Olaf Kübler

Nonlinear anisotropic filtering of MRI data

In contrast to acquisition-based noise reduction methods a postprocess based on anisotropic diffusion is proposed. Extensions of this technique support 3-D and multiecho magnetic resonance imaging (MRI), incorporating higher spatial and spectral dimensions. The procedure overcomes the major drawbacks of conventional filter methods, namely the blurring of object boundaries and the suppression of fine structural details. The simplicity of the filter algorithm permits an efficient implementation, even on small workstations. The efficient noise reduction and sharpening of object boundaries are demonstrated by applying this image processing technique to 2-D and 3-D spin echo and gradient echo MR data. The potential advantages for MRI, diagnosis, and computerized analysis are discussed in detail.

Parametrization of closed surfaces for 3-D shape description

This paper presents procedures for the explicit parametric representation and global description of surfaces of simply connected 3-D objects. The novel techniques overcome severe limitations of earlier methods (restriction to star-shaped objects (D. H. Ballard and Ch. M. Brown, Computer Vision, Prentice-Hall, Englewood Cliffs, NJ, 1981), constraints on positioning and shape of cross-sections (F. Solina and R. Bajcsy, IEEE Trans. Pattern Anal. Much. Intell. 12(2), 1990, 131-147; L. H. Staib and J. S. Duncan, in Visualization in Biomedical Computing 1992 (R. A. Robb, Ed.), Vol. Proc. SPIE 108, pp. 90-104, 1992), and nonhomogeneous distribution of parameter space). We parametrize the surface by defining a continuous, one-to-one mapping from the surface of the original object to the surface of a unit sphere. The parametrization is formulated as a constrained optimization problem. Practicable starting values are obtained by an initial mapping based on a heat conduction model. The parametrization enables us to expand the object surface into a series of spherical harmonic functions, extending to 3-D the concept of elliptical Fourier descriptors for 2-D closed curves (E. Persoon and K. S. Fu, IEEE Trans. Syst. Man Cybernetics 7(3), 1977, 388-397; F. P. Kuhl and Ch. R. Giardina, Comput. Graphics Image Process. 18(3), 1982, 236-258). Invariant, object-centered descriptors are obtained by rotating the parameter net and the object into standard positions. The new methods are illustrated with 3-D test objects. Potential applications are recognition, classification, and comparison of convoluted surfaces or parts of surfaces of 3-D shapes.

Hierarchic Voronoi skeletons

Abstract Robust and time-efficient skeletonization of a (planar) shape, which is connectivity preserving and based on Euclidean metrics, can be achieved by first regularizing the Voronoi diagram (VD) of a shapes boundary points, i.e. by removal of noise-sensitive parts of the tessellation and then by establishing a hierarchic organization of skeleton constituents. Each component of the VD is attributed with a measure of prominence which exhibits the expected invariance under geometric transformations and noise. The second processing step, a hierarchic clustering of skeleton branches, leads to a multiresolution representation of the skeleton, termed skeleton pyramid.

Symbolic Description of 3-D Structures Applied to Cerebral Vessel Tree Obtained from MR Angiography Volume Data

The present paper focuses on the conversion of multidimensional image structures to an object-centered, abstract description encoding shape features and structure relationships. We describe a prototype system that extracts three-dimensional (3-D) curvilinear structures from volume image data and transforms them into a symbolic description which represents topological and geometrical features of tree-like, filamentous objects.

Ziplock Snakes

We propose a snake-based approach that allows a user to specify only the distant end points of the curve he wishes to delineate without having to supply an almost complete polygonal approximation. This greatly simplifies the initialization process and yields excellent convergence properties. This is achieved by using the image information around the end points to provide boundary conditions and by introducing an optimization schedule that allows a snake to take image information into account first only near its extremities and then, progressively, toward its center. In effect, the snakes are clamped onto the image contour in a manner reminiscent of a ziplock being closed.These snakes can be used to alleviate the often repetitive task practitioners face when segmenting images by eliminating the need to sketch a feature of interest in its entirety, that is, to perform a painstaking, almost complete, manual segmentation.

