Shape representation via harmonic embedding

Duci,; Yezzi,; Mitter,; Soatto,

doi:10.1109/iccv.2003.1238410

Cited by 19 publications

(13 citation statements)

References 28 publications

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“…These correspondences are often found by applying optimization techniques, particularly dynamic programming (e.g., [4], [23], [47]) or the fast marching method [22]. Various abstract shape spaces are proposed based, e.g., on conformal maps [48], harmonic embedding [17], or suitable parameterization of closed curves [31].…”

Section: Related Workmentioning

confidence: 99%

Shape Representation and Classification Using the Poisson Equation

Gorelick

Galun

Sharon

et al. 2006

IEEE Trans. Pattern Anal. Machine Intell.

219

176

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Abstract-We present a novel approach that allows us to reliably compute many useful properties of a silhouette. Our approach assigns, for every internal point of the silhouette, a value reflecting the mean time required for a random walk beginning at the point to hit the boundaries. This function can be computed by solving Poisson's equation, with the silhouette contours providing boundary conditions. We show how this function can be used to reliably extract various shape properties including part structure and rough skeleton, local orientation and aspect ratio of different parts, and convex and concave sections of the boundaries. In addition to this, we discuss properties of the solution and show how to efficiently compute this solution using multigrid algorithms. We demonstrate the utility of the extracted properties by using them for shape classification and retrieval.

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Section: Related Workmentioning

confidence: 99%

Shape Representation and Classification Using the Poisson Equation

Gorelick

Galun

Sharon

et al. 2006

IEEE Trans. Pattern Anal. Machine Intell.

219

176

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show abstract

“…Due to the geometry of the space of closed curves, there is no unique way to define the error vector field; its construction is a design choice when defining an observer for closed curves. Here, the method chosen is a Laplace-equation-based approach [44], [45], [46], whose error vector field induced flow is a diffeomorphism, which is easy to implement and fast to compute.…”

Section: The Error Vector Fieldmentioning

confidence: 99%

Geometric Observers for Dynamically Evolving Curves

Niethammer

Vela

Tannenbaum

2008

IEEE Trans. Pattern Anal. Mach. Intell.

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This paper proposes a deterministic observer design for visual tracking based on nonparametric implicit (level-set) curve descriptions. The observer is continuous discrete with continuous-time system dynamics and discrete-time measurements. Its state-space consists of an estimated curve position augmented by additional states (e.g., velocities) associated with every point on the estimated curve. Multiple simulation models are proposed for state prediction. Measurements are performed through standard static segmentation algorithms and optical-flow computations. Special emphasis is given to the geometric formulation of the overall dynamical system. The discrete-time measurements lead to the problem of geometric curve interpolation and the discrete-time filtering of quantities propagated along with the estimated curve. Interpolation and filtering are intimately linked to the correspondence problem between curves. Correspondences are established by a Laplace-equation approach. The proposed scheme is implemented completely implicitly (by Eulerian numerical solutions of transport equations) and thus naturally allows for topological changes and subpixel accuracy on the computational grid.

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“…The alignment of curves and matching of shapes is discussed in Ref. [4] based on local curvature information, and often produces good results. However, curvature, being a second derivative, is intrinsically susceptible to noise.…”

Section: Introductionmentioning

confidence: 99%

“…[3][4][5][6][7][8][9] Shape description defines an anatomical structure at several scales of observations. A comprehensive overview of shape representation with respect to application categories is given in Refs.…”

Section: Introductionmentioning

confidence: 99%

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Shape localization, quantification and correspondence using Region Matching Algorithm

Janan

Brady

2015

JBGC

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We propose a method for local, region-based matching of planar shapes, especially as those shapes that change over time. This is a problem fundamental to medical imaging, specifically the comparison over time of mammograms. The method is based on the non-emergence and non-enhancement of maxima, as well as the causality principle of integral invariant scale space. The core idea of our Region Matching Algorithm (RMA) is to divide a shape into a number of "salient" regions and then to compare all such regions for local similarity in order to quantitatively identify new growths or partial/complete occlusions. The algorithm has several advantages over commonly used methods for shape comparison of segmented regions. First, it provides improved key-point alignment for optimal shape correspondence. Second, it identifies localized changes such as new growths as well as complete/partial occlusion in corresponding regions by dividing the segmented region into sub-regions based upon the extrema that persist over a sufficient range of scales. Third, the algorithm does not depend upon the spatial locations of mammographic features and eliminates the need for registration to identify salient changes over time. Finally, the algorithm is fast to compute and requires no human intervention. We apply the method to temporal pairs of mammograms in order to detect potentially important differences between them.

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Shape representation via harmonic embedding

Abstract: We

Cited by 19 publications

References 28 publications

Shape Representation and Classification Using the Poisson Equation

Shape Representation and Classification Using the Poisson Equation

Geometric Observers for Dynamically Evolving Curves

Shape localization, quantification and correspondence using Region Matching Algorithm

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