Optimisation of photometric stereo methods by non-convex variational minimisation

TL;DR

This paper introduces a novel non-convex variational approach for photometric stereo that directly estimates scene depth from images, offering improved accuracy over existing methods through advanced optimization and convergence analysis.

Contribution

It presents a new variational model for photometric stereo using depth reprojection error and employs matrix differential calculus with convergence analysis, advancing the theoretical understanding of the optimization process.

Findings

Achieves more accurate depth estimation than competing methods.

Provides a detailed convergence analysis of the non-convex optimization scheme.

Discusses computational complexity reduction strategies.

Abstract

Estimating shape and appearance of a three dimensional object from a given set of images is a classic research topic that is still actively pursued. Among the various techniques available, PS is distinguished by the assumption that the underlying input images are taken from the same point of view but under different lighting conditions. The most common techniques provide the shape information in terms of surface normals. In this work, we instead propose to minimise a much more natural objective function, namely the reprojection error in terms of depth. Minimising the resulting non-trivial variational model for PS allows to recover the depth of the photographed scene directly. As a solving strategy, we follow an approach based on a recently published optimisation scheme for non-convex and non-smooth cost functions. The main contributions of our paper are of theoretical nature. A technical novelty in our framework is the usage of matrix differential calculus. We supplement our approach by a detailed convergence analysis of the resulting optimisation algorithm and discuss possibilities to ease the computational complexity. At hand of an experimental evaluation we discuss important properties of the method. Overall, our strategy achieves more accurate results than competing approaches. The experiments also highlights some practical aspects of the underlying optimisation algorithm that may be of interest in a more general context.