← 研踪 PaperTrailCVF · CVPR 2026:cvf:caa80fd104f3093279c3975076e90c6c · 记录 #1
Solving Minimal Problems Without Matrix Inversion Using FFT-Based Interpolation
来源日期（仅到年份） 2026
来源记录日期 2026
雷达观测 2026-11-01 23:04
摘要
Estimating camera geometry typically involves solving minimal problems formulated as systems of multivariate polynomial equations, which often pose computational challenges when using existing Grobner-basis or resultant-based methods due to matrix inversion needed in the online solver. Here we propose a sampling-based, matrix inversion-free method that constructs the solvers using sparse hidden-variable resultants. The determinant polynomial in the hidden variable is efficiently reconstructed via inverse fast Fourier transform interpolation from sampled evaluations, avoiding symbolic expansion. Solving this polynomial yields the hidden variable, and the remaining unknowns are recovered by identifying rank-1 deficient submatrices and applying Cramer's rule. A greatest common divisor-based criterion ensures robust submatrix identification under noise. Experiments on diverse minimal problems demonstrate that the proposed solver achieves strong numerical stability and competitive runtime, particularly for small-scale problems, providing a practical alternative to traditional Grobner-basis and resultant-based solvers.
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记录 #1 · 2026 · 最新观测版本
Solving Minimal Problems Without Matrix Inversion Using FFT-Based Interpolation
Estimating camera geometry typically involves solving minimal problems formulated as systems of multivariate polynomial equations, which often pose computational challenges when using existing Grobner-basis or resultant-based methods due to matrix inversion needed in the online solver. Here we propose a sampling-based, matrix inversion-free method that constructs the solvers using sparse hidden-variable resultants. The determinant polynomial in the hidden variable is efficiently reconstructed via inverse fast Fourier transform interpolation from sampled evaluations, avoiding symbolic expansion. Solving this polynomial yields the hidden variable, and the remaining unknowns are recovered by identifying rank-1 deficient submatrices and applying Cramer's rule. A greatest common divisor-based criterion ensures robust submatrix identification under noise. Experiments on diverse minimal problems demonstrate that the proposed solver achieves strong numerical stability and competitive runtime, particularly for small-scale problems, providing a practical alternative to traditional Grobner-basis and resultant-based solvers.
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