{"title":"Discrete Half-Plane Morphology for Restricted Domains","authors":"T. Kanungo, R. Haralick","doi":"10.1201/9781482277234-9","DOIUrl":"https://doi.org/10.1201/9781482277234-9","url":null,"abstract":"","PeriodicalId":184840,"journal":{"name":"Mathematical Morphology in Image Processing","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115200115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Efficient Design Strategies for the Optimal Binary Digital Morphological Filter: Probabilities, Constraints, and Structuring-Element Libraries","authors":"E. Dougherty, R. Loce","doi":"10.1201/9781482277234-2","DOIUrl":"https://doi.org/10.1201/9781482277234-2","url":null,"abstract":"","PeriodicalId":184840,"journal":{"name":"Mathematical Morphology in Image Processing","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114340211","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Morphological Analysis Of Pavement Surface Condition","authors":"C. Bhagvati, D. Grivas, M. Skolnick","doi":"10.1201/9781482277234-4","DOIUrl":"https://doi.org/10.1201/9781482277234-4","url":null,"abstract":"","PeriodicalId":184840,"journal":{"name":"Mathematical Morphology in Image Processing","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128165379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Training Structuring Elements in Morphological Networks","authors":"Stephen S. Wilson","doi":"10.1201/9781482277234-1","DOIUrl":"https://doi.org/10.1201/9781482277234-1","url":null,"abstract":"","PeriodicalId":184840,"journal":{"name":"Mathematical Morphology in Image Processing","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114780100","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Anamorphoses and Function Lattices (Multivalued Morphology)","authors":"J. Serra","doi":"10.1201/9781482277234-13","DOIUrl":"https://doi.org/10.1201/9781482277234-13","url":null,"abstract":"","PeriodicalId":184840,"journal":{"name":"Mathematical Morphology in Image Processing","volume":"31 21","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120857322","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On a Distance Function Approach for Gray-Level Mathematical Morphology","authors":"F. Prêteux","doi":"10.1201/9781482277234-10","DOIUrl":"https://doi.org/10.1201/9781482277234-10","url":null,"abstract":"","PeriodicalId":184840,"journal":{"name":"Mathematical Morphology in Image Processing","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132159835","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Mathematical Morphology with Noncommutative Symmetry Groups","authors":"J. Roerdink","doi":"10.1201/9781482277234-7","DOIUrl":"https://doi.org/10.1201/9781482277234-7","url":null,"abstract":"Mathematical morphology as originally developed by Matheron and Serra is a theory of set mappings, modeling binary image transformations, that are invariant under the group of Euclidean translations. Because this framework turns out to be too restricted for many practical applications, various generalizations have been proposed. First, the translation group may be replaced by an arbitrary commutative group. Second, one may consider more general object spaces, such as the set of all convex subsets of the plane or the set of gray-level functions on the plane, requiring a formulation in terms of complete lattices. So far, symmetry properties have been incorporated by assuming that the allowed image transformations are invariant under a certain commutative group of automorphisms on the lattice. In this chapter we embark on another generalization of mathematical morphology by dropping the assumption that the invariance group is commutative. To this end we consider an arbitrary homogeneous space (the plane with the Euclidean translation group is one example, the sphere with the rotation group another), that is, a set 2e on which a transitive but not necessarily commutative transformation group f is defined. As our object space we then take the Boolean algebra 0P(2e) of all subsets of this homogeneous space. First we consider the case in which the transformation group is simply transitive or, equivalently, the basic set 2e is itself a group, so that we may study the Boolean algebra '2?(f). The general transitive case is subsequently treated by embedding the object space 0P(2e) into '2f(f), using the results for the simply transitive case and translating the results back to 0P(2e). Generalizations of dilations, erosions, openings, and","PeriodicalId":184840,"journal":{"name":"Mathematical Morphology in Image Processing","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126464520","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Graph Morphology in Image Analysis","authors":"Luc Vincent, Henk Heijmans","doi":"10.1201/9781482277234-6","DOIUrl":"https://doi.org/10.1201/9781482277234-6","url":null,"abstract":"Mathematical morphology can be considered as a set-based approach for the analysis of images [22, 23, 15]. One of its underlying ideas is to use so-called structuring elements to de ne neighborhoods of points. Recently it has been recognized that these ideas more generally apply to any space V which has the structure of a vector space, or at least a group [11]. In that case one can de ne a neighborhood of a point x 2 V as","PeriodicalId":184840,"journal":{"name":"Mathematical Morphology in Image Processing","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116477737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Morphological Approach to Segmentation: The Watershed Transformation","authors":"S. Beucher, F. Meyer","doi":"10.1201/9781482277234-12","DOIUrl":"https://doi.org/10.1201/9781482277234-12","url":null,"abstract":"Segmentation is one of the key problems in image processing. ln fact, one should say segmentations because there exist as many techniques as there are specifie situations. Among them, gray-tone images segmentation is very important and the relative techniques may be divided into two groups: the techniques based on contour detection and those involving region growing. Many authors have tried to define general schemes of contour detection using low-level tools [1,2]. Unfortunately, because they work at a very primitive level, a great number of algorithms must be used to emphasize their results. An original method of segmentation based on the use of watershed lines has been developed in the framework of mathematical morphology. This technique, which may appear to be close to the region-growing methods, leads in fact to a general methodology of segmentation and has been applied with success in many different situations. ln this chapter, the principles of morphological segmentation will be presented and illustrated by means of examples, starting from the simplest ones and introducing step by step more complex segmentation tools. ln Section II, we shal! review briefly various morphologie al tools which are used throughout this chapter. These basic transformations are useful for the description of sorne algorithms used in morphological segmentation. We shall not introduce the basic notions of mathematical morphology; the reader not farniliar with them is invited to refer to [3,4].","PeriodicalId":184840,"journal":{"name":"Mathematical Morphology in Image Processing","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115646402","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On Two Inverse Problems in Mathematical Morphology","authors":"M. Schmitt","doi":"10.1201/9781482277234-5","DOIUrl":"https://doi.org/10.1201/9781482277234-5","url":null,"abstract":"","PeriodicalId":184840,"journal":{"name":"Mathematical Morphology in Image Processing","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117148643","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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