Specification and Implementation of Age, Period and Cohort Models

Abstract

Observation-based object modeling often requires integration of shape descriptions from different views. In current conventional methods, to sequentially merge multiple views, accurate description of each surface patch has to be precisely known in each view and trans- formation between any adjacent views needs to be accurately recovered. When noisy data and mismatches are present, recovered transformation becomes erroneous. In addition, the transformation error accumulates and propagates along the sequence, which results in an inaccurate object model. To overcome these problems, we have developed a weighted least square (WLS) approach which simultaneously recovers object shape and transformation among different views without recovering inter-frame motion as an intermediate step. We show that object modeling from a sequence of range images is a problem of principal component analysis with missing data (PCAMD), which can be generalized as a WLS mini- mization problem. Andefficient algorithm is devised to solve the problem of PCAMD. After we have segmented surface regions in each view and tracked over all the sequence, we con- struct a 3F x P normal measurementmatrix of surface normals, and an F x P distancemea- surement matrix of normal distances to the origin for all visible P regions appeared over the whole sequence of F views, respectively. These two measurement 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, which employs the quaternion representation of the rotation matrix, is presented to compute surface descriptions and transformations among different views simultaneously. After sur- face equations are extracted, spatial connectivity among these surfaces is established to enable the object model to be reconstructed. Experiments using synthetic data and real range images show that our approach is robust against noise and mismatching and generates accurate object model by averaging over all visible surfaces. Specifically, using a sequence of real range images, we illustrate the recon- struction of a toy house model.