Related papers: PLMP -- Point-Line Minimal Problems for Projective…
Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate…
This paper investigates two related optimal input selection problems for fixed (non-switched) and switched structured systems. More precisely, we consider selecting the minimum cost of inputs from a prior set of inputs, and selecting the…
This paper proposes minimal solvers that use combinations of imaged translational symmetries and parallel scene lines to jointly estimate lens undistortion with either affine rectification or focal length and absolute orientation. We use…
We show that any submodular minimization (SM) problem defined on a linear constraint set with constraints having up to two variables per inequality, are 2-approximable in polynomial time. If the constraints are monotone (the two variables…
We develop a new `subspace layered least squares' interior point method (IPM) for solving linear programs. Applied to an $n$-variable linear program in standard form, the iteration complexity of our IPM is up to an $O(n^{1.5} \log n)$…
Structure from Motion (SfM) estimates camera poses and reconstructs point clouds, forming a foundation for various tasks. However, applying SfM to driving scenes captured by multi-camera systems presents significant difficulties, including…
We consider robust submodular maximization problems (RSMs), where given a set of $m$ monotone submodular objective functions, the robustness is with respect to the worst-case (scaled) objective function. The model we consider generalizes…
Numerous machine learning and industrial problems can be modeled as the minimization of a sum of $N$ so-called clipped convex functions (SCC), i.e. each term of the sum stems as the pointwise minimum between a constant and a convex…
In this paper, we address two minimal controllability problems, where the goal is to determine a minimal subset of state variables in a linear time-invariant system to be actuated to ensure controllability under additional constraints.…
Despite major advancements in nonlinear programming (NLP) and convex relaxations, most system operators around the world still predominantly use some form of linear programming (LP) approximation of the AC power flow equations. This is…
Structure-from-Motion -- the process of simultaneously estimating camera poses and 3D scene structure from a collection of images -- remains a central challenge in computer vision, with many open problems yet to be solved. Recent advances…
We consider manifolds $M^{2n}$ which admit smooth maps into a connected sum of $S^1\times S^n$ with only finitely many critical points, for $n\in\{2,4,8\}$, and compute the minimal number of critical points.
Can Vision-Language Models (VLMs) imagine the full scene from just a few views, like humans do? Humans form spatial mental models naturally, internal representations of unseen space, to reason about layout, perspective, and motion. Our…
We propose new estimates for the frontier of a set of points. They are defined as kernel estimates covering all the points and whose associated support is of smallest surface. The estimates are written as linear combinatio- ns of kernel…
The optimization conditions for minimum error discrimination of linearly independent pure states comprise of two kinds: stationary conditions over the space of rank one projective measurements and the global maximization conditions. A…
Vision-language models such as CLIP are capable of mapping the different modality data into a unified feature space, enabling zero/few-shot inference by measuring the similarity of given images and texts. However, most existing methods…
We study the problem of one-dimensional regression of data points with total-variation (TV) regularization (in the sense of measures) on the second derivative, which is known to promote piecewise-linear solutions with few knots. While there…
In this work, we consider a nonsmooth minimisation problem in which the objective function can be represented as the maximum of finitely many smooth ``subfunctions''. First, we study a smooth min-max reformulation of the problem. Due to…
Submodular functions describe a variety of discrete problems in machine learning, signal processing, and computer vision. However, minimizing submodular functions poses a number of algorithmic challenges. Recent work introduced an…
A linear inverse problem is proposed that requires the determination of multiple unknown signal vectors. Each unknown vector passes through a different system matrix and the results are added to yield a single observation vector. Given the…