Photometric stereo applied to diffuse surfaces that violate Lambert's law

Area of Science:

• Computer Vision
• Surface Metrology
• Optical Engineering

Background:

• Photometric stereo (PS) typically assumes Lambertian reflectance, limiting its application to idealized surfaces.
• Real-world surfaces often exhibit non-Lambertian diffuse reflectance, such as those modeled by the Oren-Nayar (ON) function.
• Understanding the limitations and applicability of PS for non-Lambertian surfaces is crucial for accurate 3D reconstruction.

Purpose of the Study:

• To investigate the efficacy of standard photometric stereo (PS) for surfaces with non-Lambertian reflectance.
• To define criteria for the successful application of PS beyond Lambertian surfaces.
• To evaluate the performance of PS using the Oren-Nayar (ON) reflectance model for rough surfaces.

Main Methods:

• Simulations were conducted using the ON reflectance model to predict surface reflectance functions.
• PS was applied to both simulated and real rough test surfaces.
• Surface microstructure was characterized by root-mean-square (rms) slope.

Main Results:

• Standard PS demonstrated applicability to non-Lambertian surfaces under specific light source arrangements (90° intervals).
• The ON model accurately predicted reflectance functions for tested rough surfaces.
• PS simulations showed good performance for moderate microroughness (rms slope <0.3).
• Real-surface experiments revealed high correlation between estimated and actual slopes, but significant errors for rougher samples.

Conclusions:

• Photometric stereo can be extended to non-Lambertian surfaces, particularly with specific lighting geometries.
• The Oren-Nayar model is suitable for representing reflectance of rough surfaces.
• PS accuracy is dependent on surface microroughness, with performance degrading for rougher samples.