Title:	MinBackProp – Backpropagating through Minimal Solvers
Authors:	Sungatullina, Diana Pajdla, Tomáš
Citation:	Journal of WSCG. 2024, vol. 32, no. 1-2, p. 41-50.
Issue Date:	2024
Publisher:	Václav Skala - UNION Agency
Document type:	článek article
URI:	http://hdl.handle.net/11025/57343
ISSN:	1213 – 6972 1213 – 6980 (CD-ROM) 1213 – 6964 (on-line)
Keywords:	minimální řešitelé;epipolární geometrie;zpětné šíření;odstranění odlehlých hodnot;implicitní funkce
Keywords in different language:	minimal solvers;epipolar geometry;backpropagation;outlier removal;implicit function theorem
Abstract in different language:	We present an approach to backpropagating through minimal problem solvers in end-to-end neural network train ing. Traditional methods relying on manually constructed formulas, finite differences, and autograd are laborious, approximate, and unstable for complex minimal problem solvers. We show that using the Implicit function the orem (IFT) to calculate derivatives to backpropagate through the solution of a minimal problem solver is simple, fast, and stable. We compare our approach to (i) using the standard autograd on minimal problem solvers and relate it to existing backpropagation formulas through SVD-based and Eig-based solvers and (ii) implementing the backprop with an existing PyTorch Deep Declarative Networks (DDN) framework [GHC22]. We demonstrate our technique on a toy example of training outlier-rejection weights for 3D point registration and on a real application of training an outlier-rejection and RANSAC sampling network in image matching. Our method provides 100% stability and is 10 times faster compared to autograd, which is unstable and slow, and compared to DDN, which is stable but also slow
Rights:	© Václav Skala - UNION Agency © Václav Skala - UNION Agency
Appears in Collections:	Volume 32, number 1-2 (2024)

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