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Acquiring 3D geometry of real world objects has various applications in 3D digitization, such as navigation and content generation in virtual environments. Image remains one of the most popular media for such visual tasks due to its…
Single-image piece-wise planar 3D reconstruction aims to simultaneously segment plane instances and recover 3D plane parameters from an image. Most recent approaches leverage convolutional neural networks (CNNs) and achieve promising…
In this paper we present algorithms for a number of problems in geometric pattern matching where the input consist of a collections of segments in the plane. Our work consists of two main parts. In the first, we address problems and…
We consider a coordinated complexity-aware 4D trajectory planning problem in this paper. A case study of multiple aircraft traversing through a sector that contains a network of airways and waypoints is utilized to illustrate the model and…
We present some algorithms that provide useful topological information about curves in surfaces. One of the main algorithms computes the geometric intersection number of two properly embedded 1-manifolds $C_1$ and $C_2$ in a compact…
In most recent substructuring methods, a fundamental role is played by the coarse space. For some of these methods (e.g. BDDC and FETI-DP), its definition relies on a 'minimal' set of coarse nodes (sometimes called corners) which assures…
Hierarchical, multi-resolution volumetric mapping approaches are widely used to represent large and complex environments as they can efficiently capture their occupancy and connectivity information. Yet widely used path planning methods…
Closed form expressions are given for computing the parameters and vectors that identify and define the $n-1$ dimensional conic section that results from the intersection of a hyperplane with an $n$-dimensional conic section: cone,…
We present a, hopefully, elementary mathematical treatment of the computational aspects of congruent numbers, such that an amateur could understand the problem and perform their own calculations.
In this work, we carry out structural and algorithmic studies of a problem of barrier forming: selecting theminimum number of straight line segments (barriers) that separate several sets of mutually disjoint objects in the plane. The…
In this paper, we introduce a novel parametric method for segmentation of three-dimensional images. We consider a piecewise constant version of the Mumford-Shah and the Chan-Vese functionals and perform a region-based segmentation of 3D…
The topologies of existing interface elements used to discretize cohesive cracks are such that they can be used to compute the relative displacements (displacement discontinuities) of two opposing segments (in 2D) or of two opposing facets…
3D object proposals, quickly detected regions in a 3D scene that likely contain an object of interest, are an effective approach to improve the computational efficiency and accuracy of the object detection framework. In this work, we…
In this paper, we present an innovative technique for the path planning of flying robots in a 3D environment in Rough Mereology terms. The main goal was to construct the algorithm that would generate the mereological potential fields in…
A novel iterative algorithm for the efficient computation of the intersection areas of an arbitrary number of circles is presented. The algorithm, based on a trellis-structure, hinges on two geometric results which allow the existence-check…
Scene understanding has been of high interest in computer vision. It encompasses not only identifying objects in a scene, but also their relationships within the given context. With this goal, a recent line of works tackles 3D semantic…
We present a real-time algorithm that finds the Penetration Depth (PD) between general polygonal models based on iterative and local optimization techniques. Given an in-collision configuration of an object in configuration space, we find…
Traditional volumetric fusion algorithms preserve the spatial structure of 3D scenes, which is beneficial for many tasks in computer vision and robotics. However, they often lack realism in terms of visualization. Emerging 3D Gaussian…
We establish new bounds on the number of tangencies and orthogonal intersections determined by an arrangement of curves. First, given a set of $n$ algebraic plane curves, we show that there are $O(n^{3/2})$ points where two or more curves…
Simulations of many rigid bodies colliding with each other sometimes yield particularly interesting results if the colliding objects differ significantly in size and are non-spherical. The most expensive part within such a simulation code…