Inverse rendering of Lambertian surfaces using subspace methods.

Area of Science:

• Computer Vision
• Computer Graphics
• Computational Geometry

Background:

• Inverse rendering aims to recover object properties and lighting from images.
• Lambertian objects and distant light sources simplify rendering but pose challenges for inverse problems.
• Existing methods often struggle with noise and computational complexity.

Purpose of the Study:

• To develop a robust vector space approach for inverse rendering of Lambertian convex objects.
• To recover both object texture and arbitrary lighting conditions from multiple images.
• To formulate inverse rendering as a matrix factorization problem solvable via spherical harmonics.

Main Methods:

• Utilizing a low-dimensional linear subspace spanned by spherical harmonics to represent object images.
• Formulating inverse rendering as matrix factorization, encoding subspace basis in a spherical harmonic matrix (S).
• Introducing a 'nonseparable full rank' matrix property for unique factorization and employing Singular Value Decomposition (SVD) for noiseless cases, with alternating and optimization-based algorithms for noisy data.

Main Results:

• A necessary and sufficient condition for unique matrix factorization is derived.
• An exact factorization algorithm using SVD is presented for noiseless scenarios.
• Robust algorithms are proposed to handle different noise types, with a Random Sample Consensus (RANSAC) algorithm to optimize problem size.

Conclusions:

• The proposed vector space approach offers an effective method for inverse rendering of Lambertian objects.
• The matrix factorization framework based on spherical harmonics provides a theoretically sound and practically implementable solution.
• The algorithms demonstrate successful application on real-world datasets, highlighting their practical utility.