Lambertian Case | Photometric Stereo

Lambertian Case | Photometric Stereo

by Shree Nayar

Formal & Physical Sciences AI — Models & Research UYQArtificial intelligence (AI)UYQVComputer vision
🎙 Shree Nayar 👥 96K 📅 March 21, 2021 ⏱ 18 min 👁 12K 📄 tutorial 🧭 2026-08-17
Available in: English (current) Français

Keywords

photometric stereoLambertiansurface normalalbedoleast squares

Summary

This lecture from the ‘First Principles of Computer Vision’ series, presented by Shree Nayar, focuses on the Lambertian case in photometric stereo. It begins by deriving the image intensity equations for multiple light sources, leading to a matrix formulation I = S N, where S is the source matrix and N combines albedo and surface normal. With three non-coplanar light sources, the matrix can be inverted to recover both surface normal and albedo at each point. The lecture discusses conditions where this fails, such as when light sources lie in a plane, and illustrates this with the equinox and winter solstice for outdoor photometric stereo. It then extends to using more than three light sources, introducing the least squares solution via the pseudo-inverse. A key property is presented: for Lambertian surfaces, multiple light sources can be replaced by a single effective point light source. The lecture concludes with experimental results on a sphere, a mask, and a toy, demonstrating normal and albedo maps, and noting limitations with non-Lambertian surfaces.

169 words

Critical Evaluation

Value of the Information & Strength of the Argument

The lecture provides high-value information by clearly explaining the mathematical foundations of photometric stereo for Lambertian surfaces. It systematically derives the equations, discusses the invertibility condition, and introduces the least squares method for robustness. The argumentation is solid, building from basic principles to practical applications, and includes illustrative examples and visual results. The explanation of the effective light source property is particularly insightful, offering a deeper understanding of Lambertian reflectance.

79 words

Title / Content Match

The title accurately reflects the content, which focuses on the Lambertian case in photometric stereo.

Quality & Reliability

9/10

The content is a rigorous lecture by a leading expert (Shree Nayar) from Columbia University, presenting mathematical derivations and practical considerations for photometric stereo. The explanations are clear, well-structured, and based on established principles. The video is part of a reputable educational series.

Key Moments

Markers derived by PSI from the transcript: the creator did not define chapters.

Contribution & Novelties

The lecture provides a clear and comprehensive explanation of photometric stereo for Lambertian surfaces, including the mathematical derivation, practical considerations, and the effective light source property. It is valuable for students and practitioners new to computer vision.

Pour aller plus loin :

82 words

Radar Profile

The radar profile shows high scores in quality and reliability, with slightly lower but still strong scores in quantity and technical level. This indicates a well-produced, informative lecture that is technically sound and reliable.

Reliability 9/10