Distance transform

About: Distance transform is a research topic. Over the lifetime, 2886 publications have been published within this topic receiving 59481 citations.

A distance metric for multidimensional histograms

Abstract: A metric is defined on the space of multidimensional histograms. Such histograms store in thexth location the number of events with feature vectorx; examples are gray level histograms and co-occurrence matrices of digital images. Given two multidimensional histograms, each is “unfolded” and a minimum distance pairing is performed using a distance metric on the feature vectorsx. The sum of the distances in the minimal pairing is used as the “match distance” between the histograms. This distance is shown to be a metric, and in the one-dimensional case is equal to the absolute difference of the two cumulative distribution functions. Among other applications, it facilitates direct computation of the distance between co-occurrence matrices or between point patterns. The problem of finding a translation to minimize the distance between point patterns is also discussed.

Interactive SPH simulation and rendering on the GPU

Abstract: In this paper we introduce a novel parallel and interactive SPH simulation and rendering method on the GPU using CUDA which allows for high quality visualization. The crucial particle neighborhood search is based on Z-indexing and parallel sorting which eliminates GPU memory overhead due to grid or hierarchical data structures. Furthermore, it overcomes limitations imposed by shading languages allowing it to be very flexible and approaching the practical limits of modern graphics hardware. For visualizing the SPH simulation we introduce a new rendering pipeline. In the first step, all surface particles are efficiently extracted from the SPH particle cloud exploiting the simulation data. Subsequently, a partial and therefore fast distance field volume is rasterized from the surface particles. In the last step, the distance field volume is directly rendered using state-of-the-art GPU raycasting. This rendering pipeline allows for high quality visualization at very high frame rates.

Using distance maps for accurate surface representation in sampled volumes

Abstract: High quality rendering and physics based modeling in volume graphics have been limited because intensity based volumetric data do not represent surfaces well. High spatial frequencies due to abrupt intensity changes at object surfaces result in jagged or terraced surfaces in rendered images. The use of a distance-to-closest-surface function to encode object surfaces is proposed. This function varies smoothly across surfaces and hence can be accurately reconstructed from sampled data. The zero value iso surface of the distance map yields the object surface and the derivative of the distance map yields the surface normal. Examples of rendered images are presented along with a new method for calculating distance maps from sampled binary data.

Efficient computation of a simplified medial axis

Abstract: Applications of of the medial axis have been limited because of its instability and algebraic complexity. In this paper, we use a simplification of the medial axis, the θ-SMA, that is parameterized by a separation angle (θ) formed by the vectors connecting a point on the medial axis to the closest points on the boundary. We present a formal characterization of the degree of simplification of the θ-SMA as a function of θ, and we quantify the degree to which the simplified medial axis retains the features of the original polyhedron.We present a fast algorithm to compute an approximation of the θ-SMA. It is based on a spatial subdivision scheme, and uses fast computation of a distance field and its gradient using graphics hardware. The complexity of the algorithm varies based on the error threshold that is used, and is a linear function of the input size. We have applied this algorithm to approximate the SMA of models with tens or hundreds of thousands of triangles. Its running time varies from a few seconds, for a model consisting of hundreds of triangles, to minutes for highly complex models.