QRkit: Sparse, Composable QR Decompositions for Efficient and Stable Solutions to Problems in Computer Vision

TL;DR

QRkit provides efficient, stable, and sparse QR decomposition solvers tailored for common computer vision sparsity patterns, enabling accurate single-precision optimization solutions.

Contribution

Introduces an open-source suite of sparse QR solvers for Eigen, allowing composable and efficient solutions for specific sparsity patterns in computer vision.

Findings

Competitive performance in computer vision tasks

Effective in single-precision arithmetic

Supports common sparsity patterns in matrices

Abstract

Embedded computer vision applications increasingly require the speed and power benefits of single-precision (32 bit) floating point. However, applications which make use of Levenberg-like optimization can lose significant accuracy when reducing to single precision, sometimes unrecoverably so. This accuracy can be regained using solvers based on QR rather than Cholesky decomposition, but the absence of sparse QR solvers for common sparsity patterns found in computer vision means that many applications cannot benefit. We introduce an open-source suite of solvers for Eigen, which efficiently compute the QR decomposition for matrices with some common sparsity patterns (block diagonal, horizontal and vertical concatenation, and banded). For problems with very particular sparsity structures, these elements can be composed together in 'kit' form, hence the name QRkit. We apply our methods to several computer vision problems, showing competitive performance and suitability especially in single precision arithmetic.