Masters Theses

Date of Award

12-1999

Degree Type

Thesis

Degree Name

Master of Science

Major

Electrical Engineering

Major Professor

M. A. Abidi

Abstract

Range images differ from conventional reflectance images because they give direct 3-D information about a scene. The last five years have seen a substantial increase in the use of range imaging technology in the areas of robotics, hazardous materials handling, and manufacturing. This has been fostered by a cost reduction of reliable range scanning products, resulting primarily from advanced development of computing resources. In addition, the improved performance of modern range cameras has spurred an interest in new calibrations which take account of their unconventional design.

Calibration implies both modeling and a numerical technique for finding parameters within the model. Researchers often refer to spherical coordinates when modeling range cameras. Spherical coordinates, however, only approximate the behavior of the cameras. We seek, therefore, a more analytical approach based on analysis of the internal scanning mechanisms of the cameras. This research demonstrates that the Householder matrix [14] is a better tool for modeling these devices.

We develop a general calibration technique which is both accurate and simple to implement. The method proposed here compares target points taken from range images to the known geometry of the target. The calibration is considered complete if the two point sets can be made to match closely in a least squares sense by iteratively modifying model parameters. The literature, fortunately, is replete with numerical algorithms suited to this task. We have selected the simplex algorithm because it is particularly well suited for solving systems with many unknown parameters.

In the course of this research, we implement the proposed calibration. We will find that the error in the range image data can be reduced from more that 60 mm per point rms to less than 10 mm per point. We consider this result to be a success because analysis of the results shows the residual error of 10 mm is due solely to random noise in the range values, not from calibration. This implies that accuracy is limited only by the quality of the range measuring device inside the camera.

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