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Although 3D shape matching and interpolation are highly interrelated, they are often studied separately and applied sequentially to relate different 3D shapes, thus resulting in sub-optimal performance. In this work we present a unified…

We propose a novel point-based representation, Gaussian surfels, to combine the advantages of the flexible optimization procedure in 3D Gaussian points and the surface alignment property of surfels. This is achieved by directly setting the…

Most of existing superpixel methods are designed to segment standard planar images as pre-processing for computer vision pipelines. Nevertheless, the increasing number of applications based on wide angle capture devices, mainly generating…

Applying convolutional neural networks to spherical images requires particular considerations. We look to the millennia of work on cartographic map projections to provide the tools to define an optimal representation of spherical images for…

Information transfer between triangle meshes is of great importance in computer graphics and geometry processing. To facilitate this process, a smooth and accurate map is typically required between the two meshes. While such maps can…

A compressive sensing based circular polarization snapshot spectral imaging system is proposed in this paper to acquire two-dimensional spatial, one-dimensional circular polarization (the right and left circular polarization), and…

Writing an uncomplicated, robust, and scalable three-dimensional convex hull algorithm is challenging and problematic. This includes, coplanar and collinear issues, numerical accuracy, performance, and complexity trade-offs. While there 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…

A new exact projective penalty method is proposed for the equivalent reduction of constrained optimization problems to nonsmooth unconstrained ones. In the method, the original objective function is extended to infeasible points by summing…

We fully characterize orthogonal projections of infinite right circular (round) cones in real Hilbert spaces. Another interpretation is that, given two vectors in a real Hilbert space, we establish the optimal estimate on the angle between…

We prove global convergence of classical projection algorithms for feasibility problems involving union convex sets, which refer to sets expressible as the union of a finite number of closed convex sets. We present a unified strategy for…

We propose a new modified primal-dual proximal best approximation method for solving convex not necessarily differentiable optimization problems. The novelty of the method relies on introducing memory by taking into account iterates…

We use a Simons type equation in order to characterize complete non-minimal pmc surfaces with non-negative Gaussian curvature.

We study a general smallest intersecting ball problem and its soft-margin variant in high-dimensional Euclidean spaces for input objects that are compact and convex. These two problems link and unify a series of fundamental problems in…

In shape optimisation it is desirable to obtain deformations of a given mesh without negative impact on the mesh quality. We propose a new algorithm using least square formulations of the Cauchy-Riemann equations. Our method allows to…

Geometry processing presents a variety of difficult numerical problems, each seeming to require its own tailored solution. This breadth is largely due to the expansive list of geometric primitives, e.g., splines, triangles, and hexahedra,…

A projection-based formulation is presented for non-linear model reduction of problems with extreme scale disparity. The approach allows for the selection of an arbitrary, but complete, set of solution variables while preserving the…

With the advancement of computer technology, there is a surge of interest in effective mapping methods for objects in higher-dimensional spaces. To establish a one-to-one correspondence between objects, higher-dimensional quasi-conformal…

In this paper, we consider a modified projected Gauss-Newton method for solving constrained nonlinear least-squares problems. We assume that the functional constraints are smooth and the the other constraints are represented by a simple…

The need for fast, effective and accurate surveys have become increasingly necessary. A major part of the research is supported by photographic surveys which are used for capturing expansive natural surfaces using a wide range of sensors --…