Journal ArticleDOI
Morphological representation of discrete and binary images
John Goutsias,Dan Schonfeld +1 more
TLDR
A unified theory is developed for the mathematical description of the morphological skeleton decomposition of discrete and binary images through repeated erosions and set transformations.Abstract:
A general theory for the morphological representation of discrete and binary images is presented. The basis of this theory relies on the generation of a set of nonoverlapping segments of an image via repeated erosions and set transformations, which in turn produces a decomposition that guarantees exact reconstruction. The relationship between the proposed representation and some existing shape analysis tools (e.g., discrete size transform, pattern spectrum, skeletons) is investigated, thus introducing the representation as the basis of a unified theory for geometrical image analysis. Particular cases of the general representation scheme are shown to yield a number of useful image decompositions which are directly related to various forms of morphological skeletons. The relationship between the representation and the various forms of morphological skeletons is studied. As a result of this study, a unified theory is developed for the mathematical description of the morphological skeleton decomposition of discrete and binary images. >read more
Citations
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Journal ArticleDOI
A survey of shape analysis techniques
TL;DR: This paper provides a review of shape analysis methods, which play an important role in systems for object recognition, matching, registration, and analysis.
Journal ArticleDOI
Nonlinear multiresolution signal decomposition schemes. II. Morphological wavelets
H.J.A.M. Heijmans,John Goutsias +1 more
TL;DR: A general theory for constructing linear as well as nonlinear pyramid decomposition schemes for signal analysis and synthesis and provides the foundation of a general approach to constructing nonlinear wavelet decompositions schemes and filter banks.
Journal ArticleDOI
Theoretical Foundations of Spatially-Variant Mathematical Morphology Part I: Binary Images
TL;DR: The ubiquity of SV morphological operators is demonstrated by providing an SV kernel representation of increasing operators by a generalization of Matheron's representation theorem of increasing and translation-invariant operators.
Journal ArticleDOI
Disconnected Skeleton: Shape at Its Absolute Scale
TL;DR: In this paper, a new skeletal representation along with a matching framework is presented to address the deformable shape recognition problem, which relies on stable properties of the shape instead of inaccurately measured secondary details.
Journal ArticleDOI
Skeleton-based morphological coding of binary images
Renato Kresch,David Malah +1 more
TL;DR: New properties of the discrete morphological skeleton representation of binary images are presented, along with a novel coding scheme for lossless binary image compression that is based on these properties and substantially improves the results obtained by previous skeleton-based coders, and performs better than classical coders.
References
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Book
Image Analysis and Mathematical Morphology
TL;DR: This invaluable reference helps readers assess and simplify problems and their essential requirements and complexities, giving them all the necessary data and methodology to master current theoretical developments and applications, as well as create new ones.
Journal ArticleDOI
Image Analysis Using Mathematical Morphology
TL;DR: The tutorial provided in this paper reviews both binary morphology and gray scale morphology, covering the operations of dilation, erosion, opening, and closing and their relations.
Journal ArticleDOI
Biological shape and visual science (part I)
TL;DR: A new geometry based on the primitive notions of a point and a growth is explored in this article, which leads to new properties and descriptions which are particularly suitable for many biological objects.
Journal ArticleDOI
Shape description using weighted symmetric axis features
Harry Blum,Roger N. Nagel +1 more
TL;DR: An application of symmetric axis geometry to shape classification and description, in which a sequential string of features is derived, and a weighting measure is developed which evaluates the importance of these shape descriptors.