Fast geometric trim fitting using partial incremental sorting and accumulation

TL;DR

This paper introduces a fast, efficient algorithm for geometric trim fitting in outlier-affected regression problems, leveraging partial sorting and incremental updates to improve computational speed and reliability.

Contribution

The paper presents a novel algorithm that uses partial sorting and incremental updates for robust trim fitting in geometric regression, applicable to both linear and non-linear problems.

Findings

Significantly faster trim fitting in geometric problems

Reliable performance in camera resectioning tasks

Applicable to both linear and non-linear energy minimization

Abstract

We present an algorithmic contribution to improve the efficiency of robust trim-fitting in outlier affected geometric regression problems. The method heavily relies on the quick sort algorithm, and we present two important insights. First, partial sorting is sufficient for the incremental calculation of the x-th percentile value. Second, the normal equations in linear fitting problems may be updated incrementally by logging swap operations across the x-th percentile boundary during sorting. Besides linear fitting problems, we demonstrate how the technique can be additionally applied to closed-form, non-linear energy minimization problems, thus enabling efficient trim fitting under geometrically optimal objectives. We apply our method to two distinct camera resectioning algorithms, and demonstrate highly efficient and reliable, geometric trim fitting.