3D Shape Recovery from Endoscope Image Based on Both Photometric and Geometric Constraints

Abstract

An endoscope is a medical instrument that acquires images inside the human body. Sometimes, diagnosis requires assessment of the 3-D shape of observed tissue. For example, the pathology of a polyp often is related its geometrical shape. This chapter proposes a new approach for the 3-D shape recovery under the conditions of both point light illumination and perspective projection. The purpose of the proposed approach is to recover the direct shape of an object from an endoscope image using shape-from-shading approach. Observation model is assumed under the condition that both of a camera view point and a point light source are located at the origin and the goal is to recover the (X,Y,Z) coordinates at each point on the object. The previous approaches recover the shape based on Fast Marching Method (FMM) under the condition of parallel light source and orthographic projection, while proposed approach uses optimization technique based on the constraints of image irradiance equation and geometrical constraint. Photometric constraints are derived from the relation of observed image intensity and the surface gradient parameters and the depth parameter at each point, while the geometrical constraints use the geometrical relation between the depth at a point and the surface gradient parameters at the neighboring points. Optimization is used to determine the unique depth parameter at any point using both constraints from an initial point at the local brightest point. Proposed approach is evaluated via simulation and demonstrated through experiment. It is confirmed that the recovered shape improves the better performance than that by the previous approaches.