Related papers: Robust and Accurate Cylinder Triangulation
We consider the problem of segmenting an image into superpixels in the context of $k$-means clustering, in which we wish to decompose an image into local, homogeneous regions corresponding to the underlying objects. Our novel approach…
Recent efforts on solving inverse problems in imaging via deep neural networks use architectures inspired by a fixed number of iterations of an optimization method. The number of iterations is typically quite small due to difficulties in…
In recent publications, the author and his coworkers have shown robust approximation error estimates for B-splines of maximum smoothness and have proposed multigrid methods based on them. These methods allow to solve the linear system…
We show how to compute the circular area invariant of planar curves, and the spherical volume invariant of surfaces, in terms of line and surface integrals, respectively. We use the Divergence Theorem to express the area and volume…
A fundamental way to study 3-manifolds is through the geometric lens, one of the most prominent geometries being the hyperbolic one. We focus on the computation of a complete hyperbolic structure on a connected orientable hyperbolic…
A triangulation of a punctured or pinched surface is irreducible if no edge can be shrunk without producing multiple edges or changing the topological type of the surface. The finiteness of the set of (non-isomorphic) irreducible…
This paper presents a state-of-the-art approach in object detection for being applied in future SLAM problems. Although, many SLAM methods are proposed to create suitable autonomy for mobile robots namely ground vehicles, they still face…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…
We address high dimensional covariance estimation for elliptical distributed samples, which are also known as spherically invariant random vectors (SIRV) or compound-Gaussian processes. Specifically we consider shrinkage methods that are…
This paper proposes a method for computing the visible occluding contours of subdivision surfaces. The paper first introduces new theory for contour visibility of smooth surfaces. Necessary and sufficient conditions are introduced for when…
Translation averaging aims to recover camera locations from pairwise relative translation directions and is a fundamental component of global Structure-from-Motion pipelines. The problem is challenging because direction measurements contain…
We present an algorithm for sampling tightly confined random equilateral closed polygons in three-space which has runtime linear in the number of edges. Using symplectic geometry, sampling such polygons reduces to sampling a moment…
This extended abstract is about an effort to build a formal description of a triangulation algorithm starting with a naive description of the algorithm where triangles, edges, and triangulations are simply given as sets and the most complex…
In this paper, it is proposed to solve the problem of triangulation for calibrated omnidirectional cameras through the optimisation of ray-pairs on the projective sphere. The proposed solution boils down to finding the roots of a quadratic…
This paper uses mathematics to analyze the challenges of geometrically noisy environments on triangulation. Given widely accepted algorithmic triangulation methods, such as O (n ln n) or a simpler O (n^3) method, we can mathematically prove…
With the $[0,1,2]$-family of cyclic triangulations we introduce a rich class of vertex-transitive triangulations of surfaces. In particular, there are infinite series of cyclic $q$-equivelar triangulations of orientable and non-orientable…
The Circle Packing Theorem states that every planar graph can be represented as the tangency graph of a family of internally-disjoint circles. A well-known generalization is the Primal-Dual Circle Packing Theorem for 3-connected planar…
Cylindrical algebraic decomposition is one of the most important tools for computing with semi-algebraic sets, while triangular decomposition is among the most important approaches for manipulating constructible sets. In this paper, for an…
Tight triangulations are exotic, but highly regular objects in combinatorial topology. A triangulation is tight if all its piecewise linear embeddings into a Euclidean space are as convex as allowed by the topology of the underlying…
Images are an important source of information for spacecraft navigation and for three-dimensional reconstruction of observed space objects. Both of these applications take the form of a triangulation problem when the camera has a known…