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

  • Authors:

  • Heung-Yeung Shum;Katsushi Ikeuchi;Raj Reddy

  • Affiliations:

  • Robotics Institute, Carnegie Mellon University, Pittsburgh, PA;Robotics Institute, Carnegie Mellon University, Pittsburgh, PA;Robotics Institute, Carnegie Mellon University, Pittsburgh, PA

  • Venue:
  • IEEE Transactions on Pattern Analysis and Machine Intelligence
  • Year:
  • 1995

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Abstract

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 surface patch has to be precisely known in each view, and the transformation between adjacent views needs to be accurately recovered. When noisy data and mismatches are present, the recovered transformation become erroneous. In addition, the transformation errors accumulate and propagate 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 transformation among different views without recovering interframe 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 minimization problem. An 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 sequence of 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 is presented to computer planar surface descriptions and transformations among different views simultaneously. After surface equations are extracted, spatial connectivity among these 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 by averaging over all visible surfaces. Two examples are presented to illustrate the reconstruction of polyhedral object models from sequences of real range images.