerical solutions of the eikonal equation of optics. We also review some nonlinear PDEs that model the evolution of multiscale morphological operators and use morphological derivatives. Among the new ideas presented, we develop some general 2-D max/min-sum difference equations that model the space dynamics of 2-D morphological systems (including the distance computations) and some nonlinear signal transforms, called slope transforms, that can analyze these systems in a transform domain in ways conceptually similar to the application of Fourier transforms to linear systems. Thus, distance transforms are shown to be bandpass slope filters. We view the analysis of the multiscale morphological PDEs and of the eikonal PDE solved via weighted distance transforms as a unified area in nonlinear image processing, which we call differential morphology, and briefly discuss its potential applications to image processing and computer vision}, author = {Maragos, P.}, booktitle = {Image Processing, IEEE Transactions on}, citeulike-article-id = {2289607}, citeulike-linkout-0 = {http://dx.doi.org/10.1109/83.503909}, citeulike-linkout-1 = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=503909}, doi = {10.1109/83.503909}, journal = {Image Processing, IEEE Transactions on}, keywords = {differential, distance, eikonal, grey-weighted, morphology, propagation, transform}, number = {6}, pages = {922--937}, posted-at = {2008-01-25 15:08:53}, priority = {5}, title = {Differential morphology and image processing}, url = {http://dx.doi.org/10.1109/83.503909}, volume = {5}, year = {1996} }

TY - JOUR ID - citeulike:2289607 L3 - citeulike-article-id:2289607 N2 - Image processing via mathematical morphology has traditionally used geometry to intuitively understand morphological signal operators and set or lattice algebra to analyze them in the space domain. We provide a unified view and analytic tools for morphological image processing that is based on ideas from differential calculus and dynamical systems. This includes ideas on using partial differential or difference equations (PDEs) to model distance propagation or nonlinear multiscale processes in images. We briefly review some nonlinear difference equations that implement discrete distance transforms and relate them to numerical solutions of the eikonal equation of optics. We also review some nonlinear PDEs that model the evolution of multiscale morphological operators and use morphological derivatives. Among the new ideas presented, we develop some general 2-D max/min-sum difference equations that model the space dynamics of 2-D morphological systems (including the distance computations) and some nonlinear signal transforms, called slope transforms, that can analyze these systems in a transform domain in ways conceptually similar to the application of Fourier transforms to linear systems. Thus, distance transforms are shown to be bandpass slope filters. We view the analysis of the multiscale morphological PDEs and of the eikonal PDE solved via weighted distance transforms as a unified area in nonlinear image processing, which we call differential morphology, and briefly discuss its potential applications to image processing and computer vision IS - 6 JF - Image Processing, IEEE Transactions on EP - 937 TI - Differential morphology and image processing VL - 5 T2 - Image Processing, IEEE Transactions on SP - 922 KW - differential KW - distance KW - eikonal KW - grey-weighted KW - morphology KW - propagation KW - transform AU - Maragos, P PY - 1996/// UR - http://dx.doi.org/10.1109/83.503909 ER -