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We propose a scalable method to find a subspace $\widehat{\mathcal{H}}$ of low-rank tensors that simultaneously approximates a set of integral operators. The method can be seen as a generalization of the Tucker-2 decomposition model, which…
This paper is devoted to the study of directional minimal time functions that specify the minimal time for a vector to reach an object following its given direction. We provide a careful analysis of general and generalized differentiation…
We show that the minimum distance projection in the L1-norm from an interior point onto the boundary of a convex set is achieved by a single, unidimensional projection. Application of this characterization when the convex set is a…
The distance transform algorithm is popular in computer vision and machine learning domains. It is used to minimize quadratic functions over a grid of points. Felzenszwalb and Huttenlocher (2004) describe an O(N) algorithm for computing the…
Let \({\mathbb K}\) be any field, let \(X\subset {\mathbb P}^{k-1}\) be a set of \(n\) distinct \({\mathbb K}\)-rational points, and let \(a\geq 1\) be an integer. In this paper we find lower bounds for the minimum distance \(d(X)_a\) of…
The (unweighted) point-separation problem asks, given a pair of points $s$ and $t$ in the plane, and a set of candidate geometric objects, for the minimum-size subset of objects whose union blocks all paths from $s$ to $t$. Recent work has…
This work provides closed-form solutions and minimum achievable errors for a large class of low-rank approximation problems in Hilbert spaces. The proposed theorem generalizes to the case of bounded linear operators the previous results…
In this paper we study the problem of locating a given number of hyperplanes minimizing an objective function of the closest distances from a set of points. We propose a general framework for the problem in which norm-based distances…
A suitable operator for the time-of-arrival at a detector is defined for the free relativistic particle in 3+1 dimensions. For each detector position, there exists a subspace of detected states in the Hilbert space of solutions to the Klein…
This paper deals with a bilevel approach of the location-allocation problem with dimensional facilities. We present a general model that allows us to consider very general shapes of domains for the dimensional facilities and we prove the…
For several tasks, ranging from manipulation to inspection, it is beneficial for robots to localize a target object in their surroundings. In this paper, we propose an approach that utilizes coarse point clouds obtained from miniaturized…
The efficient use of a multipole expansion of the far field for rapid numerical modeling and optimization of the optical response from ordered and disordered arrays of various structural elements is complicated by the ambiguity in choosing…
We provide a method for detecting and localizing objects near a robot arm using arm-mounted miniature time-of-flight sensors. A key challenge when using arm-mounted sensors is differentiating between the robot itself and external objects in…
We introduce a novel approach for object segmentation from 3D images using modified minimal path Eikonal equation. The proposed method utilizes an implicit constraint - a second order correction to the inhomogeneous minimal path Eikonal -…
Due to the multi-linearity of tensors, most algorithms for tensor optimization problems are designed based on the block coordinate descent method. Such algorithms are widely employed by practitioners for their implementability and…
Hyper spectral imaging is a remote sensing technology, providing variety of applications such as material identification, space object identification, planetary exploitation etc. It deals with capturing continuum of images of the earth…
In this paper, we propose a new framework for segmenting feature-based moving objects under affine subspace model. Since the feature trajectories in practice are high-dimensional and contain a lot of noise, we firstly apply the sparse PCA…
This paper considers the problem of optimally deploying omnidirectional sensors, with potentially limited sensing radius, in a network-like environment. This model provides a compact and effective description of complex environments as well…
This paper studies the motion planning problem of the pick-and-place of an aerial manipulator that consists of a quadcopter flying base and a Delta arm. We propose a novel partially decoupled motion planning framework to solve this problem.…
We introduce a relaxed-projection splitting algorithm for solving variational inequalities in Hilbert spaces for the sum of nonsmooth maximal monotone operators, where the feasible set is defined by a nonlinear and nonsmooth continuous…