1989 |
Petros Maragos A Representation Theory for Morphological Image and Signal Processing Journal Article IEEE Trans. on Pattern Analysis and Machine Intelligence, 11 (6), pp. 586–599, 1989, ISSN: 01628828. Abstract | BibTeX | Links: [PDF] [PDF] @article{86c, title = {A Representation Theory for Morphological Image and Signal Processing}, author = {Petros Maragos}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=24793 http://robotics.ntua.gr/wp-content/uploads/sites/2/Maragos_RepresentationTheory_ieeetPAMI89.pdf}, doi = {10.1109/34.24793}, issn = {01628828}, year = {1989}, date = {1989-06-01}, journal = {IEEE Trans. on Pattern Analysis and Machine Intelligence}, volume = {11}, number = {6}, pages = {586--599}, abstract = {A unifying theory for many concepts and operations encountered in or related to morphological image and signal analysis is presented. The unification requires a set-theoretic methodology, where signals are modeled as sets, systems (signal transformations) are viewed as set mappings, and translational-invariant systems are uniquely characterized by special collections of input signals. This approach leads to a general representation theory, in which any translation-invariant, increasing, upper semicontinuous system can be presented exactly as a minimal nonlinear superposition of morphological erosions or dilations. The theory is used to analyze some special cases of image/signal analysis systems, such as morphological filters, median and order-statistic filters, linear filters, and shape recognition transforms. Although the developed theory is algebraic, its prototype operations are well suited for shape analysis; hence, the results also apply to systems that extract information about the geometrical structure of signals}, keywords = {}, pubstate = {published}, tppubtype = {article} } A unifying theory for many concepts and operations encountered in or related to morphological image and signal analysis is presented. The unification requires a set-theoretic methodology, where signals are modeled as sets, systems (signal transformations) are viewed as set mappings, and translational-invariant systems are uniquely characterized by special collections of input signals. This approach leads to a general representation theory, in which any translation-invariant, increasing, upper semicontinuous system can be presented exactly as a minimal nonlinear superposition of morphological erosions or dilations. The theory is used to analyze some special cases of image/signal analysis systems, such as morphological filters, median and order-statistic filters, linear filters, and shape recognition transforms. Although the developed theory is algebraic, its prototype operations are well suited for shape analysis; hence, the results also apply to systems that extract information about the geometrical structure of signals |
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