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A.: Optimable Separable Algorithms to compute the Reverse Euclidean Distance Transformation and Discrete Medial Axis in Arbitrary Dimension.
 IEEE Trans. on PAMI
, 2007
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Visual hull construction using adaptive sampling
 IEEE Workshops Appl. Comput. Vision
, 2005
"... Volumetric visual hulls have become very popular in many computer vision applications including human body pose estimation and virtualized reality. In these applications, the visual hull is used to approximate the 3D geometry of an object. Existing volumetric visual hull construction techniques, ..."
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Volumetric visual hulls have become very popular in many computer vision applications including human body pose estimation and virtualized reality. In these applications, the visual hull is used to approximate the 3D geometry of an object. Existing volumetric visual hull construction techniques, however, produce a 3color volume data that merely serves as a bounding volume. In other words it lacks an accurate surface representation. Polygonization can produce satisfactory results only at high resolutions. In this study we extend the binary visual hull to an implicit surface in order to capture the geometry of the visual hull itself. In particular, we introduce an octreebased visual hull specific adaptive sampling algorithm to obtain a volumetric representation that provides accuracy proportional to the level of detail. Moreover, we propose a method to process the resulting octree to extract a crackfree polygonal visual hull surface. Experimental results illustrate the performance of the algorithm. 1.
dDimensional reverse Euclidean distance transformation and Euclidean medial axis extraction in optimal time
 in DGCI 2003
, 2003
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Cited by 8 (1 self)
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© 2004 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted
Weighted distance transforms generalized to modules and their computation on point lattices.
 Centre for Image Analysis, Uppsala University,
, 2006
"... Abstract This paper presents the generalization of weighted distances to modules and their computation through the chamfer algorithm on general point lattices. The first part is dedicated to formalization of definitions and properties (distance, metric, norm) of weighted distances on modules. It re ..."
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Abstract This paper presents the generalization of weighted distances to modules and their computation through the chamfer algorithm on general point lattices. The first part is dedicated to formalization of definitions and properties (distance, metric, norm) of weighted distances on modules. It resumes tools found in literature to express the weighted distance of any point of a module and to compute optimal weights in the general case to get rotation invariant distances. The second part of this paper proves that, for any point lattice, the sequential twoscan chamfer algorithm produces correct distance maps. Finally, the definitions and computation of weighted distances are applied to the facecentered cubic (FCC) and bodycentered cubic (BCC) grids.
Lookup tables for medial axis on squared Euclidean distance transform, in:
 Proceedings of 11th Conference on Discrete Geometry for Computer Imagery,
, 2003
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The "dead reckoning" signed distance transform
 COMPUTER VISION AND IMAGE UNDERSTANDING 95 (2004) 317–333
, 2004
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Finding a Minimum Medial Axis of a Discrete Shape is NPhard
, 2008
"... The medial axis is a classical representation of digital objects widely used in many applications. However, such a set of balls may not be optimal: subsets of the medial axis may exist without changing the reversivility of the input shape representation. In this article, we first prove that finding ..."
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The medial axis is a classical representation of digital objects widely used in many applications. However, such a set of balls may not be optimal: subsets of the medial axis may exist without changing the reversivility of the input shape representation. In this article, we first prove that finding a minimum medial axis is an NPhard problem for the Euclidean distance. Then, we compare two algorithms which compute an approximation of the minimum medial axis, one of them providing bounded approximation results.
Appearance Radii in Medial Axis Test Mask for Small Planar Chamfer Norms
"... Abstract. The test mask TM is the minimum neighbourhood sufficient to extract the medial axis of any discrete shape, for a given chamfer distance mask M. We propose an arithmetical framework to study TM in the case of chamfer norms. We characterize TM for 3×3 and 5×5 chamfer norm masks, and we give ..."
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Abstract. The test mask TM is the minimum neighbourhood sufficient to extract the medial axis of any discrete shape, for a given chamfer distance mask M. We propose an arithmetical framework to study TM in the case of chamfer norms. We characterize TM for 3×3 and 5×5 chamfer norm masks, and we give an algorithm to compute the appearance radius of the vector (2, 1) in TM.
The Frobenius Problem in a Free Monoid
, 2008
"... Given positive integers c1, c2,..., ck with gcd(c1, c2,..., ck) = 1, the Frobenius problem (FP) is to compute the largest integer g(c1, c2,..., ck) that cannot be written as a nonnegative integer linear combination of c1, c2,..., ck. The Frobenius problem in a free monoid (FPFM) is a noncommu ..."
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Given positive integers c1, c2,..., ck with gcd(c1, c2,..., ck) = 1, the Frobenius problem (FP) is to compute the largest integer g(c1, c2,..., ck) that cannot be written as a nonnegative integer linear combination of c1, c2,..., ck. The Frobenius problem in a free monoid (FPFM) is a noncommutative generalization of the Frobenius problem. Given words x1, x2,..., xk such that there are only finitely many words that cannot be written as concatenations of words in {x1, x2,..., xk}, the FPFM is to find the longest such words. Unlike the FP, where the upper bound g(c1, c2,..., ck) ≤ max1≤i≤k c2i is quadratic, the upper bound on the length of the longest words in the FPFM can be exponential in certain measures and some of the exponential upper bounds are tight. For the 2FPFM, where the given words
Farey Sequences and the Planar Euclidean Medial Axis Test Mask
"... Abstract. The Euclidean test mask T (r) is the minimum neighbourhood sufficient to detect the Euclidean Medial Axis of any discrete shape whose inner radius does not exceed r. We establish a link between T (r) and the wellknown Farey sequences, which allows us to propose two new algorithms. The fi ..."
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Abstract. The Euclidean test mask T (r) is the minimum neighbourhood sufficient to detect the Euclidean Medial Axis of any discrete shape whose inner radius does not exceed r. We establish a link between T (r) and the wellknown Farey sequences, which allows us to propose two new algorithms. The first one computes T (r) in time O(r 4 ) and space O(r 2 ). The second one computes for any vector − → v the smallest r for which − → v ∈ T (r), in time O(r 3 ) and constant space.