Related papers: Reconstruction of Convex Bodies from Projection Cu…
This paper is concerned with possibility of recovery of motion and structure parameters from multiframes under perspective projection when only points on a rigid body are traced. Free (unrestricted and uncontrolled) pattern of motion…
We consider the problem of reconstructing binary images from their horizontal and vertical projections. We present a condition that the projections must necessarily satisfy when there exist two disjoint reconstructions from those…
It is known that, in finite dimensions, the support function of a compact convex set with non empty interior is differentiable excepting the origin if and only if the set is strictly convex. In this paper we realize a thorough study of the…
We investigate algorithms for reconstructing a convex body $K$ in $\mathbb {R}^n$ from noisy measurements of its support function or its brightness function in $k$ directions $u_1,...,u_k$. The key idea of these algorithms is to construct a…
We establish new geometric inequalities comparing the volumes of sections and projections of a convex body, whose barycenter or Santal\'o point is at the origin, with those of its inner and outer regularizations. We also provide functional…
Convex hulls are fundamental objects in computational geometry. In moderate dimensions or for large numbers of vertices, computing the convex hull can be impractical due to the computational complexity of convex hull algorithms. In this…
This work proposes a new formulation to the long-standing problem of convex decomposition through learning feature fields, enabling the first feed-forward model for open-world convex decomposition. Our method produces high-quality…
Reconstructing and simulating dynamic 3D scenes with both visual realism and physical consistency remains a fundamental challenge. Existing neural representations, such as NeRFs and 3DGS, excel in appearance reconstruction but struggle to…
In geometry, there are several challenging problems studying numbers associated to convex bodies. For example, the packing density problem, the kissing number problem, the covering density problem, the packing-covering constant problem,…
Obtaining complete information about the shape of an object by looking at it from a single direction is impossible in general. In this paper, we theoretically study obtaining differential geometric information of an object from orthogonal…
Let $K$ and $L$ be two convex bodies in ${\mathbb R^4}$, such that their projections onto all $3$-dimensional subspaces are directly congruent. We prove that if the set of diameters of the bodies satisfy an additional condition and some…
In this paper, we construct two convex bodies $K$ and $L$ in $\mathbb{R}^n$, $n\geq 3$, such that their projections $K|H$, $L|H$ onto every subspace $H$ are congruent, but nevertheless, $K$ and $L$ do not coincide up to a translation or a…
The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they have a computational advantage over some alternatives and that this makes them successful in real-world applications.…
Reconstructing a composition (union) of convex polytopes that perfectly fits the corresponding input point-cloud is a hard optimization problem with interesting applications in reverse engineering and rigid body dynamics simulations. We…
The paper uses a frame-theoretic setting to study the injectivity of a ReLU-layer on the closed ball of $\mathbb{R}^n$ and its non-negative part. In particular, the interplay between the radius of the ball and the bias vector is emphasized.…
In this paper, we give an overview of some results concerning best and random approximation of convex bodies by polytopes. We explain how both are linked and see that random approximation is almost as good as best approximation.
An approach is proposed which, given a family of linearly independent functions, constructs the appropriate biorthogonal set so as to represent the orthogonal projector operator onto the corresponding subspace. The procedure evolves…
In this work, we consider a class of convex optimization problems in a real Hilbert space that can be solved by performing a single projection, i.e., by projecting an infeasible point onto the feasible set. Our results improve those…
The convergence of the projection algorithm for solving the convex feasibility problem for a family of closed convex sets, is in connection with the regularity properties of the family. In the paper [18] are pointed out four cases of such a…
Finding a point in the intersection of a collection of closed convex sets, that is the convex feasibility problem, represents the main modeling strategy for many computational problems. In this paper we analyze new stochastic reformulations…