The Information Available to a Moving Observer on Shape with Unknown, Isotropic BRDFs

Area of Science:

• Computer Vision
• Computational Imaging
• Robotics

Background:

• Shape perception relies on motion cues, even with unknown surface reflectance.
• Existing methods recover object shape using light source or object motion for unknown Bidirectional Reflectance Distribution Functions (BRDFs).

Purpose of the Study:

• To develop a theory for shape recovery from differential camera motion for unknown isotropic BRDFs.
• To generalize traditional Lambertian assumptions in shape from motion studies.

Main Methods:

• Derivation of a differential stereo relation connecting camera motion to surface depth.
• Analysis under orthographic and perspective projection models.
• Investigation of constraints imposed by BRDF properties and lighting conditions.

Main Results:

• The differential stereo relation generalizes Lambertian assumptions.
• Under orthographic projection, shape is not always determined but invariants exist for restricted BRDFs.
• Under perspective projection, surface depth is determined for unknown isotropic BRDFs and directional lighting.

Conclusions:

• The derived theory provides a fundamental framework for shape recovery from camera motion with unknown BRDFs.
• The complexity of the imaging setup influences the difficulty of surface reconstruction.
• The intrinsic limits of shape recovery are independent of the chosen reconstruction method.