Curve Evolution, Differential Morphology, and Distance Transforms Applied to Multiscale and Eikonal Problems

Maragos, Petros; Butt, Muhammad Akmal

doi:10.3233/fi-2000-411204

Cited by 30 publications

(6 citation statements)

References 65 publications

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“…Such connections have stimulated many interesting approaches in solving shape related problems. 35 The importance of Tari, Shah and Pien approach is that it is the first attempt to unify segmentation and local symmetry computation into a single formulation by exploiting the connection between (16) and the Mumford and Shah 37 segmentation functional (via its Ambrosio and Tortorelli 38 approximation). It naturally extends to shapes in arbitrary dimension.…”

Section: Comparison To Recent Decomposition Methods By MI and De-mentioning

confidence: 99%

Extracting Parts of 2d Shapes Using Local and Global Interactions Simultaneously

Tari

2009

Handbook of Pattern Recognition and Computer Vision

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Perception research provides strong evidence in favor of part based representation of shapes in human visual system. Despite considerable differences among different theories in terms of how part boundaries are found, there is substantial agreement on that the process depends on many local and global geometric factors. This poses an important challenge from the computational point of view. In the first part of the chapter, I present a novel decomposition method by taking both local and global interactions within the shape domain into account. At the top of the partitioning hierarchy, the shape gets split into two parts capturing, respectively, the gross structure and the peripheral structure. The gross structure may be conceived as the least deformable part of the shape which remains stable under visual transformations. The peripheral structure includes limbs, protrusions, and boundary texture. Such a separation is in accord with the behavior of the artists who start with a gross shape and enrich it with details. The method is particularly interesting from the computational point of view as it does not resort to any geometric notions (e.g. curvature, convexity) explicitly. In the second part of the chapter, I relate the new method to PDE based shape representation schemes.

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Section: Comparison To Recent Decomposition Methods By MI and De-mentioning

confidence: 99%

Extracting Parts of 2d Shapes Using Local and Global Interactions Simultaneously

Tari

2009

Handbook of Pattern Recognition and Computer Vision

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“…Indeed, our approach only depends on the p value and the weight function w. In Sect. 4, experiments show how the framework can be adapted to address image segmentation or data clustering.…”

Section: Eikonal Equation On Weighted Graphsmentioning

confidence: 99%

“…Solutions of the nonlinear eikonal equation have found numerous applications. One can quote for instance, geometric optics, image analysis or computer vision including shape from shading [1,2], median axis or skeleton extraction [3], topographic segmentation (watershed) [4] or geodesic distance computation on discrete and parametric surfaces [5][6][7][8][9]. The latter works consider both structured and unstructured meshes on cartesian or non-cartesian domains.…”

Section: Introductionmentioning

confidence: 99%

Adaptation of Eikonal Equation over Weighted Graph

Elmoataz

Lézoray

2009

Lecture Notes in Computer Science

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In this paper, an adaptation of the eikonal equation is proposed by considering the latter on weighted graphs of arbitrary structure. This novel approach is based on a family of discrete morphological local and nonlocal gradients expressed by partial difference equations (PdEs). Our formulation of the eikonal equation on weighted graphs generalizes local and nonlocal configurations in the context of image processing and extends this equation for the processing of any unorganized high dimensional discrete data that can be represented by a graph. Our approach leads to a unified formulation for image segmentation and high dimensional irregular data processing.

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“…The AT function of shape is related to a variety of morphological concepts. For instance, it is a weighted distance transform [11,12] with its level curves approximating curvature-dependent motion [16,10]. Thus, it enables extraction of local symmetries and skeletons directly from grayscale images; that is, it bridges image segmentation and shape description.…”

Section: Introductionmentioning

confidence: 99%

From a Modified Ambrosio-Tortorelli to a Randomized Part Hierarchy Tree

Genctav

2012

Lecture Notes in Computer Science

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We demonstrate the possibility of coding parts, features that are higher level than boundaries, using a modified AT field after augmenting the interaction term of the AT energy with a non-local term and weakening the separation into boundary/not-boundary phases. The iteratively extracted parts using the level curves with double point singularities are organized as a proper binary tree. Inconsistencies due to non-generic configurations for level curves as well as due to visual changes such as occlusion are successfully handled once the tree is endowed with a probabilistic structure. The work is a step in establishing the AT function as a bridge between low and high level visual processing.

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Curve Evolution, Differential Morphology, and Distance Transforms Applied to Multiscale and Eikonal Problems

Cited by 30 publications

References 65 publications

Extracting Parts of 2d Shapes Using Local and Global Interactions Simultaneously

Extracting Parts of 2d Shapes Using Local and Global Interactions Simultaneously

Adaptation of Eikonal Equation over Weighted Graph

From a Modified Ambrosio-Tortorelli to a Randomized Part Hierarchy Tree

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