Principal Component Analysis with Missing Data and its Application to Polyhedral Object Modeling

Abstract

Observation-based object modeling often requires integration of shape descriptions from different views. To overcome the problems of errors and their accumulation, we have developed a weighted least-squares (WLS) approach which simultaneously recovers object shape and transformation among different views without recovering interframe motion. We show that object modeling from a range image sequence is a problem of principal component analysis with missing data (PCAMD), which can be generalized as a WLS minimization problem. An efficient algorithm is devised. After we have segmented planar surface regions in each view and tracked them over the image sequence, we construct a normal measurement matrix of surface normals, and a distance measurement matrix of normal distances to the origin for all visible regions over the whole sequence of views, respectively. These two matrices, which have many missing elements due to noise, occlusion, and mismatching, enable us to formulate multiple view merging as a combination of two WLS problems. A two-step algorithm is presented. After surface equations are extracted, spatial connectivity among the surfaces is established to enable the polyhedral object model to be constructed. Experiments using synthetic data and real range images show that our approach is robust against noise and mismatching and generates accurate polyhedral object models.