Extending Fast Marching Method under Point Light Source Illumination and Perspective Projection

An endoscope is a medical instrument that acquires images inside the human body. An endoscope carries its own light source. Classic shape-from-shading can be used to recover the 3-D shape of objects in view. Recent implementations have used the Fast Marching Method (FMM). Previous FMM approaches recover 3-D shape under assumptions of parallel light source illumination and orthographic projection. This paper extends the FMM approach to recover the 3-D shape under more realistic conditions of endoscopy, namely nearby point light source illumination and perspective projection. The new approach is demonstrated through experiment and is seen to improve performance.