On the Regularising Levenberg-Marquardt Method for Blinn-Phong Photometric Stereo

TL;DR

This paper investigates the regularising Levenberg-Marquardt method for solving the non-linear optimization problem in photometric stereo using Blinn-Phong reflectance, providing convergence analysis and experimental validation.

Contribution

It introduces a convergence bound for the Levenberg-Marquardt scheme in Blinn-Phong photometric stereo and demonstrates its numerical correctness through experiments.

Findings

Derived explicit convergence bounds for the method

Provided experimental evidence supporting theoretical results

Validated approach with real-world images

Abstract

Photometric stereo refers to the process to compute the 3D shape of an object using information on illumination and reflectance from several input images from the same point of view. The most often used reflectance model is the Lambertian reflectance, however this does not include specular highlights in input images. In this paper we consider the arising non-linear optimisation problem when employing Blinn-Phong reflectance for modeling specular effects. To this end we focus on the regularising Levenberg-Marquardt scheme. We show how to derive an explicit bound that gives information on the convergence reliability of the method depending on given data, and we show how to gain experimental evidence of numerical correctness of the iteration by making use of the Scherzer condition. The theoretical investigations that are at the heart of this paper are supplemented by some tests with real-world imagery.