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Author

Azriel Rosenfeld

Other affiliations: Meiji University
Bio: Azriel Rosenfeld is an academic researcher from University of Maryland, College Park. The author has contributed to research in topics: Image processing & Feature detection (computer vision). The author has an hindex of 94, co-authored 595 publications receiving 49426 citations. Previous affiliations of Azriel Rosenfeld include Meiji University.


Papers
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Journal ArticleDOI
TL;DR: In this paper, prime semigroups and semirings are discussed in the American Mathematical Monthly: Vol. 74, No. 8, pp. 933-938.
Abstract: (1967). Prime Semigroups and Semirings. The American Mathematical Monthly: Vol. 74, No. 8, pp. 933-938.

1 citations

ReportDOI
01 Aug 1980
TL;DR: In this article, a method of linking compatible straight edges is presented and discussed, which is based on information about the geometrical configurations of the edges, the similarity of the gray levels on their object sides, and the similarity with the line joining their endpoints.
Abstract: : A method of linking compatible straight edges is presented and discussed. The linking is based on information about the geometrical configurations of the edges, the similarity of the gray levels on their object sides, and the similarity of their object sides with the line joining their endpoints. Three figures of merit are defined for evaluating pairs of segments for possible linking. Examples are shown of applying the method to high resolution aerial photographs. Results indicate that cultural features such as roads and buildings can be extracted and that a significant reduction in the complexity of the image description can be obtained. This approach should be especially useful for defining the degrees of compatibility of pairs of edges in a relaxation scheme for classifying linear feature segments.

1 citations

01 Jan 1992
TL;DR: A Generalized Image Point Correspondence (GIPC) algorithm, which enables the determination of 3-D motion parameters of an object in a configuration where both the object and the camera are moving, is discussed and its accuracy was determined.
Abstract: A Generalized Image Point Correspondence (GIPC) algorithm, which enables the determination of 3-D motion parameters of an object in a configuration where both the object and the camera are moving, is discussed. A detailed error analysis of this algorithm has been carried out. Furthermore, the algorithm was tested on both simulated and video-acquired data, and its accuracy was determined.

1 citations

Book ChapterDOI
01 Jan 2000
TL;DR: This chapter considers the topology of two-dimensional fuzzy digital pictures, and discusses topology-preserving deformations of these fuzzy pictures that generalize deformationsof two-valued digital pictures.
Abstract: This chapter considers the topology of two-dimensional fuzzy digital pictures, and discusses topology-preserving deformations of these fuzzy pictures that generalize deformations of two-valued digital pictures. It is shown that an arbitrary fuzzy picture can be transformed by this type of deformation into a coherent fuzzy picture. As another application, it is shown that the genus of a fuzzy picture is a linear combination of local property values.

1 citations

Book ChapterDOI
05 Mar 1990
TL;DR: This note briefly examines the process of repeatedly selecting maximal sets of nonoverlapping instances of a subgraph and shows that doing so “decimates” the graph in the sense that the number of nodes shrinks exponentially; but that unfortunately, the degree of the graph may grow exponentially.
Abstract: To avoid paradoxes in parallel graph rewriting, it is desirable to forbid overlapping instances of a subgraph to be rewritten simultaneously. The selection of maximal sets of nonoverlapping instances corresponds to the selection of maximal independent sets of nodes in a derived graph. This note briefly examines the process of repeatedly selecting such sets of nodes. It shows that doing so “decimates” the graph in the sense that the number of nodes shrinks exponentially; but that unfortunately, the degree of the graph may grow exponentially.

1 citations


Cited by
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Journal ArticleDOI
TL;DR: There is a natural uncertainty principle between detection and localization performance, which are the two main goals, and with this principle a single operator shape is derived which is optimal at any scale.
Abstract: This paper describes a computational approach to edge detection. The success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points. These goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution. We define detection and localization criteria for a class of edges, and present mathematical forms for these criteria as functionals on the operator impulse response. A third criterion is then added to ensure that the detector has only one response to a single edge. We use the criteria in numerical optimization to derive detectors for several common image features, including step edges. On specializing the analysis to step edges, we find that there is a natural uncertainty principle between detection and localization performance, which are the two main goals. With this principle we derive a single operator shape which is optimal at any scale. The optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a Gaussian-smoothed image. We extend this simple detector using operators of several widths to cope with different signal-to-noise ratios in the image. We present a general method, called feature synthesis, for the fine-to-coarse integration of information from operators at different scales. Finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge.

