Showing papers by "Azriel Rosenfeld published in 2004"

Digital Geometry: Geometric Methods for Digital Picture Analysis

Abstract: Introduction. Grids and Digitization. Metrics. Adjacency Graphs. Incidence Pseudographs. Topology: Basics. Curves and Surfaces: Topology. Curves and Surfaces: Geometry. Straightness. Arc Length and Curvature. 3D Straightness and Planarity. Surface and Area Curvature. Hulls and Diagrams. Transformations. Morphological Operations. Deformations. Other Properties and Relations. Bibliography.

Digital geometry

Abstract: Digital geometry is the study of geometrical properties of subsets of digital images. If the digitization is sufficiently fine-grained, such properties can be regarded as approximations to the corresponding properties of the "real" sets that gave rise, by digitization, to the digital sets; but it is also important to define how the properties can be computed for the digital sets themselves. Questions of particular interest include how images and image subsets are digitized; how geometric properties are defined for digitized sets; the computational complexity of computing them--in particular, whether they can be computed using simple (e.g., local) operations; characterizing image operations that preserve them; and characterizing digital objects that could be the digitizations of real objects that have given geometric properties. Concepts that have been extensively studied include topological properties (connected components, boundaries); curves and surfaces; straightness, curvature, convexity, and elongatedness; distance, extent, length, area, surface area, volume, and moments; shape description, similarity, symmetry, and relative position; shape simplification and skeletonization.

Digital straightness: a review

Abstract: A digital arc is called 'straight' if it is the digitization of a straight line segment. Since the concept of digital straightness was introduced in the mid-1970s, dozens of papers on the subject have appeared; many characterizations of digital straight lines have been formulated, and many algorithms for determining whether a digital arc is straight have been defined. This paper reviews the literature on digital straightness and discusses its relationship to other concepts of geometry, the theory of words, and number theory.

On degrees of end nodes and cut nodes in fuzzy graphs

Abstract: The notion of strong arcs in a fuzzy graph was introduced by Bhutani and Rosenfeld in (1) and fuzzy end nodes in the subsequent paper (2) using the concept of strong arcs. In Mordeson and Yao (7), the notion of "degrees" for concepts fuzzified from graph theory were defined and studied. In this note, we discuss degrees for fuzzy end nodes and study further some properties of fuzzy end nodes and fuzzy cut nodes.

Sparse, variable-representation active contour models

Abstract: Active contours are a widely used class of models that locate object boundaries in an image by minimizing an energy function which depends on "internal" terms such as the length and curvature of the contour, and "external" terms which are functions of the image values on and near the contour. If we use the inverse rate of change of the image value as the external term, the energy is low when the contour coincides with a strong, short, smooth boundary in the image. It is well known that this basic active contour model has difficulties in detecting object boundaries that are initially far from the contour; in locating boundary shape details; and in avoiding local minima due to image noise. The first two difficulties can be overcome by varying the energy function during the minimization process, and we show in this paper that the third difficulty can be overcome by modifying the contour representation during the process.