SHAPE: Linear-Time Camera Pose Estimation With Quadratic Error-Decay

TL;DR

SHAPE is a new linear-time camera pose estimation algorithm that guarantees quadratic decay of reconstruction error with increasing feature points, outperforming existing methods in accuracy and efficiency.

Contribution

The paper introduces SHAPE, a novel PnP algorithm based on consistency regions and half-space intersections, with proven quadratic error decay and linear time complexity.

Findings

Quadratic error decay verified through experiments

SHAPE outperforms state-of-the-art methods in accuracy

Algorithm operates in linear time with respect to feature points

Abstract

We propose a novel camera pose estimation or perspective-n-point (PnP) algorithm, based on the idea of consistency regions and half-space intersections. Our algorithm has linear time-complexity and a squared reconstruction error that decreases at least quadratically, as the number of feature point correspondences increase. Inspired by ideas from triangulation and frame quantisation theory, we define consistent reconstruction and then present SHAPE, our proposed consistent pose estimation algorithm. We compare this algorithm with state-of-the-art pose estimation techniques in terms of accuracy and error decay rate. The experimental results verify our hypothesis on the optimal worst-case quadratic decay and demonstrate its promising performance compared to other approaches.