A hybrid steepest descent method for L-infinity geometry problems

Abstract

Recent work on geometric vision problems has exploited convexity properties to obtain globally optimal solutions. The way based on L-infinity norm makes it possible to obtain a provably global optimal solution. But the computation time increases rapidly according to the size of measurement data, so the time cost is unbearable for large scale data. We validate that L-infinity geometry problems is a variational inequality problem essentially and present a hybrid steepest descent method instead of traditional interior point algorithm to compute L-infinity solutions for large scale geometry problem. We give both theoretic justification and experimental verification. Experimental results verify that our method is extremely fast than traditional ones while keeps the accuracy. © 2012 Springer-Verlag.