Distance transform

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

Fast skeletonization algorithm for 3D elongated objects

Abstract: A novel one-pass 3D thinning algorithm is proposed in this paper. 3D thinning can be regarded as an essential step in many image-processing tasks such as image quantification, image compression, motion tracking, path generation, and object navigation. The proposed algorithm generates both connected and non-connected skeletons. It is faster and more accurate than currently available techniques in the literature. In addition, it adaptively removes spurious branches of the skeleton, and hence, generates a smooth and refined skeleton, representing the essential structure of 3D elongated objects such as vessels, airways, and other similar organic shapes.

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 polyhedronWe 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

Two and three dimensional skeletonization

Abstract: A method is disclosed for determining skeletons of any two dimensional images and three-dimensional skeletons of vessel trees. In the three dimensional case, the method takes a binary volume of any vessel tree as input and produces centred, connected and one-voxel wide skeleton of the input vessel tree. In the two dimensional case, centred, connected and one-pixel wide skeletons of input binary images are produced. The method includes the steps of: (1) calculating a 3D/2D distance transform, (2) locating local maximum voxels/pixels, one-voxel/pixel wide valley voxels/pixels, and two-voxel/pixel wide valley voxels/pixels, (3) propagating skeletal elements to get a full set of skeletal elements, and (4) removing redundant local maximum voxels/pixels to obtain a one-voxel/pixel wide skeleton.

Theoretical Foundations of Computer Vision

Abstract: Attentive Visual Motion Processing: Computations in the Log-Polar Plane.- Invariant Thinning and Distance Transform.- Recognition of Images Degraded by Linear Motion Blur without Restoration.- Symmetric Bi- and Trinocular Stereo: Tradeoffs between Theoretical Foundations and Heuristics.- Surface from Motion-without and with Calibration.- Properties of Pyramidal Representations.- A Robust Approach to Estimation of Parametric Models.- Computer Vision and Mathematical Morphology.- A Variational Approach to the Design of Early Vision Algorithms.- Banach Constructor and Image Compression.- Piecewise Linear Approximation of Planar Jordan Curves and Arcs: Theory and Applications.- Segmentation with Volumetric Part Models.- Theoretical Foundations of Anisotropic Diffusion in Image Processing.- Stability and Likelihood of Views of Three Dimensional Objects.