Representing and Analyzing 3D Digital Shape Using Distance Information

Stina Svensson

Akademisk avhandling i bild- och fjärranalys som, för vinnande av filosofie doktorsexamen, kommer att offentligen försvaras i sal 10132, Ångströmlaboratoriet, Uppsala, fredagen den 23 november 2001, kl. 13.00.

Abstract

The increase in number and decrease in cost for devices giving digital three-dimensional (3D) images have implied that the number of application areas where 3D images are used has increased lately. In fact, 3D images are important in many medical and industrial applications. Using a computer for analyzing images facilitates quantitative studies of image data. This is even more relevant when dealing with 3D images as they contain huge amounts of data and cannot be directly inspected by humans.

Many basic image analysis tools used for 2D images are not yet fully developed for 3D images. A goal would be to be able to use all methods introduced for 2D images also for 3D images. With this thesis, we want to fill part of this gap. We deal with algorithms used when the interesting part of the image, the object, has already been identified.

We present theoretical results on optimization done for computing distances in the image, giving results more stable under rotation without loss of computation simplicity. We also present various shape analysis methods using distance based algorithms. The shape analysis methods included are multiresolution representations of the object, where the object is represented by images at different resolutions, a decomposition scheme for the object, where the object is decomposed into simpler parts, and skeletonization of the object, where the object is represented by a structure of lower dimension.

Finally, distance based methods are applied to 3D images of paper. The aim is to have a deeper understanding of the 3D geometrical structure of the fibre network and of its effect on the optical and mechanical properties of paper.

Key words: image analysis, volume images, shape description, distance transformation, multiresolution representation, decomposition, skeletonization, fibre network, paper structure.

Distribution:
Swedish University of Agricultural Sciences
Centre for Image Analysis
Lägerhyddsvägen 17
SE-752 37 Uppsala, Sweden

Uppsala 2001
ISSN 1401-6230
ISBN 91-576-6095-6