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13
Shape from Texture and Contour by Weak Isotropy
 J. of Artificial Intelligence
, 1993
"... A unified framework for shape from texture and contour is proposed. It is based on the assumption that the surface markings are not systematically compressed, or formally, that they are weakly isotropic. The weak isotropy principle is based on analysis of the directional statistics of the projected ..."
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Cited by 26 (6 self)
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A unified framework for shape from texture and contour is proposed. It is based on the assumption that the surface markings are not systematically compressed, or formally, that they are weakly isotropic. The weak isotropy principle is based on analysis of the directional statistics of the projected surface markings. It builds on several previous theories, in particular by Witkin [25] and Kanatani [15]. It extends these theories in various ways, most notably to perspective projection. The theory also provides an exact solution to an estimation problem earlier solved approximately by Kanatani. The weak isotropy principle leads to a computationally efficient algorithm, WISP, for estimation of surface orientation. WISP uses simple image observables that are shown to be direct correlates of the surface orientation to compute an initial approximate estimate in a single step. In certain simple cases this first estimate is exact, and in experiments with natural images it is typically within 5...
Approximate symmetry detection for reverse engineering
 Proc. 6th ACM Symp. Solid Modeling and Applications
, 2001
"... The authors are developing an automated reverse engineering system for reconstructing the shape of simple mechanical parts. Brep models are created by fitting surfaces to point clouds obtained by scanning an object using a 3D laser scanner. The resulting models, although valid, are often not suitab ..."
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Cited by 19 (12 self)
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The authors are developing an automated reverse engineering system for reconstructing the shape of simple mechanical parts. Brep models are created by fitting surfaces to point clouds obtained by scanning an object using a 3D laser scanner. The resulting models, although valid, are often not suitable for purposes such as redesign because expected regularities and constraints are not present. This information is lost because each face of the model is determined independently. A global approach is required, in particular one that is capable of finding symmetries originally present. This paper describes a practical algorithm for finding global symmetries in suitable Brep models built from planes, spheres, cylinders, cones and tori. It has been implemented and used to determine approximate symmetries of models with up to about 200 vertices in reasonable time. The time performance of the algorithm in the worst case is bounded by O(n^3.5 log^4 n), and a justification is given that on common engineering objects it takes about O(n^2 log^4 n), making it a practical tool for use in a reverse engineering package. Details of the algorithm are given, along with some results from a number of illustrative test runs.
Discrete groups and visualization of threedimensional manifolds
 In Computer Graphics, Annual Conference Proceedings. ACM SIGGRAPH
, 1993
"... We describe a software implementation for interactive visualization of a wide class of discrete groups. In addition to familiar Euclidean space, these groups act on the curved geometries of hyperbolic and spherical space. We construct easily computable models of our geometric spaces based on project ..."
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Cited by 11 (1 self)
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We describe a software implementation for interactive visualization of a wide class of discrete groups. In addition to familiar Euclidean space, these groups act on the curved geometries of hyperbolic and spherical space. We construct easily computable models of our geometric spaces based on projective geometry; and establish algorithms for visualization of threedimensional manifolds based upon the close connection between discrete groups and manifolds. We describe an objectoriented implementation of these concepts, and several novel visualization applications. As a visualization tool, this software breaks new ground in two directions: interactive exploration of curved spaces, and of topological manifolds modeled on these spaces. It establishes a generalization of the application of projective geometry to computer graphics, and lays the groundwork for visualization of spaces of nonconstant curvature.
Approximate congruence detection of model features for reverse engineering. In: Proc. int. conf. shape modelling and applications
, 2003
"... Reverse engineering allows the geometric reconstruction of simple mechanical parts. However, the resulting models suffer from inaccuracies caused by errors in measurement and reconstruction so such models do not have the exact congruences, symmetries and other regularities the original designer inte ..."
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Cited by 9 (7 self)
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Reverse engineering allows the geometric reconstruction of simple mechanical parts. However, the resulting models suffer from inaccuracies caused by errors in measurement and reconstruction so such models do not have the exact congruences, symmetries and other regularities the original designer intended. We wish to impose such regularities in a beautification process. This paper discusses the particular problem of detecting approximate congruences between parts (e.g. a pair of handles) of a reconstructed Brep model, so that a subsequent step can enforce them exactly. A practical detection algorithm is given for models defined using planes, spheres, cylinders, cones and tori. Analysis of the algorithm and experimental results show that expected congruences are detected reasonably quickly.
Tools for Asymmetry Rectification in Shape Design
 Journal of Systems Engineering
, 1996
"... This paper considers the task of asymmetry rectification. We start by giving various reasons why the possession of symmetry may be beneficial for designed shapes, and mention how various construction methods may produce shapes which are less symmetric than desired. ..."
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Cited by 6 (3 self)
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This paper considers the task of asymmetry rectification. We start by giving various reasons why the possession of symmetry may be beneficial for designed shapes, and mention how various construction methods may produce shapes which are less symmetric than desired.
Constructing Regularity Feature Trees for Solid Models
 Proc. Geometric Modeling and Processing; LNCS
, 2006
"... Approximate geometric models, e.g. as created by reverse engineering, describe the approximate shape of an object, but do not record the underlying design intent. Automatically inferring geometric aspects of the design intent, represented by feature trees and geometric constraints, enhances the util ..."
