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...

Traditionally variational level set model for image segmentation is solved by using gradient descent method, which has low computational efficiency and needs complex re-initialization of level set functions as signed distance functions. In this paper, we first reformulate the variational model as a constrained optimization problem. Then we present an augmented Lagrangian projection method to pr...

We present a numerical method for computing the signed distance to a piecewise-smooth surface defined as the zero set of a function. It is based on a marching method by Kim [Kim01] and a hybrid discretization of firstand second-order discretizations of the signed distance function equation. If the solution is smooth at a point and at all of the points in the domain of dependence of that point, ...

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 ...

When we use range finders to observe the shape of an object, many occluded areas may occur. These become holes and gaps in the model and make it undesirable to utilize the model for various applications. We propose a novel method to fill holes and gaps and complement such an incomplete model. We use a signed distance field (SDF) as an intermediate representation, which stores Euclidean signed d...

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...

We present a surface compression method that stores surfaces as wavelet-compressed signed-distance volumes. Our approach enables the representation of surfaces with complex topology and arbitrary numbers of components within a single multiresolution data structure. This data structure elegantly handles topological modification at high compression rates. Our method does not require the costly an...