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23
A Survey of Shape Analysis Techniques
 Pattern Recognition
, 1998
"... This paper provides a review of shape analysis methods. Shape analysis methods play an important role in systems for object recognition, matching, registration, and analysis. Researchin shape analysis has been motivated, in part, by studies of human visual form perception systems. ..."
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Cited by 200 (2 self)
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This paper provides a review of shape analysis methods. Shape analysis methods play an important role in systems for object recognition, matching, registration, and analysis. Researchin shape analysis has been motivated, in part, by studies of human visual form perception systems.
Hierarchic Voronoi Skeletons
, 1995
"... Robust and timeefficient skeletonization of a (planar) shape, which is connectivity preserving and based on Euclidean metrics, can be achieved by first regularizing the Voronoi diagram (VD) of a shape's boundary points, i.e., by removal of noisesensitive parts of the tessellation and then by estab ..."
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Cited by 123 (3 self)
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Robust and timeefficient skeletonization of a (planar) shape, which is connectivity preserving and based on Euclidean metrics, can be achieved by first regularizing the Voronoi diagram (VD) of a shape's boundary points, i.e., by removal of noisesensitive parts of the tessellation and then by establishing a hierarchic organization of skeleton constituents. Each component of the VD is attributed with a measure of prominence which exhibits the expected invariance under geometric transformations and noise. The second processing step, a hierarchic clustering of skeleton branches, leads to a multiresolution representation of the skeleton, termed skeleton pyramid.
Finding the Medial Axis of a Simple Polygon in Linear Time
 Discrete Comput. Geom
, 1995
"... We give a lineartime algorithm for computing the medial axis of a simple polygon P , This answers a longstanding open question  previously, the best deterministic algorithm ran in O(n log n) time. We decompose P into pseudonormal histograms, then influence histograms and xy monotone histograms. ..."
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Cited by 68 (4 self)
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We give a lineartime algorithm for computing the medial axis of a simple polygon P , This answers a longstanding open question  previously, the best deterministic algorithm ran in O(n log n) time. We decompose P into pseudonormal histograms, then influence histograms and xy monotone histograms. We can compute the medial axes for xy monotone histograms and merge to obtain the medial axis for P .
An Active Contour Model For Mapping The Cortex
 IEEE TRANS. ON MEDICAL IMAGING
, 1995
"... A new active contour model for finding and mapping the outer cortex in brain images is developed. A crosssection of the brain cortex is modeled as a ribbon, and a constant speed mapping of its spine is sought. A variational formulation, an associated force balance condition, and a numerical approac ..."
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Cited by 64 (13 self)
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A new active contour model for finding and mapping the outer cortex in brain images is developed. A crosssection of the brain cortex is modeled as a ribbon, and a constant speed mapping of its spine is sought. A variational formulation, an associated force balance condition, and a numerical approach are proposed to achieve this goal. The primary difference between this formulation and that of snakes is in the specification of the external force acting on the active contour. A study of the uniqueness and fidelity of solutions is made through convexity and frequency domain analyses, and a criterion for selection of the regularization coefficient is developed. Examples demonstrating the performance of this method on simulated and real data are provided.
Approximating Polygons and Subdivisions with MinimumLink Paths
, 1991
"... We study several variations on one basic approach to the task of simplifying a plane polygon or subdivision: Fatten the given object and construct an approximation inside the fattened region. We investigate fattening by convolving the segments or vertices with disks and attempt to approximate object ..."
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Cited by 60 (11 self)
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We study several variations on one basic approach to the task of simplifying a plane polygon or subdivision: Fatten the given object and construct an approximation inside the fattened region. We investigate fattening by convolving the segments or vertices with disks and attempt to approximate objects with the minimum number of line segments, or with near the minimum, by using efficient greedy algorithms. We give some variants that have linear or O(n log n) algorithms approximating polygonal chains of n segments. We also show that approximating subdivisions and approximating with chains with no selfintersections are NPhard.
Cut locus and medial axis in global shape interrogation and representation
 MIT Design Laboratory Memorandum 922 and MIT Sea Grant Report
, 1992
"... The cut locus CA of a closed set A in the Euclidean space E is defined as the closure of the set containing all points p which have at least two shortest paths to A. We present a theorem stating that the complement of the cut locus i.e. E\(CA∪A) is the maximal open set in (E\A) where the distance fu ..."
