Veinerization: a new shape description for flexible skeletonization

Deseilligny, Marc Pierrot; Stamon, Georges; Suen, Ching Y.

doi:10.1109/34.682180

Cited by 39 publications

(16 citation statements)

References 26 publications

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“…The map is obviously antisymmetric. One can demonstrate that the combinatorial map is connected, and that a bijection between the faces (ϕ-orbits) of the combinatorial map and the local minima of I exists [13]. Homotopic transformations can then be applied in order to simplify the combinatorial map, and to get rid of the undesired edges.…”

Section: Gray-tone Skeletonsmentioning

confidence: 98%

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Homotopic Transformations of Combinatorial Maps

Marchadier

Kropatsch

Hanbury

2003

Discrete Geometry for Computer Imagery

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Abstract. In this contribution, we propose the notion of homotopy for both combinatorial maps and weighted combinatorial maps. We also describe transformations that are homotopic in the defined sense. The usefulness of the concept introduced is illustrated using two applications. The first one consists in calculating a skeleton using homotopic transformations of weighted combinatorial maps. The result is a compact combinatorial map describing the structure of the skeleton which may be viewed as a "combinatorial map skeleton". The second application consists in run length encoding of all the regions described by a combinatorial map. Although these demonstrations are defined on combinatorial maps defined on a square grid, the major insights of the paper are independent of the embedding.

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Section: Gray-tone Skeletonsmentioning

confidence: 98%

“…The definition of homotopy of transformations on gray-level images has also been proposed [15,12], as well as on ordered sets [2]. Homotopy is an important concept, as it characterizes topological properties of skeletons, graytone skeletons and watersheds [15,12,13,14]. Combinatorial maps have been introduced as a code for planar graphs.…”

Section: Introductionmentioning

confidence: 99%

Homotopic Transformations of Combinatorial Maps

Marchadier

Kropatsch

Hanbury

2003

Discrete Geometry for Computer Imagery

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“…Shape is the geometrical information that remains when location, scale and rotational effects are filtered out from an object [11]. Shape representation and analysis has generated a rich array of approaches from simpler ones that use anatomical or mathematical landmarks, simpler shapes [12][13] and polygonalization [13] to more advanced ones that extend to obtaining numerical vectors from various transformations of the boundary. Such techniques include the Fourier transform [14][15][16][17], wavelet transform [18][19][20][21], moments of inertia [22] or extraction of self-similarity properties expressed by fractal dimension [23][24].…”

Section: Introductionmentioning

confidence: 99%

“…Shape characterization techniques can be utilized to represent the boundaries of region structures and have been primarily employed for 2D shape analysis [9,[13][14][20][21]. Unfortunately, most of these 2D methods do not generalize directly to 3D shape characterization and similarity assessment [10], while being also computationally expensive.…”

Section: Introductionmentioning

confidence: 99%

Fast and effective characterization for classification and similarity searches of 2D and 3D spatial region data

Kontos

Megalooikonomou

2005

Pattern Recognition

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We propose a method for characterizing spatial region data. The method efficiently constructs a kdimensional feature vector using concentric spheres in 3D (circles in 2D) radiating out of a region's center of mass. These signatures capture structural and internal volume properties. We evaluate our approach by performing experiments on classification and similarity searches, using artificial and real datasets. To generate artificial regions we introduce a region growth model. Similarity searches on artificial data demonstrate that our technique, although straightforward, compares favorably to mathematical morphology, while being two orders of magnitude faster. Experiments with real datasets show its effectiveness and general applicability.

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“…So there have been many attempts to get around this implausible phenomenon. Mainly, there has been the so-called pruning approach [8,25], which prunes the less important part of the medial axis transform, leaving only the essential part. Some have also tried to smooth the boundary of the domain so that the resulting medial axis transform becomes more simple, hopefully capturing only important features [13,17,24].…”

Section: Introductionmentioning

confidence: 99%

Hyperbolic Hausdorff Distance for Medial Axis Transform

Choi

Seidel

2001

Graphical Models

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Although the Hausdorff distance is a popular device to measure the differences between sets, it is not natural for some specific classes of sets, especially for the medial axis transform which is defined as the set of all pairs of the centers and the radii of the maximal balls contained in another set. In spite of its many advantages and possible applications, the medial axis transform has one great weakness, namely its instability under the Hausdorff distance when the boundary of the original set is perturbed. Though many attempts have been made for the resolution of this phenomenon, most of them are heuristic in nature and lack precise error analysis. In this paper, we show that this instability can be remedied by introducing a new metric called the hyperbolic Hausdorff distance, which is most natural for measuring the differences between medial axis transforms. Using the hyperbolic Hausdorff distance, we obtain error bounds, which make the operation of medial axis transform almost an isometry. By various examples, we also show that the bounds obtained are sharp. In doing so, we show that bounding both the Hausdorff distance between domains and the Hausdorff distance between their boundaries is necessary and sufficient for bounding the hyperbolic Hausdorff distance between their medial axis transforms. These results drastically improve the previous results and open a new way to practically control the Hausdorff distance error of the domains under its medial axis transform error, and vice versa. c 2001 Elsevier Science (USA)

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Veinerization: a new shape description for flexible skeletonization

Cited by 39 publications

References 26 publications

Homotopic Transformations of Combinatorial Maps

Homotopic Transformations of Combinatorial Maps

Fast and effective characterization for classification and similarity searches of 2D and 3D spatial region data

Hyperbolic Hausdorff Distance for Medial Axis Transform

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