Shape matching: similarity measures and algorithms

Veltkamp, Remco C.

doi:10.1109/sma.2001.923389

Cited by 281 publications

(207 citation statements)

References 54 publications

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“…In terms of distance computation cost, the AAD has the lowest cost due to its small feature vector size. [Tangelder03b], and our own set of models (about 300). Note also that the black faces (e.g., the model of vase in Figure 9a, rank 8) are due to "back-facing" polygons having flipped normal vectors.…”

Section: Comparison With the Other Methodsmentioning

confidence: 99%

Shape-similarity search of 3D models by using enhanced shape functions

Ohbuchi¹,

Minamitani²,

Takei³

2005

IJCAT

138

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Section: Comparison With the Other Methodsmentioning

confidence: 99%

Shape-similarity search of 3D models by using enhanced shape functions

Ohbuchi¹,

Minamitani²,

Takei³

2005

IJCAT

138

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“…Numerous measures have been proposed that can be used to express the difference (or similarity) in shape between two surfaces; most notably in the area of image retrieval [7][8][9] and shape retrieval [10,11]. However, most of these measures, such as the commonly used Hausdorff distance, only express similarity at a global level.…”

Section: Comparative Visualization Of 3d Surfacesmentioning

confidence: 99%

Image-based rendering of intersecting surfaces for dynamic comparative visualization

et al. 2010

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Nested or intersecting surfaces are proven techniques for visualizing shape differences between static 3D objects (Weigle and Taylor II, IEEE Visualization, Proceedings, pp. 503-510, 2005). In this paper we present an imagebased formulation for these techniques that extends their use to dynamic scenarios, in which surfaces can be manipulated or even deformed interactively. The formulation is based on our new layered rendering pipeline, a generic image-based approach for rendering nested surfaces based on depth peeling and deferred shading.We use layered rendering to enhance the intersecting surfaces visualization. In addition to enabling interactive performance, our enhancements address several limitations of the original technique. Contours remove ambiguity regard- ing the shape of intersections. Local distances between the surfaces can be visualized at any point using either depth fogging or distance fields: Depth fogging is used as a cue for the distance between two surfaces in the viewing direction, whereas closest-point distance measures are visualized interactively by evaluating one surface's distance field on the other surface. Furthermore, we use these measures to define a three-way surface segmentation, which visualizes regions of growth, shrinkage, and no change of a test surface compared with a reference surface.Finally, we demonstrate an application of our technique in the visualization of statistical shape models. We evaluate our technique based on feedback provided by medical image analysis researchers, who are experts in working with such models.

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“…We will focus on methods from the field of computational geometry. Excellent surveys can be found in [AG96] and [Vel01]. There are many variants of this problem, depending on the nature of the inputs, the allowable group of aligning transformations, and the distance function employed.…”

Section: Introductionmentioning

confidence: 99%

Improved Approximation Bounds for Planar Point Pattern Matching

Cho

Mount

2007

Algorithmica

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Abstract. We consider the well known problem of matching two planar point sets under rigid transformations so as to minimize the directed Hausdorff distance. This is a well studied problem in computational geometry. Goodrich, Mitchell, and Orletsky [GMO94] presented a very simple approximation algorithm for this problem, which computes transformations based on aligning pairs of points. They showed that their algorithm achieves an approximation ratio of 4. We consider a minor modification to their algorithm, which is based on aligning midpoints rather than endpoints. We show that this algorithm achieves an approximation ratio not greater than 3.13. Our analysis is sensitive to the ratio between the diameter of the pattern set and the Hausdorff distance, and we show that the approximation ratio approaches 3 in the limit. Finally, we provide lower bounds that show that our approximation bounds are nearly tight.

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Shape matching: similarity measures and algorithms

Cited by 281 publications

References 54 publications

Shape-similarity search of 3D models by using enhanced shape functions

Shape-similarity search of 3D models by using enhanced shape functions

Image-based rendering of intersecting surfaces for dynamic comparative visualization

Improved Approximation Bounds for Planar Point Pattern Matching

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