A Minimal Closed-Form Solution for Multi-perspective Pose Estimation using Points and Lines

Abstract

We propose a minimal solution for pose estimation using both points and lines for a multi-perspective camera. In this paper, we treat the multi-perspective camera as a collection of rigidly attached perspective cameras. These type of imaging devices are useful for several computer vision applications that require a large coverage such as surveillance, self-driving cars, and motion-capture studios. While prior methods have considered the cases using solely points or lines, the hybrid case involving both points and lines has not been solved for multi-perspective cameras. We present the solutions for two cases. In the first case, we are given 2D to 3D correspondences for two points and one line. In the later case, we are given 2D to 3D correspondences for one point and two lines. We show that the solution for the case of two points and one line can be formulated as a fourth degree equation. This is interesting because we can get a closed-form solution and thereby achieve high computational efficiency. The later case involving two lines and one point can be mapped to an eighth degree equation. We show simulations and real experiments to demonstrate the advantages and benefits over existing methods.

Minimal Solvers for Mini-Loop Closures in 3D Multi-Scan Alignment

“…Several solutions were proposed for the absolute pose for central perspective cameras (three 3D point correspondences between the world and image), see for example [19,17,55,41]. The pose estimation has also been studied for the pose of multi-perspective systems, such as [54,24,7,34]. When considering the relative pose estimation, several approaches have also been proposed for solving the minimal relative pose problem.…”

Method for Horizontal Alignment Deviation Measurement Using Binocular Camera Without Common Target

“…By introducing a nonlinear cost function, such as the reprojection error and collinear error of spatial points, the Gauss-Newton, Levenberg-Marquardt(LM) and other optimization algorithms are used to solve the problem iteratively [13], [14]. The other category comprises noniterative methods, which uses the mapping relationship between the cooperation targets and image projection points or the constraint relationship between the cooperation targets to establish the linear equations [15]- [18]. By using the method with the parameterized rotation matrix, the position problem is transformed into an optimization problem of the rotation parameters; subsequently, the polynomial equations of the rotation parameters are solved to obtain the closedform solution to calculate the position [19]- [22].…”

PLMP - Point-Line Minimal Problems in Complete Multi-View Visibility

“…Informally, a minimal problem is a 3D reconstruction problem recovering camera poses and world coordinates from given images such that random input instances have a finite positive number of solutions. Figure 1: (1-st row) Points (red) and lines (blue) get detected independently as well as in arrangements with points incident to lines [36]. (2-nd row) Examples of some interesting arrangements of points and lines providing new minimal problems.…”

“…Complete point-line incidence correspondences arise when, e.g. , SIFT point features [32] are considered together with their orientation, lines are constructed from matched affine frames [35], or obtained as simultaneous point and line detections [36], Fig. 1 1 .…”

“…Real images from[36] by courtesy of S. Ramalingam 2. Proving that the minimal problems with three or more views cannot be reformulated in a way that decreases the degrees that we report, or finding reformulations, may require more advanced algebraic techniques and presents a challenge for the future research.…”