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The same-object problem for polyhedral solids
Abstracts
of Papers Accepted
for Publication
PAPERS B-Spline Cwves and Surfaces Viewed as Digital Filters. ARDESHIR GOSHTA~BY AND FUHIJA CHENG. Department of Computer Science, University of Kentucky, Lexington, Kentucky 40506. BRSAN A. BARSKY. Computer Science Division-EECS, University of California Berkeley, Berkeley, California 94720. Received March 29, 1988; accepted October 7, 1988. In this paper we show that B-spline curves and surfaces can be viewed as digital filters. Viewing B-spline problems as digital filters allows one to predict some properties of the generated curves and surfaces. We find that even-order B-splines and odd-order B-splines behave differently when used in curve and surface interpolation. Even-order B-splines generate smoother curves and surfaces than do odd-order B-splines.
Aakrptive Multiscale Feature Extraction from Range Data. B. PARVIN AND G. MEDIONI. Institute of Robotics and Intelligent Systems, Department of Electrical Engineering, Powel Hall, 233, University of Southern California, Los Angeles, California 90089-0272. Received February 17, 1988; accepted October 7. 1988. In this paper, we present a method to extract meaningful features from range images which introduces some novel ideas: First, our primitives are a richer set than the usual one, as we not only extract high frequency events, which correspond to jump boundaries and sharp creases, but also low frequency events such as smooth ridges and ravines. These last features are generally discarded as they tend to hide in noise; however, they provide a coarse description of the shape, and we believe they may help in inferring volumetric descriptions. The method works at multiple scales to improve reliability, and we have designed a control strategy to automatically select the most appropriate mask size. We present a result on images of different levels of complexity from three different sensors.
Finite Topohqy as Applied to Image Analysis. V. A. KOVALEVSKY. Central Information Processing, Kurstrasse 33, 1086 Berlin, German Democratic 10, 1988; accepted September 7, 1988.
Institute of Cybernetics and Republic. Received August
The notion of a cellular complex which is well known in the topology is applied to describe the structure of images. It is shown that the topology of cellular complexes is the only possible topology of finite sets. Under this topology no contradictions or paradoxes arise when defining connected subsets and their boundaries. Ways of encoding images as cellular complexes are discussed. The process of image segmentation is considered as splitting (in the topological sense) a cellular complex into blocks of cells. The notion of a cell list is introduced as a precise and compact data structure for encoding segmented images. Some applications of this data structure to the image analysis are demonstrated.
The Same-Object Problem for Polyltedal York 14853 and McGill University, September 16. 1988.
So/i& Montreal,
MICHAEL Quebec,
KARASICK. Canada.
Cornell Received
University, Ithaca, New, March 8, 1988; revised
The problem of deciding if two representations describe the same object arises in many applications in solid modeling. Using constructive solid geometry, the best known algorithm for the problem requires time O(n4), where n bounds the number of surface/surface interactions of the symmetric set-difference of the two solids. By using a new canonical boundary representation for polyhedral solids, the 266 0734-189X/89
$3.00
Cop~nght ’ IYXY by Acadcmx Pres. Inc All rights of rcproductton ill any form rewncd
ABSTRACTS
OF PAPERS ACCEPTED
FOR PUBLICATION
267
same-object problem is solved for many different boundary representations in time U( F log F + D log D + V) and space O(F + D), where F, D, and V are the numbers of faces, directed edges, and vertices, respectively, in the two boundary representations. In addition, the problem of converting from a boundary representation to the canonical boundary representation is shown to have an Q( F log F) lower bound. A New
Method
for
Image
Electrical Engineering, September 28, 1988.
S. D. YANOWITZ AND A. M. BRUCKSTEIN. Faculty of Segmentation Technion, IIT, 32000 Haifa, Israel. Received February 4, 1988; revised
In applications involving visual inspection, it is often required to separate objects from background, in conditions of poor and nonuniform illumination. In such cases one has to rely on adaptive methods that learn the illumination from the given images and base the object/background decision on this information. We here present a new method for image segmentation via adaptive thresholding. The threshold surface is determined by interpolating the image grey levels at points where the gradient is high, indicating probable object edges. Several methods of data interpolation to levels given at scattered points in the image plane are discussed. One method is tested on several examples and the segmentation results are compared to previously proposed adaptive thresholding algorithms. Visual Potential: One Conuex Polygon. J. ANTHONY GUALTIER~ AND SAM BAUGHER. Center for Automation Research, University of Maryland, College Park, Maryland 20742. MICHAEL WERMAN. IMA, Vincent Hall, University of Minnesota, Minneapolis, Minnesota 55455. Received April 6, 1987; accepted October 7, 1988.