28,073 citations

Journal ArticleDOI
01 Nov 1973
TL;DR: These results indicate that the easily computable textural features based on gray-tone spatial dependancies probably have a general applicability for a wide variety of image-classification applications.
Abstract: Texture is one of the important characteristics used in identifying objects or regions of interest in an image, whether the image be a photomicrograph, an aerial photograph, or a satellite image. This paper describes some easily computable textural features based on gray-tone spatial dependancies, and illustrates their application in category-identification tasks of three different kinds of image data: photomicrographs of five kinds of sandstones, 1:20 000 panchromatic aerial photographs of eight land-use categories, and Earth Resources Technology Satellite (ERTS) multispecial imagery containing seven land-use categories. We use two kinds of decision rules: one for which the decision regions are convex polyhedra (a piecewise linear decision rule), and one for which the decision regions are rectangular parallelpipeds (a min-max decision rule). In each experiment the data set was divided into two parts, a training set and a test set. Test set identification accuracy is 89 percent for the photomicrographs, 82 percent for the aerial photographic imagery, and 83 percent for the satellite imagery. These results indicate that the easily computable textural features probably have a general applicability for a wide variety of image-classification applications.

20,442 citations

Journal ArticleDOI
TL;DR: In this paper, it is shown that the difference of information between the approximation of a signal at the resolutions 2/sup j+1/ and 2 /sup j/ (where j is an integer) can be extracted by decomposing this signal on a wavelet orthonormal basis of L/sup 2/(R/sup n/), the vector space of measurable, square-integrable n-dimensional functions.
Abstract: Multiresolution representations are effective for analyzing the information content of images. The properties of the operator which approximates a signal at a given resolution were studied. It is shown that the difference of information between the approximation of a signal at the resolutions 2/sup j+1/ and 2/sup j/ (where j is an integer) can be extracted by decomposing this signal on a wavelet orthonormal basis of L/sup 2/(R/sup n/), the vector space of measurable, square-integrable n-dimensional functions. In L/sup 2/(R), a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi (x). This decomposition defines an orthogonal multiresolution representation called a wavelet representation. It is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters. Wavelet representation lies between the spatial and Fourier domains. For images, the wavelet representation differentiates several spatial orientations. The application of this representation to data compression in image coding, texture discrimination and fractal analysis is discussed. >

20,028 citations

Journal ArticleDOI
TL;DR: The analogy between images and statistical mechanics systems is made and the analogous operation under the posterior distribution yields the maximum a posteriori (MAP) estimate of the image given the degraded observations, creating a highly parallel ``relaxation'' algorithm for MAP estimation.
Abstract: We make an analogy between images and statistical mechanics systems. Pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice-like physical system. The assignment of an energy function in the physical system determines its Gibbs distribution. Because of the Gibbs distribution, Markov random field (MRF) equivalence, this assignment also determines an MRF image model. The energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the MRF. For a range of degradation mechanisms, including blurring, nonlinear deformations, and multiplicative or additive noise, the posterior distribution is an MRF with a structure akin to the image model. By the analogy, the posterior distribution defines another (imaginary) physical system. Gradual temperature reduction in the physical system isolates low energy states (``annealing''), or what is the same thing, the most probable states under the Gibbs distribution. The analogous operation under the posterior distribution yields the maximum a posteriori (MAP) estimate of the image given the degraded observations. The result is a highly parallel ``relaxation'' algorithm for MAP estimation. We establish convergence properties of the algorithm and we experiment with some simple pictures, for which good restorations are obtained at low signal-to-noise ratios.

18,761 citations