Simulation of neural contour mechanisms : representing anomalous contours

Abstract We present a computational model of a contour mechanism first identified by neurophysiological methods in monkey visual cortex. The scope is the definition of occluding contours in static monocular images. The model employs convolutions and non-linear operations, but does not require feedback loops. Contours are defined by the local response maxima of a contour operator applied in six orientations. The operator sums the activities of a ‘C-operator’, sensitive to contrast borders and a ‘grouping operator’ that integrates collinear aggregations of termination features, such as line-ends and corners. The grouping process is selective for termination features which are consistent with the interpretation of occlusion. Contrast edges are represented by C-operators simulating the function of cortical complex cells, termination features by ES-operators simulating the function of cortical end-stopped cells. The concepts of ortho and para curvilinear grouping are introduced. Ortho grouping applies to terminations of the background, which tend to be orthogonal to the occluding contour. Para grouping applies to discontinuities of the foreground and is used to interpolate the contour in the direction of termination. Both grouping modes also identify the direction of figure and ground at such contours. The simulation reproduces well-known illusory figures, including curved Kanizsa triangles and the circular disk of the four-armed Ehrenstein figure. Further, it improves the definition of occluding contours in natural, gray value images.

Unsupervised tissue type segmentation of 3D dual-echo MR head data

Abstract The visualization of 3D phenomena and the extraction of quantitative information from magnetic resonance (MR) image data require efficient semiautomated or automated segmentation techniques. The application of multivariate statistical classification to the segmentation of dual-echo volume data of the human head into tissue types (grey matter, white matter and fluid spaces) is studied in this paper. Tests of the radiometric variability of tissue classes within the data volume demonstrate the improvement of the image acquisition technology and the suitability of statistical methods to perform brain tissue segmentation. Supervised classification is successfully applied to a study of 16 MR volume images of the human head, illustrating the robustness of this method in segmenting brain (white and grey matter) and cerebrospinal fluid (CSF). To avoid subjective criteria involved in the supervised approach, ISODATA clustering as well as clustering based on nonparametric probability density estimation were tested. Both methods performed well (success rates 93.8% and 87.5%, respectively), indicating that the classification procedure can be completely automated. The reproducibility and reliability of supervised and unsupervised classfication were studied by comparing results of segmentation performed by five expert operators. Results suggest that the interoperator and intraoperator variations could be reduced using automated clustering techniques. The accuracy of the volume calculations was quantified by applying the MR imaging and segmentation process to a phantom resembling shape and tissue characteristics of brain tissue. The segmented brain objects are displayed using 3D surface rendering.

Characterization and recognition of 3D organ shape in medical image analysis using skeletonization

Describes a procedure for the generation of the Blum skeleton (Medial Axis) of large, complex, digitized 3D objects. The proposed algorithm is a 3D generalization of the Voronoi Skeleton concept, which is already in routine use for 2D shapes. A specific algorithm for the generation of 3D Voronoi Diagrams of very large point sets (containing several 100,000 generating points) is described. The pitfalls and drawbacks of pruning procedures are discussed, and a topologically correct regularization algorithm is given for the necessary regularization of the resulting Voronoi diagram. The performance of the developed procedures is illustrated on synthetic objects, as well as on large, complex anatomical data, e.g. the segmented white matter of a human brain extracted from MR data.

Detection of General Edges and Keypoints

A computational framework for extracting (1) edges with an arbitrary profile function and (2) keypoints such as corners, vertices and terminations is presented. Using oriented filters with even and odd symmetry we combine their convolution outputs to oriented energy resulting in a unified representation of edges, lines and combinations thereof. We derive an ” edge quality” measure which allows to test the validity of a general edge model. A detection scheme for keypoints is proposed based on an analysis of oriented energy channels using differential geometry.

3D Voronoi Skeletons and Their Usage for the Characterization and Recognition of 3D Organ Shape

The paper describes a procedure for the generation of the Blum skeleton (medial axis) of large, complex, digitized 3D objects. The proposed algorithm is a 3D generalization of the Voronoi skeleton concept, which is already in routine use for 2D shapes. A specific algorithm for the generation of 3D Voronoi diagrams of very large point sets (containing several 100,000 generating points) is described. The pitfalls and drawbacks of pruning procedures are discussed, and a topologically correct regularization algorithm is given for the necessary regularization of the resulting Voronoi diagram. The performance of the developed procedures is illustrated on synthetic objects as well as on large, complex anatomical data, e.g., the segmented white matter of a human brain extracted from MR data.