Divide-and-conquer strategy in shape from shading problem

A divide-and-conquer strategy in shape from shading problem under fully perspective condition is proposed for the information recovery of book surfaces. The whole recovery process is composed of three sequential steps : preprocessing, apparent shape recovery, and ortho-image generation. Pure shade images are extracted at preprocessing step by introducing phenomenological model of interreflection and by removing pigment parts from observed images. Using existing invariances, equations of slope and that of ortho-image being explicit are derived from equation of shading and that of observation being implicit. Recurrence relation is derived from definition of mean slope in discrete image. Theoretically, it become possible to recover unique shape without iteration using derived equations in case of Lambertian cylinder. However, a feed-back shape recovery process is implemented as practical algorithm in order to overcome self-shadows. Results of simulations and real experiments show the properness and acceptability of the proposed strategy and implemented algorithms.