Related papers: Learning to Solve Hard Minimal Problems

Current automatic vision systems face two major challenges: scalability and extreme variability of appearance. First, the computational time required to process an image typically scales linearly with the number of pixels in the image,…

This work provides a theoretical framework for the pose estimation problem using total least squares for vector observations from landmark features. First, the optimization framework is formulated with observation vectors extracted from…

In this paper, we formulate a generic non-minimal solver using the existing tools of Polynomials Optimization Problems (POP) from computational algebraic geometry. The proposed method exploits the well known Shor's or Lasserre's…

This paper focuses on developing efficient and robust evaluation metrics for RANSAC hypotheses to achieve accurate 3D rigid registration. Estimating six-degree-of-freedom (6-DoF) pose from feature correspondences remains a popular approach…

Accurate and robust visual localization under a wide range of viewing condition variations including season and illumination changes, as well as weather and day-night variations, is the key component for many computer vision and robotics…

We investigate approximation algorithms for several fundamental optimization problems on geometric packing. The geometric objects considered are very generic, namely $d$-dimensional convex fat objects. Our main contribution is a versatile…

We present gP4Pc, a new method for computing the absolute pose of a generalized camera with unknown internal scale from four corresponding 3D point-and-ray pairs. Unlike most pose-and-scale methods, gP4Pc is based on constraints arising…

Convex optimization is a well-established research area with applications in almost all fields. Over the decades, multiple approaches have been proposed to solve convex programs. The development of interior-point methods allowed solving a…

Camera pose tracking attracts much interest both from academic and industrial communities, of which the methods based on planar markers are easy to be implemented. However, most of the existing methods need to identify multiple points in…

Relative pose estimation, a fundamental computer vision problem, has been extensively studied for decades. Existing methods either estimate and decompose the essential matrix or directly estimate the rotation and translation to obtain the…

We propose a method for finding approximate solutions to multiple-choice knapsack problems. To this aim we transform the multiple-choice knapsack problem into a bi-objective optimization problem whose solution set contains solutions of the…

We reconsider the classic problem of estimating accurately a 2D transformation from point matches between images containing outliers. RANSAC discriminates outliers by randomly generating minimalistic sampled hypotheses and verifying their…

In this paper, we propose three methods to solve the PageRank problem for the transition matrices with both row and column sparsity. Our methods reduce the PageRank problem to the convex optimization problem over the simplex. The first…

Homographies are among the most prevalent transformations occurring in geometric computer vision and projective geometry, and homography estimation is consequently a crucial step in a wide assortment of computer vision tasks. When working…

In this paper we propose a global optimization-based approach to jointly matching a set of images. The estimated correspondences simultaneously maximize pairwise feature affinities and cycle consistency across multiple images. Unlike…

Energy minimization algorithms, such as graph cuts, enable the computation of the MAP solution under certain probabilistic models such as Markov random fields. However, for many computer vision problems, the MAP solution under the model is…

An understanding of the nature of objects could help robots to solve both high-level abstract tasks and improve performance at lower-level concrete tasks. Although deep learning has facilitated progress in image understanding, a robot's…

Polynomial optimization problems represent a wide class of optimization problems, with a large number of real-world applications. Current approaches for polynomial optimization, such as the sum of squares (SOS) method, rely on large-scale…

Pose Graph Optimization involves the estimation of a set of poses from pairwise measurements and provides a formalization for many problems arising in mobile robotics and geometric computer vision. In this paper, we consider the case in…

We present a mathematical and algorithmic scheme for learning the principal geometric elements in an image or 3D object. We build on recent work that convexifies the basic problem of finding a combination of a small number shapes that…