Critical Points for Two-view Triangulation

TL;DR

This paper derives a polynomial to identify local minimizers in two-view triangulation, simplifying the process of finding critical points and building on Hartley-Sturm's foundational work.

Contribution

It introduces a new polynomial formulation for local minimizers in two-view triangulation, providing a simpler derivation based on Lagrange multipliers.

Findings

Derived a polynomial encoding local minimizers

Simplified the derivation of critical points

Built upon Hartley-Sturm's previous results

Abstract

Two-view triangulation is a problem of minimizing a quadratic polynomial under an equality constraint. We derive a polynomial that encodes the local minimizers of this problem using the theory of Lagrange multipliers. This offers a simpler derivation of the critical points that are given in Hartley-Sturm [6].