Statistical angular error-based triangulation for efficient and accurate multi-view scene reconstruction

Abstract

This paper presents a framework for N -view triangulation of scene points, which improves processing time and final reprojection error with respect to standard methods, such as linear triangulation. The framework introduces an angular error-based cost function, which is robust to outliers and inexpensive to compute, and designed such that simple adaptive gradient descent can be applied for convergence. Our method also presents a statistical sampling component based on confidence levels, that reduces the number of rays to be used for triangulation of a given feature track. It is shown how the statistical component yields a meaningful yet much reduced set of representative rays for triangulation, and how the application of the cost function on the reduced sample can efficiently yield faster and more accurate solutions. Results are demonstrated on real and synthetic data, where it is proven to significantly increase the speed of triangulation and optimize reprojection error in most cases. This makes it especially attractive for efficient triangulation of large scenes given the speed and low memory requirements.

Fury of the Swarm: Efficient and Very Accurate Triangulation for Multi-view Scene Reconstruction

“…To this end, a recent triangulator by Recker et al [16] solves several of these issues. Their framework introduces an angular error-based L 1 cost function, which is robust to outliers and inexpensive to compute.…”

“…It is not plagued by numerical stability or precision issues. The algorithm is based on applying swarm optimization based on Recker et al's triangulation cost function [16], both of which will be discussed in detail.…”

“…Recker et al [16] proposed an L 1 triangulation cost function based on an angular error measure for a candidate 3D position, p, with respect to a feature track t. As input, a set of feature tracks across N images and their respective 3 × 4 camera projection matrices P i are known. The error for a candidate 3D position p is computed as follows.…”

“…sTherefore, while this two-phase procedure can be very accurate, there is always a risk of converging to a local minima of the cost function, especially when starting far from the solution. A recent triangulator by Recker et al [16] uses a novel L 1 angular error cost function, which is optimized with adaptive gradient descent given an initial midpoint estimate. It shows a significant speed increase and better reprojection errors than other triangulators, such as N -view linear.…”

“…There are two main novelties of this framework with respect to the previous literature. The first is a non-polynomial solution to the optimization problem, based on minimizing an L 1 -based cost function [16]. The second is the introduction of a swarm optimization algorithm, applied on this cost function.…”