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

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 transformation 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 minimization problem. An efficient 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 construct a 3F x P normal measurement matrix of surface normals, and an F x P distance measurement 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.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1993
Accession Number
ADA276644

Entities

People

  • Heung-yeung Shum
  • Katsushi Ikeuchi
  • Raj Reddy

Organizations

  • Carnegie Mellon University

Tags

Communities of Interest

  • Air Platforms
  • Ground and Sea Platforms
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • Algorithms
  • Computational Science
  • Computer Science
  • Computer Vision
  • Coordinate Systems
  • Equations
  • Extrapolation
  • Factor Analysis
  • Gaussian Noise
  • Geometry
  • Image Segmentation
  • Object Recognition
  • Polygons
  • Shape
  • Statistics
  • Virtual Reality

Fields of Study

  • Computer science

Readers

  • Computational Modeling and Simulation
  • Computer Vision.