# Solving Uncalibrated Photometric Stereo Using Fewer Images by Jointly Optimizing Low-rank Matrix Completion and Integrability

## TL;DR

This paper presents an integrated optimization method for uncalibrated photometric stereo that effectively reconstructs 3D shapes from as few as 4-6 images by jointly enforcing low-rank and integrability constraints.

## Contribution

It introduces a novel unified optimization framework using ADMM that incorporates rank, integrability, and missing data constraints for better 3D reconstruction.

## Key findings

- Improved 3D reconstruction quality with fewer images (4-6)
- Effective handling of missing data in photometric stereo
- Significant performance gains over prior methods in experiments

## Abstract

We introduce a new, integrated approach to uncalibrated photometric stereo. We perform 3D reconstruction of Lambertian objects using multiple images produced by unknown, directional light sources. We show how to formulate a single optimization that includes rank and integrability constraints, allowing also for missing data. We then solve this optimization using the Alternate Direction Method of Multipliers (ADMM). We conduct extensive experimental evaluation on real and synthetic data sets. Our integrated approach is particularly valuable when performing photometric stereo using as few as 4-6 images, since the integrability constraint is capable of improving estimation of the linear subspace of possible solutions. We show good improvements over prior work in these cases.