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Cited by 35 (1 self)
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The cut locus CA of a closed set A in the Euclidean space E is defined as the closure of the set containing all points p which have at least two shortest paths to A. We present a theorem stating that the complement of the cut locus i.e. E\(CA∪A) is the maximal open set in (E\A) where the distance function with respect to the set A is continuously differentiable. This theorem includes also the result that this distance function has a locally Lipschitz continuous gradient on (E\A). The medial axis of a solid D in E is defined as the union of all centers of all maximal discs which fit in this domain. We assume in the medial axis case that D is closed and that the boundary ∂D of D is a topological (not necessarily connected) hypersurface of E. Under these assumptions we prove that the medial axis of D equals that part of the cut locus of ∂D which is contained in D. We prove that the medial axis has the same homotopy type as its reference solid if the solid’s boundary surface fulfills certain regularity requirements. We also show that the medial axis with its related distance function can be be used to reconstruct its reference solid. We prove that the cut locus of a solid’s boundary is nowhere dense in the Euclidean space if the solid’s boundary meets certain regularity requirements. We show that the cut locus concept offers a common frame work lucidly unifying different concepts such as Voronoi diagrams, medial axes and equidistantial point sets. In this context we prove that the equidistantial set of two disjoint
SymmetryCurvature Duality
 Computer Vision, Graphics, and Image processing
, 1987
"... Several studies have shown the importance of two very different descriptors for shape: symmetry structure and curvature extrema. The main theorem proved by this paper, i.e. the SymmetryCurvature Duality Theorem, states that there is an important relationship between symmetry and curvature extrema: ..."
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Cited by 33 (2 self)
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Several studies have shown the importance of two very different descriptors for shape: symmetry structure and curvature extrema. The main theorem proved by this paper, i.e. the SymmetryCurvature Duality Theorem, states that there is an important relationship between symmetry and curvature extrema: If we say that curvature extrema are of two opposite types, either maxima or minima, then the theorem states: Any segment of a smooth planar curve, bounded by two consecutive curvature extrema of the same type, has a unique symmetry axis, and the axis terminates at the curvature extremum of the opposite type. The theorem is initially proved using Brady’s SLS as the symmetry analysis. However, the theorem is then generalized for any differential symmetry analysis. In order to prove the theorem, a number of results are established concerning the symmetry structure of Hoffman’s and Richards ’ codons. All results are obtained first by observing that any codon is a string of two, three, or four spirals, and then by reducing the theory of codons to that of spirals. We show that the SLS of a codon is either (1) an SAT, which is a
Dressed Human Modeling, Detection, and Parts Localization
, 2001
"... This dissertation presents an integrated human shape modeling, detection, and body part localization vision system. It demonstrates that the system can (1) detect pedestrians in various shapes, sizes, postures, partial occlusion, and clothing from a moving vehicle using stereo cameras; (2) locate th ..."
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Cited by 23 (1 self)
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This dissertation presents an integrated human shape modeling, detection, and body part localization vision system. It demonstrates that the system can (1) detect pedestrians in various shapes, sizes, postures, partial occlusion, and clothing from a moving vehicle using stereo cameras; (2) locate the joints of a person automatically and accurately without employing any markers around the joints.
ARTISAN  a shape retrieval system based on boundary family indexing
, 1996
"... Successful retrieval of images by shape feature is likely to be achieved only if we can mirror human similarity judgements. Following Biederman's theory of recognitionbycomponents, we postulate that shape analysis for retrieval should characterize an image by identifying properties such as colline ..."
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Cited by 23 (1 self)
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Successful retrieval of images by shape feature is likely to be achieved only if we can mirror human similarity judgements. Following Biederman's theory of recognitionbycomponents, we postulate that shape analysis for retrieval should characterize an image by identifying properties such as collinearity, shape similarity and proximity in component boundaries. Such properties can then be used to group image components into families, from which indexing features can be derived. We are currently applying these principles in the development of the ARTISAN shape retrieval system for the UK Patent Office. The trademark images, supplied in compressed bitmap format, are processed using standard edgeextraction techniques to derive a set of region boundaries, which are approximated as a sequence of straightline and circulararc segments. These are then grouped into families using criteria such as proximity and shape similarity. Shape features for retrieval are then extracted from the image a...
Analyzing Skewed Symmetries
 International Journal of Computer Vision
, 1994
"... Symmetry is pervasive in both manmade objects and nature. Since symmetries project to skew symmetries, finding axes of skew symmetry is an important vision task. This paper presents a linear time algorithm for finding the axes of skew symmetry, where the degree of symmetry is known. First, we prese ..."
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Cited by 17 (0 self)
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Symmetry is pervasive in both manmade objects and nature. Since symmetries project to skew symmetries, finding axes of skew symmetry is an important vision task. This paper presents a linear time algorithm for finding the axes of skew symmetry, where the degree of symmetry is known. First, we present a review and critique of current methods for finding the axes of skew symmetry. Next, we decompose the problem of finding skew symmetry into the subproblems of solving for the rotational parameter of a "shear symmetry " and recovering the shear parameter of a reflexive symmetry. Using this approach, the authors derive a direct, nonheuristic momentbased technique for finding the axes of skew symmetry. For skew symmetric figures with degree of symmetry less than five we obtain a closedform solution. The method does not rely on continuous contours but assumes there is no occlusion and requires knowing the contour's degree of symmetry. It is the first algorithm to find the axes of skew sy...