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The indicator matrix plays an important role in machine learning, but optimizing it is an NP-hard problem. We propose a new relaxation of the indicator matrix and prove that this relaxation forms a manifold, which we call the Relaxed…

We present a study of the numerical solution of the two dimensional electrical impedance tomography problem, with noisy measurements of the Dirichlet to Neumann map. The inversion uses parametrizations of the conductivity on optimal grids.…

Graph representation learning is a ubiquitous task in machine learning where the goal is to embed each vertex into a low-dimensional vector space. We consider the bipartite graph and formalize its representation learning problem as a…

The existing approaches to intrinsic dimension estimation usually are not reliable when the data are nonlinearly embedded in the high dimensional space. In this work, we show that the explicit accounting to geometric properties of unknown…

Despite the impressive performance of vision-based pose estimators, they generally fail to perform well under adverse vision conditions and often don't satisfy the privacy demands of customers. As a result, researchers have begun to study…

Estimating pose from given 3D correspondences, including point-to-point, point-to-line and point-to-plane correspondences, is a fundamental task in computer vision with many applications. We present a complete solution for this task,…

In this work we investigate the practicality of stochastic gradient descent and recently introduced variants with variance-reduction techniques in imaging inverse problems. Such algorithms have been shown in the machine learning literature…

In this paper we address smoothing-that is, optimisation-based-estimation techniques for localisation problems in the case where motion sensors are very accurate. Our mathematical analysis focuses on the difficult limit case where motion…

3D human pose estimation from a monocular image or 2D joints is an ill-posed problem because of depth ambiguity and occluded joints. We argue that 3D human pose estimation from a monocular input is an inverse problem where multiple feasible…

The incremental poses computed through odometry can be integrated over time to calculate the pose of a device with respect to an initial location. The resulting global pose may be used to formulate a second, consistency based, loss term in…

Network estimation from multi-variate point process or time series data is a problem of fundamental importance. Prior work has focused on parametric approaches that require a known parametric model, which makes estimation procedures less…

Problems in differentiable rendering often involve optimizing scene parameters that cause motion in image space. The gradients for such parameters tend to be sparse, leading to poor convergence. While existing methods address this sparsity…

This paper proposes a deep recurrent Rotation Averaging Graph Optimizer (RAGO) for Multiple Rotation Averaging (MRA). Conventional optimization-based methods usually fail to produce accurate results due to corrupted and noisy relative…

Polyhedral estimate is a generic efficiently computable nonlinear in observations routine for recovering unknown signal belonging to a given convex compact set from noisy observation of signal's linear image. Risk analysis and optimal…

Point set registration is an essential step in many computer vision applications, such as 3D reconstruction and SLAM. Although there exist many registration algorithms for different purposes, however, this topic is still challenging due to…

In this paper we consider graph algorithms in models of computation where the space usage (random accessible storage, in addition to the read only input) is sublinear in the number of edges $m$ and the access to input data is constrained.…

Oscillator Ising machines (OIMs) are networks of coupled oscillators that seek the minimum energy state of an Ising model. Since many NP-hard problems are equivalent to the minimization of an Ising Hamiltonian, OIMs have emerged as a…

Quantifying the uncertainty of an object's pose estimate is essential for robust control and planning. Although pose estimation is a well-studied robotics problem, attaching statistically rigorous uncertainty is not well understood without…

We consider the Stochastic Matching problem, which is motivated by applications in kidney exchange and online dating. In this problem, we are given an undirected graph. Each edge is assigned a known, independent probability of existence and…

The two-stage object pose estimation paradigm first detects semantic keypoints on the image and then estimates the 6D pose by minimizing reprojection errors. Despite performing well on standard benchmarks, existing techniques offer no…