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31
Procedural Modeling of Buildings
"... CGA shape, a novel shape grammar for the procedural modeling of CG architecture, produces building shells with high visual quality and geometric detail. It produces extensive architectural models for computer games and movies, at low cost. Context sensitive shape rules allow the user to specify inte ..."
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Cited by 130 (11 self)
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CGA shape, a novel shape grammar for the procedural modeling of CG architecture, produces building shells with high visual quality and geometric detail. It produces extensive architectural models for computer games and movies, at low cost. Context sensitive shape rules allow the user to specify interactions between the entities of the hierarchical shape descriptions. Selected examples demonstrate solutions to previously unsolved modeling problems, especially to consistent mass modeling with volumetric shapes of arbitrary orientation. CGA shape is shown to efficiently generate massive urban models with unprecedented level of detail, with the virtual rebuilding of the archaeological site of Pompeii as a case in point.
Partial intrinsic reflectional symmetry of 3d shapes
 ACM Transactions on Graphics (TOG
"... Figure 1: Given a closed 2manifold mesh, we compute a scalar field (a), which accentuates the axes of prominent, partial intrinsic reflectional symmetries. The top few (closed) Voronoi boundaries (b) between symmetric point pairs, as induced by the scalar field, can be imperfect. We develop an iter ..."
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Cited by 22 (3 self)
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Figure 1: Given a closed 2manifold mesh, we compute a scalar field (a), which accentuates the axes of prominent, partial intrinsic reflectional symmetries. The top few (closed) Voronoi boundaries (b) between symmetric point pairs, as induced by the scalar field, can be imperfect. We develop an iterative refinement scheme to extract the final set of intrinsic reflectional symmetry axes or IRSAs (c), which can be open curves. Incorporating symmetry cues offered by IRSAs into a conventional mesh segmentation scheme leads to highly semantic results (d). While many 3D objects exhibit various forms of global symmetries, prominent intrinsic symmetries which exist only on parts of an object are also well recognized. Such partial symmetries are often seen as more natural than a global one, even when the symmetric parts are under complex pose. We introduce an algorithm to extract partial intrinsic reflectional symmetries (PIRS) of a 3D shape. Given a closed 2manifold mesh, we develop a voting scheme to obtain an intrinsic reflectional symmetry axis (IRSA) transform, which is a scalar field over the mesh that accentuates prominent IRSAs of the shape. We then extract a set of explicit IRSA curves on the shape based on a refined measure of local reflectional symmetry support along a curve. The iterative refinement procedure combines IRSAinduced region growing and regionconstrained symmetry support refinement to improve accuracy and address potential issues arising from rotational symmetries in the shape. We show how the extracted IRSA curves can be incorporated into a conventional mesh segmentation scheme so that the implied symmetry cues can be utilized to obtain more meaningful results. We also demonstrate the use of IRSA curves for symmetrydriven part repair. 1
Epistemic and Ontic Quantum Realities
, 2005
"... Quantum theory has provoked intense discussions about its interpretation since its pioneer days, beginning with Bohr’s view of quantum theory as a theory of knowledge. We show that such an epistemic perspective can be consistently complemented by Einstein’s ontically oriented position. ..."
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Cited by 21 (11 self)
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Quantum theory has provoked intense discussions about its interpretation since its pioneer days, beginning with Bohr’s view of quantum theory as a theory of knowledge. We show that such an epistemic perspective can be consistently complemented by Einstein’s ontically oriented position.
Symmetry and Computability in Anonymous Networks: A Brief Survey
 Proc. 3rd Int. Conf. on Structural Information and Communication Complexity (SIROCCO'96), Carleton
, 1996
"... . Processors in anonymous networks are as identical to each other as possible and possess "little" knowledge about the network. Anonymous networks are very useful in theoretical studies for testing "true distributivity". In this paper we give a brief survey of results illuminating how symmetry influ ..."
