DECOMPOSITION OF 3-D ARRAYS INTO SIMPLE OBJECTS.

摘要

In order to determine the physical properties of a rock sample represented digitally as a set of serial cross sections it is necessary first to decompose the sample into discrete objects and then to approximate each of those objects by another with well defined mathematical properties. In this thesis three general approaches to the decomposition problem are described: (I) Decomposition of single slices; (II) Decomposition of stacks of slices; and (III) Direct 3-D decomposition.; In single slice decomposition, individual slices are segmented independently of the other slices in the stack. We present four techniques for segmenting 2-D binary images into compact regions. In the first technique (crack following), we detect all "end-of-crack" pixels in the image, and extend these end-of-crack pixels in the direction of the cracks emanating from those pixels. In the second technique (pyramid joining), a pyramid representation of the contours is produced by iteratively applying a "contour preserving" sampling procedure which reduces the contour image while preserving the contours implicit in the original data. We then iteratively apply a downward projection operator which projects a low resolution contour image to the next higher resolution, with certain constraints that promote continuity and smoothness. The third technique, crack linking using the Voronoi diagram, makes use of a labeled Voronoi diagram to obtain closed boundaries from sets of broken boundary segments. The fourth technique uses a shrinking process.; The second method of decomposing 3-D objects into ellipsoid-like parts uses stacks of slices as input. The algorithm decomposes complex cross-sections of objects and connects single or decomposed cross-sections in order, so that the set of connected cross-sections represents a single 3-D object.; The method of direct 3-D decomposition decomposes three-dimensional complex objects into a set of compact subobjects, which are then represented by ellipsoidal approximations. The algorithm is a 3-D generalization of the technique of single slice decomposition by shrinking. However, the algorithm uses "convex enclosures" of objects for determining the compactness of the objects instead of using their 3-D convex hulls.