Photometric stereo in Computer Vision

Photometric stereo is a technique used for reconstructing the 3D geometry of an object from images captured under different lighting conditions. The process involves using multiple images of an object taken from various light sources and directions to determine the surface normal at each point on the object's surface. Once the surface normal is known, the 3D shape of the object can be reconstructed. The technique assumes that the object's surface is locally Lambertian, and the reflected light intensity is proportional to the cosine of the angle between the surface normal and the direction of the incident light.

Photometric stereo faces challenges in dealing with shadows and interreflections that violate the Lambertian assumption, leading to errors in the estimated surface normal. Despite these challenges, photometric stereo has a wide range of applications, including computer graphics, robotics, and biomedical imaging, where it can be used to create realistic 3D models of objects, recognize and manipulate objects, and reconstruct biological tissue shapes from medical images.

The goal of this part of the project is to implement a standard photometric stereo algorithm. Assume Lambertian reflectance function, but the albedo is unknown and non-constant in the image. The implementation will take in multiple images as input along with the light source direction for each image.