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Cited by 18 (4 self)
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. Processors in anonymous networks are as identical to each other as possible and possess "little" knowledge about the network. Anonymous networks are very useful in theoretical studies for testing "true distributivity". In this paper we give a brief survey of results illuminating how symmetry influences computability in anonymous networks. Problems and issues considered include leader election, spanning tree construction, orientations, randomization, processor views, and computability problems on arbitrary as well as symmetric functions. Results mentioned are applicable to several topologies ranging from the rings, tori, hypercubes, and Cayley networks to arbitrary networks. We also propose several related open problems. 1980 Mathematics Subject Classification: 68Q99 CR Categories: C.2.1 Key Words and Phrases: Anonymous network, boolean function, cayley graphs, computability, gap theorem, hypercube, leader election, ring, symmetry. SCS Technical report: TR9618 1 Introduction Id...
Kolmogorov complexity, statistical regularization of inverse problems, and Birkhoff's formalization of beauty
 BAYESIAN INFERENCE FOR INVERSE PROBLEMS, PROC. SPIE
, 1998
"... Most practical applications of statistical methods are based on the implicit assumption that if an event has a very small probability, then it cannot occur. For example, the probability that a kettle placed on a cold stove would start boiling by itself is not 0, it is positive, but it is so small, t ..."
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Cited by 13 (9 self)
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Most practical applications of statistical methods are based on the implicit assumption that if an event has a very small probability, then it cannot occur. For example, the probability that a kettle placed on a cold stove would start boiling by itself is not 0, it is positive, but it is so small, that physicists conclude that such an event is simply impossible. This assumption is difficult to formalize in traditional probability theory, because this theory only describes measures on sets (e.g., for an inverse problem, on the set of all functions) and does not allow us to divide functions into "random" (possible) and nonrandom ("impossible") ones. This distinction was made possible by the idea of algorithmic randomness, introduced by Kolmogorov and his student MartinLof in the 1960s. We show that this idea can also be used for inverse problems. In particular, we prove that for every probability measure, the corresponding set of random functions is compact, and, therefore, the corresp...
On symmetry and multipleview geometry: Structure, pose, and calibration from a single image
 IJCV
, 2004
"... Abstract. In this paper, we provide a principled explanation of how knowledge in global 3D structural invariants, typically captured by a group action on a symmetric structure, can dramatically facilitate the task of reconstructing a 3D scene from one or more images. More importantly, since every ..."
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Cited by 12 (0 self)
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Abstract. In this paper, we provide a principled explanation of how knowledge in global 3D structural invariants, typically captured by a group action on a symmetric structure, can dramatically facilitate the task of reconstructing a 3D scene from one or more images. More importantly, since every symmetric structure admits a “canonical” coordinate frame with respect to which the group action can be naturally represented, the canonical pose between the viewer and this canonical frame can be recovered too, which explains why symmetric objects (e.g., buildings) provide us overwhelming clues to their orientation and position. We give the necessary and sufficient conditions in terms of the symmetry (group) admitted by a structure under which this pose can be uniquely determined. We also characterize, when such conditions are not satisfied, to what extent this pose can be recovered. We show how algorithms from conventional multipleview geometry, after properly modified and extended, can be directly applied to perform such recovery, from all “hidden images ” of one image of the symmetric structure. We also apply our results to a wide range of applications in computer vision and image processing such as camera selfcalibration, image segmentation and global orientation, large baseline feature matching, image rendering and photo editing, as well as visual illusions (caused by symmetry if incorrectly assumed).
Central tendencies, extreme points, and prototype enhancement effects in illdefined perceptual categorization
, 2001
"... ..."
