PRINCIPAL COMPONENT ANALYSIS WITH MISSING DATA AND ITS APPLICATION TOPOLYHEDRAL OBJECT MODELING

Observation-based object modeling often requires integration of shape descriptions from different views. In current conventional methods, to sequentially merge multiple views, an accurate description of each su rface patch has to be precisely known in each view, and the transforma tion between adjacent views needs to be accurately recovered. When noi sy data and mismatches are present, the recovered transformation becom e erroneous. In addition, the transformation errors accumulate and pro pagate along the sequence, resulting in an inaccurate object model. To overcome these problems, we have developed a weighted least-squares ( WLS) approach which simultaneously recovers object shape and transform ation among different views without recovering interframe motion as an intermediate step. We show that object modeling from a sequence of ra nge images is a problem of principal component analysis with missing d ata (PCAMD), which can be generalized as a WLS minimization problem. A n efficient algorithm is devised to solve the problem of PCAMD, 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 appeared over the whole sequenc e of views, respectively. These two measurement matrices, which have m any missing elements due to noise, occlusion, and mismatching, enable us to formulate multiple view merging as a combination of two WLS prob lems. A two-step algorithm is presented to computer planar surface des criptions and transformations among different views simultaneously, Af ter surface equations are extracted, spatial connectivity among these surfaces is established to enable the polyhedral object model to be co nstructed. Experiments using synthetic data and real range images show that our approach is robust against noise and mismatching and generat es accurate polyhedral object models by averaging over all visible sur faces. Two examples are presented to illustrate the reconstruction of polyhedral object models from sequences of real range images.