Distance transform

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

Fast surface approximation for volume and surface area measurements using distance transform

Abstract: The laser triangulation technique has been widely used to obtain three-dimensional (3-D) information because of its accuracy. It is a fast, noncontact method for 3-D measurement. However, 3-D data obtained from triangulation are not dense and usually not complete for surface reconstruction, especially for objects with irregular shapes. As the result of fitting surfaces with these sparse 3-D data, inaccuracy in measuring object surface area and volume is inevitable. Accurate sur- face reconstruction from incomplete 3-D data points becomes an impor- tant step toward accurate noncontact surface area and volume measure- ments of objects moving at high speed. A novel computer vision technique combining laser triangulation and a distance transform is de- veloped to improve the 3-D measurement accuracy for objects with ir- regular shapes. The 2-D object image boundary points combined with the 3-D data obtained from laser triangulation are used to generate a 3-D wire frame. The distances from each pixel within the object boundary to its nearest boundary point are then used as the constraints for surface approximation. With this additional information from the distance trans- form, more accurate surface approximation can be achieved. This novel surface approximation technique is implemented and the measurement accuracy is compared with the accuracy using other surface interpolation techniques for the volume measurement of moving objects. © 2003 Soci-

Euclidean Skeletons of 3D Data Sets in Linear Time by the Integer Medial Axis Transform

Abstract: A general algorithm for computing Euclidean skeletons of 3D data sets in linear time is presented. These skeletons are defined in terms of a new concept, called the integer medial axis (IMA) transform. The algorithm is based upon the computation of 3D feature transforms, using a modification of an algorithm for Euclidean distance transforms. The skeletonization algorithm has a time complexity which is linear in the amount of voxels, and can be easily parallelized. The relation of the IMA skeleton to the usual definition in terms of centers of maximal disks is discussed.

Distance Transform-Based Skeleton Extraction and Its Applications in Sensor Networks

Abstract: We study the problem of skeleton extraction for large-scale sensor networks with reliance purely on connectivity information. Existing efforts in this line highly depend on the boundary detection algorithms, which are used to extract accurate boundary nodes. One challenge is that in practical this could limit the applicability of the boundary detection algorithms. For instance, in low node density networks where boundary detection algorithms do not work well, the extracted boundary nodes are often incomplete. This paper brings a new view to skeleton extraction from a distance transform perspective, bridging the distance transform of the network and the incomplete boundaries. As such, we propose a distributed and scalable algorithm for skeleton extraction, called DIST, based on DIStance Transform, while incurring low communication overhead. The proposed algorithm does not require that the boundaries are complete or accurate, which makes the proposed algorithm more practical in applications. First, we compute the distance transform of the network. Specifically, the distance (hop count) of each node to the boundaries of a sensor network is estimated. The node map consisting of the distance values is considered as the distance transform (the distance map). The distance map is then used to identify skeleton nodes. Next, skeleton arcs are generated by controlled flooding within the identified skeleton nodes, thereby connecting these skeleton arcs, to extract a coarse skeleton. Finally, we refine the coarse skeleton by building shortest path trees followed by a prune phase. The obtained skeleton is robust to boundary noise or shape variations. Besides, we present two specific applications that benefit from the extracted skeleton: identifying complete boundaries and shape segmentation. First, with the extracted skeleton using DIST, we propose to identify more boundary nodes to form a meaningful boundary curve. Second, the utilization of the derived skeleton to segment the network into approximately convex pieces has been shown to be effective.

Region Growing Euclidean Distance Transforms

Abstract: By propagating a vector for each pixel, we show that nearly Euclidean distance maps can be produced quickly by a region growing algorithm using hierarchical queues. Properties of the propagation scheme are used to detect potentially erroneous pixels and correct them by using larger neighbourhoods, without significantly affecting the computation time. Thus, Euclidean distance maps are produced in a time comparable to its commonly used chamfer approximations.