Topic
Distance transform
About: Distance transform is a research topic. Over the lifetime, 2886 publications have been published within this topic receiving 59481 citations.
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09 May 2005TL;DR: A new exact Euclidean distance transform algorithm for binary images based on the linear-time Legendre Transform algorithm that uses dimension reduction and convex analysis results on the Legendre-Fenchel transform to achievelinear-time complexity.
Abstract: We introduce a new exact Euclidean distance transform algorithm for binary images based on the linear-time Legendre Transform algorithm. The three-step algorithm uses dimension reduction and convex analysis results on the Legendre-Fenchel transform to achieve linear-time complexity. First, computation on a grid (the image) is reduced to computation on a line, then the convex envelope is computed, and finally the squared Euclidean distance transform is obtained. Examples and an extension to non-binary images are provided.
15 citations
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TL;DR: This work designs and implements an efficient and certified algorithm for the computation of Voronoi diagrams (VDs) constrained to a given domain, using the Bernstein form of polynomials and DeCasteljau's algorithm to subdivide the initial domain and isolate bisector, or domains that contain a Vor onoi vertex.
Abstract: We design and implement an efficient and certified algorithm for the computation of Voronoi diagrams (VDs) constrained to a given domain. Our framework is general and applicable to any VD-type where the distance field is given explicitly or implicitly by a polynomial, notably the anisotropic VD or VDs of non-punctual sites. We use the Bernstein form of polynomials and DeCasteljau's algorithm to subdivide the initial domain and isolate bisector, or domains that contain a Voronoi vertex. The efficiency of our algorithm is due to a filtering process, based on bounding the field over the subdivided domains. This allows to exclude functions (thus sites) that do not contribute locally to the lower envelope of the lifted diagram. The output is a polygonal description of each Voronoi cell, within any user-defined precision, isotopic to the exact VD. Correctness of the result is implied by the certified approximations of bisector branches, which are computed by existing methods for handling algebraic curves. First experiments with our C++ implementation, based on double precision arithmetic, demonstrate the adaptability of the algorithm.
15 citations
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12 Apr 2001TL;DR: In this article, a method for modeling interactions between models is described, where a first adaptively sampled distance field having a first spatial hierarchy for a first model is generated, and a second adaptive distance field with a second spatial hierarchy of a second model being generated by the first model.
Abstract: A method is described for modeling interactions between models. A first adaptively sampled distance field having a first spatial hierarchy for a first model is generated, and a second adaptively sampled distance field having a second spatial hierarchy for a second model is generated. During each time step, a potential overlap region is determined using the spatial hierarchies of the first and second adaptively sampled distance fields. When the potential overlap region is non-empty, a third adaptively sampled distance field is generated from the first and second adaptively sampled distance fields using a first interaction procedure and first properties and a fourth adaptively sampled distance field is generated from the first and second adaptively distance fields using a second interaction procedure and second properties to model the interactions between the first and second models.
15 citations
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11 Jul 2010TL;DR: A new similarity criterion, sum of squared vesselness measure difference (SSVMD) is added to three existing intensity-based similarity criteria for nonrigid lung CT image registration to show its ability in improving matching accuracy.
Abstract: Image registration plays an important role within pulmonary image analysis. Accurate registration is critical to post-analysis of lung mechanical properties. To improve registration accuracy, we utilize the rich information of vessel locations and shapes, and introduce a new similarity criterion, sum of squared vesselness measure difference (SSVMD). This metric is added to three existing intensity-based similarity criteria for nonrigid lung CT image registration to show its ability in improving matching accuracy. The registration accuracy is assessed by landmark error calculation and distance map visualization on vascular tree. The average landmark errors are reduced by over 20% and are within 0.7 mm after adding SSVMD constraint to three existing intensity-based similarity metrics. Visual inspection shows matching accuracy improvements in the lung regions near the thoracic cage and near the diaphragm. Experiments also show this vesselness constraint makes the Jacobian map of transformations physiologically more plausible and reliable.
15 citations
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26 May 2008TL;DR: This paper focuses on a CPU‐based technique, intended to deal flexibly with large polygonal models and high‐resolution grids that are often too bulky for GPU computation.
Abstract: The signed distance field for a polygonal model is a useful representation that facilitates efficient computation in many visualization and geometric processing tasks. Often it is more effective to build a local distance field only within a narrow band around the surface that holds local geometric information for the model. In this paper, we present a novel technique to construct a volumetric local signed distance field of a polygonal model. To compute the local field efficiently, exactly those cells that cross the polygonal surface are found first through a new voxelization method, building a list of intersecting triangles for each boundary cell. After their neighboring cells are classified, the triangle lists are exploited to compute the local signed distance field with minimized voxeltotriangle distance computations. While several efficient methods for computing the distance field, particularly those harnessing the graphics processing unit's (GPU's) processing power, have recently been proposed, we focus on a CPU-based technique, intended to deal flexibly with large polygonal models and high-resolution grids that are often too bulky for GPU computation.
15 citations