The signed distance function d to an embedded (hyper-) surface Γ is required in the analysis and implementation of some higher order methods for the numerical treatment of partial differential equations on surfaces. Two algorithms for the approximation of d are presented in this paper, which only require a finite element approximation of a (smooth) level set function of Γ. One method is based o...

This paper discusses a formation control problem in which a target formation is defined with both distance and signed area constraints. The control objective is to drive spatially distributed agents to reach a unique target rigid formation shape (up to rotation and translation) with desired inter-agent distances. We define a new potential function by incorporating both distance terms and signed...

We present an adaptive signed distance transform algorithm for curves in the plane. A hierarchy of bounding boxes is required for the input curves. We demonstrate the algorithm on the isocontours of a turbulence simulation. The algorithm provides guaranteed error bounds with a selective refinement approach. The domain over which the signed distance function is desired is adaptively triangulated...

MOTIVATION The double cut and join operation (abbreviated as DCJ) has been extensively used for genomic rearrangement. Although the DCJ distance between signed genomes with both linear and circular (uni- and multi-) chromosomes is well studied, the only known result for the NP-complete unsigned DCJ distance problem is an approximation algorithm for unsigned linear unichromosomal genomes. In thi...

Genome sequences mutate and rearrange through the course of evolution. Genome rearrangement is an important and rich area of computational biology, and has many applications, including inferring phylogenetic trees. Some genome rearrangement problems, such as reversal distance [6], [1] and translocation distance [5], have been studied. Reversal distance, for example, measures the number of subst...

Research works on the two topics of Semantic Segmentation and SLAM (Simultaneous Localization and Mapping) have been following separate tracks. Here, we link them quite tightly by delineating a category label fusion technique that allows for embedding semantic information into the dense map created by a volume-based SLAM algorithm such as KinectFusion. Accordingly, our approach is the first to ...

In this chapter we address the problem of reconstructing the surface geometry, topology, and color map of a 3D scene from a finite set of colored oriented points. These data sets are nowadays obtained using a variety of techniques, including multi-view stereo reconstruction methods from multiple 2D images. We describe a novel variational method which reduces the problem to the solutions of spar...

In this paper a new approach for the design of linear phase FIR filters with discrete coefficients is proposed. A mixed integer linear programming (MILP) problem is formulated that minimizes the total Hamming distance between the adjacent coefficients, i.e., the number of bit switches of the coefficients. The Hamming distance between the coefficients is a good measure of the power consumption, ...

Truncated Signed Distance Fields (TSDFs) have become a popular tool in 3D reconstruction, as they allow building very high-resolution models of the environment in realtime on GPU. However, they have rarely been used for planning on robotic platforms, mostly due to high computational and memory requirements. We propose to reduce these requirements by using large voxel sizes, and extend the stand...

The computation speed for distance transforms becomes important in a wide variety of image processing applications. Current ITK library filters do not see any benefit from a multithreading environment. We introduce a three-dimensional signed parallel implementation of the exact Euclidean distance transform algorithm developed by Maurer et al.[1] with a theoretical complexity of O(n/p) for n vox...