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 shape's 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.

The paper presents a novel method of robust skeletonization based on the Voronoi diagram (VD) of boundary points, which is characterized by correct Euclidean metrics and inherent preservation of connectivity. The regularization of the Voronoi medial axis (VMA) in the sense of Blum's prairie fire analogy is done by attributing each component of the VMA with a measure of prominence and stability. The resulting Voronoi skeletons (VSK) appear largely invariant with respect to typical noise conditions in the image and geometric transformations. Hierarchical clustering of the skeleton branches, the so-called skeleton pyramid, leads to further simplification of the skeleton. Several applications demonstrate the suitability of the Voronoi skeleton to higher order tasks such as object recognition. 1 Introduction During the last decades, skeletonization or thinning has been a constant research topic. The concept of skeletonization denotes a process, which transforms a 2D object into a 1D lin...

The medial axis transform (MAT) of a shape, better known as its skeleton, is frequently used in shape analysis and related areas. In this paper a new approach for determining the skeleton of an object, is presented. The boundary is segmented at points of maximal positive curvature and a distance map from each of the segments is calculated. The skeleton is then located by applying simple rules to the zero sets of distance maps differences. A framework is proposed for numerical approximation of distance maps that is consistent with the continuous case, hence does not suffer from digitization bias due to metrication errors of the implementation on the grid. Subpixel accuracy in distance map calculation is obtained by using gray level information along the boundary of the shape in the numerical scheme. The accuracy of the resulting efficient skeletonization algorithm is demonstrated by several examples. Keywords: Differential Geometry, Distance Map, Medial Axis Transform, Shape Analysis, S...

ral more recent papers which propose approaches to automatic drainage network calculation: Martz and De Jong (1988), Lammers and Band (1990), Qian, Ehrich, and Campbell (1990), Smith, Zhan, and Gao (1990), Zehana, Desachy, and Zahzah (1991). One common feature to all of these works is the need for mixing at least two kinds of topographic data or knowledge. One kind of data is local and is related to local features such as minima, maxima, and neighboring points which are either lower or higher. Typical data of a local nature is of scales of neighboring pixels of topographic maps, in the range of 10--50 meters. The global kind of data is composed of concepts such as saddle points, upstream, direction of flow, etc. These global data have much larger intrinsic scales (e.g., Qian, Ehrich, and Campbell (1990) and Smith, Zhan, and Gao (1990)), Not all previous work uses exactly these terms to describe their methods, but their different levels of processing (Smith, Zhan, and Ga

We present a technique for automatic detection of drainage channel networks on digital images acquired by conventional satellites such as LANDSAT and SPOT. Since these satellites are sun--synchronous, the approximate local sun angle at time of image acquisition is always known. Consequently, the spatial behavior of shading with respect to channels and other topo-morphologic features is known. This knowledge has been used to advantage in this work. We use a multilevel knowledge--based approach for this detection process. The first and lowest level deals with image processing: radiometric and edge enhancement, edge detection and consolidation, and skeletonization; resulting in a complex network of Author to whom correspondence should be addressed. 1 Ichoku & al.: Detection of Channel Networks 2 lines. The second (intermediate) level of knowledge for network extraction performs a categorization of line segments in order of resemblance to channel elements on the basis of the s...

Various time efficient procedures were developed allowing to calculate planar representations of the brain in MR and CT clearly conveying the whole surface topology. For the comparison of the provided techniques we present additional complex functionality for the transformation of cortical convolutions between different representations after extracting and marking them manually or automatically. This includes re--projection to the original volume data in order to compare our approach to results obtained with direct volume rendering. Considering brain information exclusively, and ensuring a standardized orientation for the inter--patient comparison different segmentation and registration procedures are provided for the pre--processing. All implementation was integrated in a flexible and modular extensible platform allowing for convenient manipulation and visualization. Keywords: cortical convolutions, visualization, segmentation, registration 1 Introduction Medical image data from di...

This paper gives some mathematical methods for the automatic analysis and determination of forest management parameters in particular for the measurements of geometrical sizes on terrestrial scanning laser data using segmentation of the objects with iterative contrast enhancement, fractal dimension, skeletonization and local digital geometry and topology (LDGT). 1