GAPS: 多項式方程式の自動ソルバー生成ツール

原文アブストラクト

Minimal problems in computer vision raise the demand of generating efficient automatic solvers for polynomial equation systems. Given a polynomial system repeated with different coefficient instances, the traditional Gr\"obner basis or normal form based solution is very inefficient. Fortunately the Gr\"obner basis of a same polynomial system with different coefficients is found to share consistent inner structure. By precomputing such structures offline, Gr\"obner basis as well as the polynomial system solutions can be solved automatically and efficiently online. In the past decade, several tools have been released to generate automatic solvers for a general minimal problems. The most recent tool autogen from Larsson et al. is a representative of these tools with state-of-the-art performance in solver efficiency. GAPS wraps and improves autogen with more user-friendly interface, more functionality and better stability. We demonstrate in this report the main approach and enhancement features of GAPS. A short tutorial of the software is also included.