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Thesis in Image Analysis and Remote Sensing for the degree of Doctor of Philosophy.
Keywords: image analysis, volume images, shape description, distance transformation, multiresolution representation, decomposition, skeletonization, fibre network, paper structure.
A short abstract of the thesis can be found on spikbladet.
The doctoral studies started in January 1997 and the dissertation was November 23, 2001. The research included in the thesis is briefly described below.
During the doctoral studies Gunilla Borgefors, Centre for Image Analysis, and Gabriella Sanniti di Baja, Istituto di Cibernetica, CNR, Pozzuoli (Napoli), Italy have been supervising. A lot of guidance has also been provided by Ingela Nyström, Centre for Image Analysis. Paper VIII was done in cooperation with Mattias Aronsson, Centre for Image Analysis.
This page will only be updated to change the submission/acceptance status of the included papers.
Current research activity is presented on my research page. There an updated list of publications and CV can be found.
The research is divided into the same sub groups as was used in the thesis.
In Paper I, distance transforms using from one to six steps in a 5x5x5 neighbourhood of a voxel are presented. Real-valued optimal local distances for the steps are given as well as suggestions for good integer weighted distance transforms.
The neighbourhood relations from a 5x5x5 neighbourhood are denoted a,b,c,d,e,f (after increasing Euclidean distance) and the distance transforms using a combination of steps as the steps enclosed by parenthesis. Below, balls computed using the optimal local distances for the respective combination of steps are shown.
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| (a) | (a,c) | (a,b,c) |
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| (a,b,c,e) | (a,b,c,d,e) | (a,b,c,d,e,f) |
The distance transforms are all semi-regular, i.e., a straight path is a minimal path, which is a condition necessary but not sufficient for the distance transform to indicate a metric.
A resolution pyramid is a representation consisting of a number of images with different resolution. The object is represented by a multiresolution structure. In Paper II, three different approaches for computing resolution pyramids that are shape preserving and stable under translation are presented. The result obtained by using one of the presented methods can be seen below. Note that voxels are shown with increasing size for an easier interpretation of the result.
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| level 1 | level 2 | level 3 | level 4 |
In Paper III, a method for decomposing an object into simpler parts is presented. The internal cores of the parts are detected on the distance transform of the object and the corresponding parts obtained by a region growing process from them. As any distance transform can used, a decomposition stable under rotation can be obtained. The parts can be described as nearly convex and elongated parts. The elongated parts are either necks or protrusions. The man-like object shown below is decomposed into two nearly convex parts, the head and the body, one neck, the neck, and four protrusions, the arms and the legs.
In Papers IV and V, two different approaches for computing the surface skeleton of a 3D object are proposed. The resulting surface skeleton are topologically equivalent to the original object, centred within the object, and fully reversible. As reversibility is stressed, the surface skeleton is not necessarily one-voxel thick.
In Paper IV, a general framework for thinning the distance transform of the object to a surface skeleton is presented. So far D6 and D26 distance transform have been treated. See the example below.
In Paper V, skeletal voxels are instead directly detected on the distance transform of the object in a number of scans, less than for the iterative method for thick objects. So far this approach has been followed for D6. See the example below.
Surfaces, e.g., those originating from a surface skeletonization algorithm, can be further reduced to a set of curves, a linear representation. In Papers VI and VII, two approaches to compute a linear representation starting from a surface-like object, i.e., an object where one of the three dimensions are disregardable (at most two-voxel thick), are presented.
In Paper VI, a shape descriptor of a surface-like object is extracted from the distance transform of surface-like object. The distance transform is computed by propagation of distance information from the border of the surface-like object. The approach to extract the shape descriptor is similar to the one used to extract a skeleton of a 2D planar pattern. Note that the result is not topologically equivalent to the surface-like object.
In Paper VII, an algorithm for computing the curve skeleton starting from a surface-like object is presented. The algorithm is based on thinning of the surface-like object, border after border. Voxels significant for preserving the shape and the topology of the surface-like object are kept during the thinning. We consider voxels placed in curves and junctions in the surface-like object as significant for shape preservation.
In Paper VIII, distance transform based methods are used for measuring fibres in a 3D images of paper. The measures are intended to be used for analysis of the fibre network structure and its optical and mechanical effects on the paper. For easier analysis, surface and curve representations are extracted for the fibre, the fibre wall, and the fibre lumen. The curve representation is divided into different segments corresponding to part of the fibre which is bonded to other fibres and parts with free-fibre.
Below a set of synthetic fibres are shown. The surface representation for the fibre wall, the curve representation for the fibre lumen and the division of the curve into segments are shown for the fibre with red wall in the bottom line.
Methods for computing wall thickness, fibre length, degree of collaps, fibre curl, slenderness ratio, and torsional resistance for individual fibres and for fibre segments are presented. Moreover, a method for computing the density of the paper and tools for visual inspection of the fibres are suggested. The measures are computed for a sample volume.
During my PhD studies I have participated in the following international scientific conferences and courses (oral and poster presentations as well as involvement in organizing committees are pointed out):
Part of the research activity for this thesis has been carried out at Istituto di Cibernetica, National Reseach Council of Italy (CNR), Pozzuoli (Naples), where I have been staying during four periods of time for a total of eight months, starting 1999.