The
We examine the visual potential of a single convex polygon with n faces. The visual potential (also called the aspect graph) is a mathematical representation of the stable views of a polygon and the abrupt changes in stable views brought about by moving the viewpoint. Stable views, aspects, ace described by the ropological structure-incidence relations-of the visible vertices and faces which are projected onto the retina of a cyclopian eye. While the metrical structure may vary, the topological structure is invariant to most small changes in viewpoint. Abrupt changes in aspect, visuul events, correspond to the appearance and disappearance of vertices and faces. For a convex polygon visual events occur when the viewpoint crosses any line containing a face of the polygon. These lines partition the space around the object into regions. All viewpoints within a region see the same aspect. Aspects and visual events correspond respectively to the nodes and edges of a graph that represents the visual potential. A given visual potential describes a class of object instances which have the same shape or surface topology. When metrical attributes such as scale, length, and angle are added to the class description a particular instance of the object class is realized. We examine the local and global structure of the visual potential and prove that a cylindrical chain link fence can serve as its underlying manifold. In addition we obtain an optimal algorithm, O(n), for finding the maxima/ aspects, a set of aspects which encode the entire visual potential, and an 0(n2) algorithm for generating the entire visual potential from these maximal aspects. We also give bounds on the number of isomorphism classes (i.e., number of shapes) for convex polygons with a fixed number of faces. We discuss realizability of visual potentials, relationship to other representations, extension to three dimensions, and an extension for a class of non-convex polygons. Comparison
at High
Spatial
Frequencies
of Two-Pass
and One-Pass
Geometric
Transfomtation
Algorithms.
DONALD FRASER. Department of Electrical Engineering, University of New South Wales, Australian Defence Force Academy, Canberra, ACT, Australia. Received March 10, 1987; revised September 28, 1988. Two-pass image geometric transformation algorithms, in which an image is resampled first in one dimension, forming an intermediate image, then in the resulting orthogonal dimension, have many computational advantages over traditional, one-pass algorithms. For example, interpolation and antialiasing are easier to implement, being l-dimensional operations; computer memory requirements are greatly reduced, with access to image data in external memory regularized; while pipelined parallel computation is greatly simplified. An apparent drawback of the two-pass algorithm which has tended to limit its universal adoption is a reported corruption at high spatial frequencies due to apparent undersampling, in certain cases, in the necessary intermediate image.
of Papers Accepted
for Publication
PAPERS B-Spline Cwves and Surfaces Viewed as Digital Filters. ARDESHIR GOSHTA~BY AND FUHIJA CHENG. Department of Computer Science, University of Kentucky, Lexington, Kentucky 40506. BRSAN A. BARSKY. Computer Science Division-EECS, University of California Berkeley, Berkeley, California 94720. Received March 29, 1988; accepted October 7, 1988. In this paper we show that B-spline curves and surfaces can be viewed as digital filters. Viewing B-spline problems as digital filters allows one to predict some properties of the generated curves and surfaces. We find that even-order B-splines and odd-order B-splines behave differently when used in curve and surface interpolation. Even-order B-splines generate smoother curves and surfaces than do odd-order B-splines.
Aakrptive Multiscale Feature Extraction from Range Data. B. PARVIN AND G. MEDIONI. Institute of Robotics and Intelligent Systems, Department of Electrical Engineering, Powel Hall, 233, University of Southern California, Los Angeles, California 90089-0272. Received February 17, 1988; accepted October 7. 1988. In this paper, we present a method to extract meaningful features from range images which introduces some novel ideas: First, our primitives are a richer set than the usual one, as we not only extract high frequency events, which correspond to jump boundaries and sharp creases, but also low frequency events such as smooth ridges and ravines. These last features are generally discarded as they tend to hide in noise; however, they provide a coarse description of the shape, and we believe they may help in inferring volumetric descriptions. The method works at multiple scales to improve reliability, and we have designed a control strategy to automatically select the most appropriate mask size. We present a result on images of different levels of complexity from three different sensors.
Finite Topohqy as Applied to Image Analysis. V. A. KOVALEVSKY. Central Information Processing, Kurstrasse 33, 1086 Berlin, German Democratic 10, 1988; accepted September 7, 1988.
Institute of Cybernetics and Republic. Received August
The notion of a cellular complex which is well known in the topology is applied to describe the structure of images. It is shown that the topology of cellular complexes is the only possible topology of finite sets. Under this topology no contradictions or paradoxes arise when defining connected subsets and their boundaries. Ways of encoding images as cellular complexes are discussed. The process of image segmentation is considered as splitting (in the topological sense) a cellular complex into blocks of cells. The notion of a cell list is introduced as a precise and compact data structure for encoding segmented images. Some applications of this data structure to the image analysis are demonstrated.
