Abstract—A hybrid multidimensional image segmentation algorithm is proposed, which combines edge and region-based techniques through the morphological algorithm of watersheds. An edge-preserving statistical noise reduction approach is used as a preprocessing stage in order to compute an accurate estimate of the image gradient. Then, an initial partitioning of the image into primitive regions is produced by applying the watershed transform on the image gradient magnitude. This initial segmentation is the input to a computationally efficient hierarchical (bottomup) region merging process that produces the final segmentation. The latter process uses the region adjacency graph (RAG) representation of the image regions. At each step, the most similar pair of regions is determined (minimum cost RAG edge), the regions are merged and the RAG is updated. Traditionally, the above is implemented by storing all RAG edges in a priority queue. We propose a significantly faster algorithm, which additionally maintains the so-called nearest neighbor graph, due to which the priority queue size and processing time are drastically reduced. The final segmentation provides, due to the RAG, one-pixel wide, closed, and accurately localized contours/surfaces. Experimental results obtained with two-dimensional/three-dimensional (2-D/3-D) magnetic resonance images are presented. Index Terms — Image segmentation, nearest neighbor region merging, noise reduction, watershed transform. I.

Multiscale image analysis has been used successfully in a number of applications to classify image features according to their relative scales. As a consequence, much has been learned about the scale-space behavior of intensity extrema, edges, intensity ridges, and grey-level blobs. In this paper, we investigate the multiscale behavior of gradient watershed regions. These regions are defined in terms of the gradient properties of the gradient magnitude of the original image. Boundaries of gradient watershed regions correspond to the edges of objects in an image. Multiscale analysis of intensity minima in the gradient magnitude image provides a mechanism for imposing a scale-based hierarchy on the watersheds associated with these minima. This hierarchy can be used to label watershed boundaries according to their scale. This provides valuable insight into the multiscale properties of edges in an image without following these curves through scale-space. In addition, the gradient watershed region hierarchy can be used for automatic or interactive image segmentation. By selecting subtrees of the region hierarchy, visually sensible objects in an image can be easily constructed.

Abstract—Ridges and valleys are useful geometric features for image analysis. Different characterizations have been proposed to formalize the intuitive notion of ridge/valley. In this paper, we review their principal characterizations and propose a new one. Subsequently, we evaluate these characterizations with respect to a list of desirable properties and their purpose in the context of representative image analysis tasks. Index Terms—Creases, separatrices, drainage patterns, comparative analysis. ————————— — F ——————————

Segmentation algorithms are presented which combine regularization by nonlinear partial differential equations (PDEs) with a watershed transformation with region merging. We develop efficient algorithms for two well-founded PDE methods. They use an additive operator splitting (AOS) leading to recursive and separable filters. Further speed-up can be obtained by embedding AOS schemes into a pyramid framework. Examples demonstrate that the preprocessing by these PDE techniques eases and stabilizes the segmentation. The typical CPU time for segmenting a 256² image on a workstation is less than 2 seconds.

The goal of this paper is to present segmentation algorithms which combine regularization by nonlinear partial differential equations (PDEs) with a watershed transformation with region merging. We develop efficient algorithms for two wellfounded PDE methods. They use an additive operator splitting (AOS) leading to recursive and separable filters. Further speed-up can be obtained by embedding AOS schemes into a pyramid framework. Examples are presented which demonstrate that the preprocessing by these PDE techniques eases and stabilizes the segmentation. The typical CPU time for segmenting a 256 2 image on a workstation is less than 2 seconds. Key Words: Nonlinear diffusion, additive operator splitting, Gaussian pyramid, watershed segmentation, region merging CR Subject Classification: I.4.6, I.4.3, I.4.4. 1 Introduction Segmentation is one of the bottlenecks of many image analysis and computer vision tasks ranging from medical image processing to robot navigation. Ideally it sho...

Geometric aspects of the visibility problem in the siting of air defense missile batteries were studied in this project. It theoretically analyzed the problem, produced several new and efficient algorithms, implemented them, and tested them on many cells of data. The theoretical analysis studied the terrain characteristics, formally defined the Hawk siting problem, formalized the optimal placement of observers, and considered the minimum elevation of an airplane flying over varying terrain. Three algorithms for finding the viewshed around a particular observer were studied. R3 is slow but accurate. R2 is much faster, yet almost as accurate. Xdraw computes an approximate viewshed with error bounds. Four visibility index algorithms were studied. VL runs a fixed number of lines of sight out from every possible observer. WeightF weights the points by distance. Weight approximates WeightF, and DEM/LOS skips points along each line of sight for increased speed. The visibility indices of 20 DT...

In order to investigate the deep structure of Gaussian scale space images, one needs to understand the behaviour of spatial critical points under the influence of blurring. We show how the mathematical framework of catastrophe theory can be used to describe and model the behaviour of critical point trajectories when various different types of generic events, viz. annihilations and creations of pairs of spatial critical points, (almost) coincide. Although such events are non-generic in mathematical sense, they are not unlikely to be encountered in practice. Furthermore the behaviour leads to the observation that fine-to-coarse tracking of critical points doesn't suffice, since trajectories can form closed loops in scale space. The modelling of the trajectories include these loops. We apply the theory to an artificial image and a simulated MR image and show the occurrence of the described behaviour.

In order to investigate the deep structure of Gaussian scale space images, one needs to understand the behaviour of critical points under the influence of blurring. We show how the mathematical framework of catastrophe theory can be used to describe the various different types of annihilations and the creation of pairs of critical points and how this knowledge can be exploited in a scale space hierarchy tree for the purpose of pre-segmentation. We clarify the theory with an artificial image and a simulated MR image.

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In order to investigate the deep structure of Gaussian scale space images, one needs to understand the behaviour of spatial critical points under the influence of blurring. We show how the mathematical framework of catastrophe theory can be used to describe the various different types of annihilations and creations of pairs of spatial critical points and how this knowledge can be exploited in finding and tracing these points. We clarify the theory with an artificial image and a simulated MR image.