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Cited by 6 (3 self)
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Approximate geometric models, e.g. as created by reverse engineering, describe the approximate shape of an object, but do not record the underlying design intent. Automatically inferring geometric aspects of the design intent, represented by feature trees and geometric constraints, enhances the utility of such models for downstream tasks. One approach to design intent detection in such models is to decompose them into regularity features. Geometric regularities such as symmetries may then be sought in each regularity feature, and subsequently be combined into a global, consistent description of the model’s geometric design intent. This paper describes a systematic approach for finding such regularity features based on recovering broken symmetries in the model. The output is a tree of regularity features for subsequent use in regularity detection and selection. Experimental results are given to demonstrate the operation and efficiency of the algorithm.
Detecting approximate symmetries of discrete point subsets
, 2008
"... Detecting approximate symmetries of parts of a model is important when attempting to determine the geometrical design intent of approximate boundaryrepresentation (Brep) solid models produced e.g. by reverse engineering systems. For example, such detected symmetries may be enforced exactly on the ..."
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Cited by 4 (2 self)
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Detecting approximate symmetries of parts of a model is important when attempting to determine the geometrical design intent of approximate boundaryrepresentation (Brep) solid models produced e.g. by reverse engineering systems. For example, such detected symmetries may be enforced exactly on the model to improve its shape, to simplify its analysis, or to constrain it during editing. We give an algorithm to detect local approximate symmetries in a discrete point set derived from a Brep model: the output comprises the model’s potential local symmetries at various automatically detected tolerance levels. Nontrivial symmetries of subsets of the point set are found as unambiguous permutation cycles, i.e. vertices of an approximately regular polygon or an antiprism, which are sufficiently separate from other points in the point set. The symmetries are detected using a rigorous, tolerancecontrolled, incremental approach, which expands symmetry seed sets by one point at a time. Our symmetry cycle detection approach only depends on interpoint distances. The algorithm takes time O(n 4) where n is the number of input points. Results produced by our algorithm are demonstrated using a variety of examples.
Detecting Design Intent in Approximate CAD Models Using Symmetry
"... Finding design intent embodied as highlevel geometric relations between a CAD model’s subparts facilitates various tasks such as model editing and analysis. This is especially important for boundaryrepresentation models arising from, e.g., reverse engineering or CAD data transfer. These lack expl ..."
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Cited by 4 (0 self)
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Finding design intent embodied as highlevel geometric relations between a CAD model’s subparts facilitates various tasks such as model editing and analysis. This is especially important for boundaryrepresentation models arising from, e.g., reverse engineering or CAD data transfer. These lack explicit information about design intent, and often the intended geometric relations are only approximately present. The novel solution to this problem presented is based on detecting approximate local incomplete symmetries, in a hierarchical decomposition of the model into simpler, more symmetric subparts. Design intent is detected as congruencies, symmetries and symmetric arrangements of the leafparts in this decomposition. All elementary 3D symmetry types and common symmetric arrangements are considered. They may be present only locally in subsets of the leafparts, and may also be incomplete, i.e. not all elements required for a symmetry need be present. Adaptive tolerance intervals are detected automatically for matching interpoint distances, enabling efficient, robust and consistent detection of approximate symmetries. Doing so avoids finding many spurious relations, reliably resolves ambiguities between relations, and reduces inconsistencies. Experiments show that detected relations reveal significant design intent.
In this issue … New Area Code … 1 Procedure and Operator Values … 1 Applications of String Invocation … 3 Curiosity or Problem? … 6 From the Library … 7 Dynamic Analysis of Icon Programs … 10 Subscription Renewal … 12 What’s Coming Up … 12 New Area Code
, 1995
"... area code, 602, also will work. After that, you’ll have to use 520 to reach us. A word of warning: Some automated switchboards only can dial area codes whose second digit is a 0 or 1. If you try to call us at 520 after March 19 and are unable to reach us, that may be the problem. Procedure and Opera ..."
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area code, 602, also will work. After that, you’ll have to use 520 to reach us. A word of warning: Some automated switchboards only can dial area codes whose second digit is a 0 or 1. If you try to call us at 520 after March 19 and are unable to reach us, that may be the problem. Procedure and Operator Values String invocation, described in the last issue of the Analyst, allows you to invoke procedures and operators using their string names. It’s also possible to get procedure and operator values from their string names. In past articles we’ve mentioned that procedures are Icon values, although it’s seldom necessary to use such values explicitly. For example, the
www.elsevier.com/locate/cad Detecting approximate symmetries of discrete point subsets ✩
, 2006
"... Detecting approximate symmetries of parts of a model is important when attempting to determine the geometrical design intent of approximate boundaryrepresentation (Brep) solid models produced e.g. by reverse engineering systems. For example, such detected symmetries may be enforced exactly on the ..."
Abstract
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Detecting approximate symmetries of parts of a model is important when attempting to determine the geometrical design intent of approximate boundaryrepresentation (Brep) solid models produced e.g. by reverse engineering systems. For example, such detected symmetries may be enforced exactly on the model to improve its shape, to simplify its analysis, or to constrain it during editing. We give an algorithm to detect local approximate symmetries in a discrete point set derived from a Brep model: the output comprises the model’s potential local symmetries at various automatically detected tolerance levels. Nontrivial symmetries of subsets of the point set are found as unambiguous permutation cycles, i.e. vertices of an approximately regular polygon or an antiprism, which are sufficiently separate from other points in the point set. The symmetries are detected using a rigorous, tolerancecontrolled, incremental approach, which expands symmetry seed sets by one point at a time. Our symmetry cycle detection approach only depends on interpoint distances. The algorithm takes time O(n 4) where n is the number of input points. Results produced by our algorithm are demonstrated using a variety of examples.