QRkit: Sparse, Composable QR Decompositions for Efficient and Stable Solutions to Problems in Computer Vision
| Autor: | Jan Svoboda, Thomas J. Cashman, Andrew Fitzgibbon |
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| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
FOS: Computer and information sciences
Floating point business.industry Computer science Concatenation Computer Science - Numerical Analysis Block matrix 010103 numerical & computational mathematics 02 engineering and technology Numerical Analysis (math.NA) 01 natural sciences Single-precision floating-point format QR decomposition Matrix decomposition 0202 electrical engineering electronic engineering information engineering FOS: Mathematics 020201 artificial intelligence & image processing Computer vision Computer Science - Mathematical Software Artificial intelligence 0101 mathematics business Mathematical Software (cs.MS) Cholesky decomposition Sparse matrix |
| Zdroj: | WACV |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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