Image analysis methods based on hierarchies of graphs and multi-scale mathematical morphology

This thesis is about image analysis methods based on hierarchical graph represen-tations. A hierarchical graph representation of an image is an ordered set of graphs that represent the image on different levels of abstraction. The vertices of the graph represent image structures (lines, areas). Its edges represent the relations between those structures (adjacency, collinearity). Graphs on higher levels of the hierarchy give a more global and abstract representa-ti-on of the image. A number of image analysis methods based on hierarchical graph repre-senta-tions were developed. These methods were applied to image segmentation, detection of linear structures and edge detection. It is found that a hierarchical graph is an attractive framework for image analysis, because it can easily encode and handle different structures, and because structures and there relations are encoded in the same repre-sentation. The only restriction of the method is its 'bottom-up' character. However it is suggested how this can be remedied by a 'top-down' analysis in a later stage of the proces. The second part of this study is about multiresolution morphology. Discs defined by weighted metrics were used as structuring elements. Weighted metrics can approximate the Euclidian metric to within a few percent. Algorithms were developed to perform the elementary morphological operations (erosion, dilation, opening, closing), and some advanced operations as the medial axis transform, the opening transform, and the patttern spec-trum-transform. The computational costs of these methods is comparable to the cost of conventional morphological methods using square structuring elements

Determination of ocular torsion by means of automatic pattern recognition

A new, automatic method for determination of human ocular torsion (OT) was devel-oped based on the tracking of iris patterns in digitized video images. Instead of quanti-fying OT by means of cross-correlation of circular iris samples, a procedure commonly applied, this new method automatically selects and recovers a set of 36 significant patterns in the iris by the technique of template matching as described by In den Haak et al. [16]. Each relocated landmark results in a single estimate of the torsion angle. A robust algorithm estimates OT from this total set of individually determined torsion angles, hereby largely correcting for errors which may arise due to misjudgement of the rotation centre. The new method reproduced OT in a prepared set of images of an artificial eye with an accuracy of 0.1 deg. In a sample of 256 images of human eyes, a practical reliability of 0.25 deg. was achieved. To illustrate the method's usefulness, an experiment is described in which ocular torsion was measured during two dynamic conditions of whole-body roll, namely during sinusoidally pendular motion about either an earth horizontal or earth vertical axis (that is "with" and "without" otolith stimula-tion, respectively)

Topological numbers and singularities in scalar images. Scale-space evolution properties

Singular points of scalar images in any dimensions are classified by a topological number. This number takes integer values and can efficiently be computed as a surface integral on any closed hypersurface surrounding a given point. A nonzero value of the topological number indicates that in the corresponding point the gradient field vanishes, so the point is singular. The value of the topological number classifies the singularity and extends the notion of local minima and maxima in one-dimensional signals to the higher dimensional scalar images. Topological numbers are preserved along the drift of nondegenerate singular points induced by any smooth image deformation. When interactions such as annihilations, creations or scatter of singular points occurs upon a smooth image deformation, the total topological number remains the same.Our analysis based on an integral method and thus is a nonperturbative extension of the order-by-order approach using sets of differential invariants for studying singular points.Examples of typical singularities in one- and two-dimensional images are presented and their evolution induced by isotropic linear diffusion of the image is studied.Keywords: singular points - scalar images - topology - catastrophes - scale spac

Topological numbers and singularities in scalar images. Scale-space evolution properties

Singular points of scalar images in any dimensions are classified by a topological number. This number takes integer values and can efficiently be computed as a surface integral on any closed hypersurface surrounding a given point. A nonzero value of the topological number indicates that in the corresponding point the gradient field vanishes, so the point is singular. The value of the topological number classifies the singularity and extends the notion of local minima and maxima in one-dimensional signals to the higher dimensional scalar images. Topological numbers are preserved along the drift of nondegenerate singular points induced by any smooth image deformation. When interactions such as annihilations, creations or scatter of singular points occurs upon a smooth image deformation, the total topological number remains the same.Our analysis based on an integral method and thus is a nonperturbative extension of the order-by-order approach using sets of differential invariants for studying singular points.Examples of typical singularities in one- and two-dimensional images are presented and their evolution induced by isotropic linear diffusion of the image is studied.Keywords: singular points - scalar images - topology - catastrophes - scale spac

Image Analysis Methods Based on Hierarchies of Graphs and Multi-Scale Mathematical Morphology

this paper. This is not a real restriction: if rational weights are to be used, they can be multiplied by a suitable scaling factor, yielding integer values. In practice, operations will be performed on a bounded grid and real numbers can be approximated with sufficient accuracy by rational numbers. Chamfer Metrics 113 If x and y are two points in Z