An integrated architecture for engineering problem solving
 Ph.D. dissertation, Northwestern Univ. Evanston, IL [Online]. Available: http://wwwstaff.it.uts.edu.au/˜ypisan/research/publications/ thesis/index.html. AND SALUSTRI: COMPUTATIONAL INTELLIGENCE IN PRODUCT DESIGN ENGINEERING 777
, 1998
"... An Integrated Architecture for Engineering Problem Solving Yusuf Pisan Problem solving is an essential function of human cognition. To build intelligent systems that are capable of assisting engineers and tutoring students, we need to develop an information processing model that captures the skills ..."
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Cited by 5 (0 self)
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An Integrated Architecture for Engineering Problem Solving Yusuf Pisan Problem solving is an essential function of human cognition. To build intelligent systems that are capable of assisting engineers and tutoring students, we need to develop an information processing model that captures the skills used in engineering problem solving. This thesis describes the Integrated Problem Solving Architecture (IPSA) that combines qualitative, quantitative and diagrammatic reasoning skills to produce annotated solutions to engineering problems. We focus on representing expert knowledge, and examine how control knowledge provides the structure for using domain knowledge. To demonstrate our architecture for engineering problem solving, we present a Thermodynamics Problem Solver (TPS) that uses the IPSA architecture. TPS solves over 150 thermodynamics problems taken from the first four chapters of a common thermodynamics textbook and produces expertlike solutions. iv ACKNOWLEDGMENTS I would l...
Skewed Rotation Symmetry Group Detection
, 2009
"... We present a novel and effective algorithm for affinely skewed rotation symmetry group detection from realworld images. We define a complete skewed rotation symmetry detection problem as discovering five independent properties of a skewed rotation symmetry group: (1) the center of rotation; (2) th ..."
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Cited by 5 (1 self)
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We present a novel and effective algorithm for affinely skewed rotation symmetry group detection from realworld images. We define a complete skewed rotation symmetry detection problem as discovering five independent properties of a skewed rotation symmetry group: (1) the center of rotation; (2) the affine deformation; (3) the type of the symmetry group; (4) the cardinality of the symmetry group; and (5) the supporting region of the symmetry group in the image. We propose a friezeexpansion (FE) method that transforms rotation symmetry group detection into a simple, one dimensional translation symmetry detection problem. We define and construct a pair of rotational symmetry saliency maps, complemented by a local feature method. Frequency analysis, using Discrete Fourier Transform (DFT), is applied to the Friezeexpansion patterns (FEPs) to uncover the types (cyclic, dihedral and O(2)), the cardinalities and the corresponding supporting regions, concentric or otherwise, of multiple rotation symmetry groups in an image. The phase information of the FEP is used to rectify affinely skewed rotation symmetry groups. Our result advances the state of the art in symmetry detection by offering a unique combination of regionbased, featurebased and frequencybased approaches. Experimental results on 170 synthetic and natural images demonstrate superior performance of our rotation symmetry detection algorithm over existing methods.
Using Symmetry in Robust Model Fitting
 Pattern Recognition Letters
, 2003
"... The pattern recognition and computer vision communities often employ robust methods for model fitting. In particular, high breakdownpoint methods such as least median of squares (LMedS) and least trimmed squares (LTS) have often been used in situations where the data are contaminated with outliers. ..."
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Cited by 4 (3 self)
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The pattern recognition and computer vision communities often employ robust methods for model fitting. In particular, high breakdownpoint methods such as least median of squares (LMedS) and least trimmed squares (LTS) have often been used in situations where the data are contaminated with outliers. However, though the breakdown point of these methods can be as high as 50 % (they can be robust to up to 50 % contamination), they can break down at unexpectedly lower percentages when the outliers are clustered. In this paper, we demonstrate the fragility of LMedS and LTS and analyze the reasons that cause the fragility of these methods in the situation when a large percentage of clustered outliers exist in the data. We adapt the concept of ‘‘symmetry distance’ ’ to formulate an improved regression method, called the least trimmed symmetry distance (LTSD). Experimental results are presented to show that the LTSD performs better than LMedS and LTS under a large percentage of clustered outliers and large standard variance of inliers.