Support Vector Machines (SVMs) were applied to interactive document retrieval that uses active learning. In such a retrieval system, the degree of relevance is evaluated by using a signed distance from the optimal hyperplane. It is not clear, however, how the signed distance in SVMs has characteristics of vector space model. We therefore formulated the degree of relevance by using the signed di...

We present a new method for computing the medial axis of a given closed smooth curve or surface. It is based on an algorithm for approximating the signed distance function using polynomial splines over hierarchical T-meshes, which has recently been presented in [36]. Since the signed distance function is not differentiable along the medial axis, the hierarchical T-meshes is automatically refine...

We present a method for generating shell-like objects such as surgical guides and plates from segmented computed tomography (CT) images, using signed distance fields and constructive solid geometry (CSG). We develop a userfriendly modeling tool which allows a user to quickly design such models with the help of stereo graphics, six degrees-of-freedom input, and haptic feedback, in our existing s...

Background: Osteoarthritis is a common chronic disease of the musculoskeletal system in older adults. Aim: This study aimed to compare the effects of in-person and distance exercise training on the outcomes of knee injury and osteoarthritis among the elderly with limited literacy. Method: In this two-group randomized clinical trial with a pretest-posttest design, 60 elderly patients with knee i...

We describe a new class of algorithms for generating a variety of geometric interfacial motions by alternating two steps: Construction of the signed distance function (i.e. redistancing) to the interface, and convolution with a suitable kernel. These algorithms can be seen as variants of Merriman, Bence, and Osher’s threshold dynamics [25]. The new algorithms proposed here preserve the computat...

Abstract: The bootstrap is a simple and straightforward method for calculating approximated biases, standard deviations, confidence intervals, testing statistical hypotheses, and so forth, in almost any nonparametric estimation problem. In this paper we describe a bootstrap method for variance that is designed directly for hypothesis testing in case of fuzzy data based on Yao-Wu signed distance.

An efficient algorithm for accurately simulating curvature flow for large networks of curves in two dimensions and surfaces in three dimensions on uniform grids is proposed. This motion arises in the technologically important problem of simulating grain boundary motion in polycrystalline materials. In this formulation grains are zero level sets of signed distance functions. Curvature motion is ...

Abstract. In Sussman, Smereka, and Osher [J. Comp. Phys., 94 (1994), pp. 146–159], a numerical scheme was presented for computing incompressible air–water flows using the level set method. Crucial to the above method was a new iteration method for maintaining the level set function as the signed distance from the zero level set. In this paper we implement a “constraint” along with higher order ...

We introduce a new redistancing method for level set functions. This method applies in a finite element setting and uses a gradient recovery technique. Based on the recovered gradient a quasi-normal field on the zero level of the finite element level set function is defined and from this an approximate signed distance function is determined. For this redistancing method rigorous error bounds ar...

We extend the resistance distance kernel to the domain of signed dissimilarity values, and show how it can be applied to collaborative rating prediction. The resistance distance is a graph kernel inspired by electrical network models where edges of a graph are interpreted as electrical resistances. We model the similarity between users of a large collaborative rating database using this signed ...