Estimating the Cook-Torrance BRDF Parameters In-Vivo from Laparoscopic Images

SfS (Shape-from-Shading) and view synthesis systems gener ally assume a diffuse reflection model of the in-vivo tissues where t he light is equally reflected in all directions. In other words, they approximat e the tissue’s BRDF (Bidirectional Reflectance Distribution Function) by the L ambertian model. This is however a coarse assumption since most tissues cast specu larities. We propose a method to estimate the reflectance properties of ti sues from invivo laparoscopic images. We use the Cook-Torrance BRDF mod el in order to take into account both diffuse and specular properties of th e tissues. Our method estimates online both the BRDF parameters of the observed or gan and the light model of the laparoscope. Such an estimation requires the kn owledge of the 3D shape and some geometric priors on the light source. For thes e rea ons, our estimation method relies on two assumptions: firstly, that the ti ssues undergoes rigid motion when the surgeon only explores it, and secondly that l aparoscope’s light is colinear to the viewing direction in a neighborhood ring a round the specular regions. The first assumption allows us to estimate the 3D sha pe of the organ using for instance classic RSfM (Rigid Structure-from-Mot ion). The second assumption allows us to estimate the BRDF parameters. The dete rmination of the 3D shape and the BRDF parameters allows us to assign a light di rection for each pixel of the image. Experimental results compare the perfor mance of our joint BRDF-and-light estimation method with the widely used Lamb ertian model. This validation uses both ex-vivo and real in-vivo datasets. It r eveals a substantial improvement on SfS 3D reconstruction.