# Accession Number:

## ADA276644

# Title:

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

# Descriptive Note:

# Corporate Author:

## CARNEGIE-MELLON UNIV PITTSBURGH PA DEPT OF COMPUTER SCIENCE

# Personal Author(s):

# Report Date:

## 1993-12-01

# Pagination or Media Count:

## 47.0

# 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.

# Descriptors:

- *MATHEMATICAL MODELS
- *SHAPE
- *LEAST SQUARES METHOD
- ALGORITHMS
- MEASUREMENT
- REGIONS
- PROBLEM SOLVING
- SURFACES
- MODEL TESTS
- ERRORS
- APPROACH
- FACTOR ANALYSIS
- TRANSFORMATIONS
- SEGMENTED
- SEQUENCES(MATHEMATICS)
- ROTATION
- EQUATIONS
- NOISE
- FRAMES
- IMAGES
- INTEGRATION
- WEIGHTING FUNCTIONS
- SEQUENCES
- MOTION
- MATRICES(MATHEMATICS)
- OBSERVATION

# Subject Categories:

- Numerical Mathematics
- Cybernetics