相关论文: Learning to Solve Hard Minimal Problems

This paper considers a quadratically-constrained cardinality minimization problem with applications to digital filter design, subset selection for linear regression, and portfolio selection. Two relaxations are investigated: the continuous…

We propose a new method for constructing elimination templates for efficient polynomial system solving of minimal problems in structure from motion, image matching, and camera tracking. We first construct a particular affine…

Camera pose estimation for two-view geometry traditionally relies on RANSAC. Normally, a multitude of image correspondences leads to a pool of proposed hypotheses, which are then scored to find a winning model. The inlier count is generally…

We study the minmax optimization problem introduced in [22] for computing policies for batch mode reinforcement learning in a deterministic setting. First, we show that this problem is NP-hard. In the two-stage case, we provide two…

Current traditional methods for LiDAR-camera extrinsics estimation depend on offline targets and human efforts, while learning-based approaches resort to iterative refinement for calibration results, posing constraints on their…

Solving Perspective-n-Point (PnP) problems is a traditional way of estimating object poses. Given outlier-contaminated data, a pose of an object is calculated with PnP algorithms of n = {3, 4} in the RANSAC-based scheme. However, the…

Visual localization refers to the process of determining camera poses and orientation within a known scene representation. This task is often complicated by factors such as changes in illumination and variations in viewing angles. In this…

We propose a general convex optimization problem for computing regularized geodesic distances. We show that under mild conditions on the regularizer the problem is well posed. We propose three different regularizers and provide analytical…

We study the set of image tuples arising from fixed cameras observing varying planar 3-dimensional point configurations. We derive a formula for the number of complex critical points of the triangulation problem, which seeks to reconstruct…

Recently dictionary screening has been proposed as an effective way to improve the computational efficiency of solving the lasso problem, which is one of the most commonly used method for learning sparse representations. To address today's…

Composite minimization involves a collection of smooth functions which are aggregated in a nonsmooth manner. In the convex setting, we design an algorithm by linearizing each smooth component in accordance with its main curvature. The…

We study randomized sketching methods for approximately solving least-squares problem with a general convex constraint. The quality of a least-squares approximation can be assessed in different ways: either in terms of the value of the…

We completely classify all minimal problems for Structure-from-Motion (SfM) where arrangements of points and lines are fully observed by multiple uncalibrated pinhole cameras. We find 291 minimal problems, 73 of which have unique solutions…

We present a method that can evaluate a RANSAC hypothesis in constant time, i.e. independent of the size of the data. A key observation here is that correct hypotheses are tightly clustered together in the latent parameter domain. In a…

The graph matching problem is a significant special case of the Quadratic Assignment Problem, with extensive applications in pattern recognition, computer vision, protein alignments and related fields. As the problem is NP-hard, relaxation…

Rotation Averaging is a non-convex optimization problem that determines orientations of a collection of cameras from their images of a 3D scene. The problem has been studied using a variety of distances and robustifiers. The intrinsic (or…

In an ordinary feature selection procedure, a set of important features is obtained by solving an optimization problem such as the Lasso regression problem, and we expect that the obtained features explain the data well. In this study,…

An algorithm which computes a solution of a set optimization problem is provided. The graph of the objective map is assumed to be given by finitely many linear inequalities. A solution is understood to be a set of points in the domain…

RANSAC and its variants are widely used for robust estimation, however, they commonly follow a greedy approach to finding the highest scoring model while ignoring other model hypotheses. In contrast, Iteratively Reweighted Least Squares…

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,…