The Same-Object Problem for Polyltedal York 14853 and McGill University, September 16. 1988.
So/i& Montreal,
MICHAEL Quebec,
KARASICK. Canada.
Cornell Received
University, Ithaca, New, March 8, 1988; revised
The problem of deciding if two representations describe the same object arises in many applications in solid modeling. Using constructive solid geometry, the best known algorithm for the problem requires time O(n4), where n bounds the number of surface/surface interactions of the symmetric set-difference of the two solids. By using a new canonical boundary representation for polyhedral solids, the 266 0734-189X/89
$3.00
Cop~nght ’ IYXY by Acadcmx Pres. Inc All rights of rcproductton ill any form rewncd
ABSTRACTS
OF PAPERS ACCEPTED
FOR PUBLICATION
267
same-object problem is solved for many different boundary representations in time U( F log F + D log D + V) and space O(F + D), where F, D, and V are the numbers of faces, directed edges, and vertices, respectively, in the two boundary representations. In addition, the problem of converting from a boundary representation to the canonical boundary representation is shown to have an Q( F log F) lower bound. A New
Method
for
Image
Electrical Engineering, September 28, 1988.
S. D. YANOWITZ AND A. M. BRUCKSTEIN. Faculty of Segmentation Technion, IIT, 32000 Haifa, Israel. Received February 4, 1988; revised
In applications involving visual inspection, it is often required to separate objects from background, in conditions of poor and nonuniform illumination. In such cases one has to rely on adaptive methods that learn the illumination from the given images and base the object/background decision on this information. We here present a new method for image segmentation via adaptive thresholding. The threshold surface is determined by interpolating the image grey levels at points where the gradient is high, indicating probable object edges. Several methods of data interpolation to levels given at scattered points in the image plane are discussed. One method is tested on several examples and the segmentation results are compared to previously proposed adaptive thresholding algorithms. Visual Potential: One Conuex Polygon. J. ANTHONY GUALTIER~ AND SAM BAUGHER. Center for Automation Research, University of Maryland, College Park, Maryland 20742. MICHAEL WERMAN. IMA, Vincent Hall, University of Minnesota, Minneapolis, Minnesota 55455. Received April 6, 1987; accepted October 7, 1988.
The
We examine the visual potential of a single convex polygon with n faces. The visual potential (also called the aspect graph) is a mathematical representation of the stable views of a polygon and the abrupt changes in stable views brought about by moving the viewpoint. Stable views, aspects, ace described by the ropological structure-incidence relations-of the visible vertices and faces which are projected onto the retina of a cyclopian eye. While the metrical structure may vary, the topological structure is invariant to most small changes in viewpoint. Abrupt changes in aspect, visuul events, correspond to the appearance and disappearance of vertices and faces. For a convex polygon visual events occur when the viewpoint crosses any line containing a face of the polygon. These lines partition the space around the object into regions. All viewpoints within a region see the same aspect. Aspects and visual events correspond respectively to the nodes and edges of a graph that represents the visual potential. A given visual potential describes a class of object instances which have the same shape or surface topology. When metrical attributes such as scale, length, and angle are added to the class description a particular instance of the object class is realized. We examine the local and global structure of the visual potential and prove that a cylindrical chain link fence can serve as its underlying manifold. In addition we obtain an optimal algorithm, O(n), for finding the maxima/ aspects, a set of aspects which encode the entire visual potential, and an 0(n2) algorithm for generating the entire visual potential from these maximal aspects. We also give bounds on the number of isomorphism classes (i.e., number of shapes) for convex polygons with a fixed number of faces. We discuss realizability of visual potentials, relationship to other representations, extension to three dimensions, and an extension for a class of non-convex polygons. Comparison
at High
Spatial
Frequencies
of Two-Pass
and One-Pass
Geometric
Transfomtation
Algorithms.
DONALD FRASER. Department of Electrical Engineering, University of New South Wales, Australian Defence Force Academy, Canberra, ACT, Australia. Received March 10, 1987; revised September 28, 1988. Two-pass image geometric transformation algorithms, in which an image is resampled first in one dimension, forming an intermediate image, then in the resulting orthogonal dimension, have many computational advantages over traditional, one-pass algorithms. For example, interpolation and antialiasing are easier to implement, being l-dimensional operations; computer memory requirements are greatly reduced, with access to image data in external memory regularized; while pipelined parallel computation is greatly simplified. An apparent drawback of the two-pass algorithm which has tended to limit its universal adoption is a reported corruption at high spatial frequencies due to apparent undersampling, in certain cases, in the necessary intermediate image.