When extracting features from image data, the type of information that can be extracted may be strongly dependent on the scales at which the feature detectors are applied. This article presents a systematic methodology for addressing this problem. A mechanism is presented for automatic selection of scale levels when detecting one-dimensional features, such as edges and ridges. Anovel concept of a scale-space edge is introduced, defined as a connected set of points in scale-space at which: (i) the gradient magnitude assumes a local maximum in the gradient direction, and (ii) a normalized measure of the strength of the edge response is locally maximal over scales. An important property of this definition is that it allows the scale levels to vary along the edge. Two specific measures of edge strength are analysed in detail. It is shown that by expressing these in terms of γ-normalized derivatives, an immediate consequence of this definition is that fine scales are selected for sharp edges (so as to reduce the shape distortions due to scale-space smoothing), whereas coarse scales are selected for diffuse edges, such that an edge model constitutes a valid abstraction of the intensity profile across the edge. With slight modifications, this idea can be used for formulating a ridge detector with automatic scale selection, having the characteristic property that the selected scales on a scale-space ridge instead reflect the width of the ridge.

: This paper describes a method for the enhancement of curvilinear structures such as vessels and bronchi in 3D medical images. A 3D line enhancement filter is developed with the aim of discriminating line structures from other structures and recovering line structures of various widths. The 3D line filter is based on a combination of the eigenvalues of the 3D Hessian matrix. Multi-scale integration is formulated by taking the maximum among single-scale filter responses, and its characteristics are examined to derive criteria for the selection of parameters in the formulation. The resultant multi-scale line-filtered images provide significantly improved segmentation and visualization of curvilinear structures. The usefulness of the method is demonstrated by the segmentation and visualization of brain vessels from MRI (magnetic resonance imaging) and MRA (magnetic resonance angiography), bronchi from a chest CT, and liver vessels (portal veins) from an abdominal CT. Keywords: 3D image ...

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.

This paper presents a novel, parameter-free technique for the segmentation and local description of line structures on multiple scales, both in 2-D and 3-D. The algorithm is based on a nonlinear combination of linear filters and searches for elongated, symmetric line structures, while suppressing the response to edges. The filtering process creates one sharp maximum across the line-feature profile and across scalespace. The multiscale response reflects local contrast and is independent of the local width.

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 ——————————

We explore the application of area morphology to image classification. From the input image, a scale space is created by successive application of an area morphology operator. The pixels within the scale space corresponding to the same image location form a scale space vector. A scale space vector therefore contains the intensity of a particular pixel for a given set of scales, determined in this approach by image granulometry. Using the standard-means algorithm or the fuzzy-means algorithm, the image pixels can be classified by clustering the associated scale space vectors. The scale space classifier presented here is rooted in the novel area open--close and area close--open scale spaces. Unlike other scale generating filters, the area operators affect the image by removing connected components within the image level sets that do not satisfy the minimum area criterion. To show that the area open--close and area close--open scale spaces provide an effective multiscale structure for image classification, we demonstrate the fidelity, causality, and edge localization properties for the scale spaces. The analysis also reveals that the area open--close and area close--open scale spaces improve classification by clustering members of similar objects more effectively than the fixed scale classifier. Experimental results are provided that demonstrate the reduction in intraregion classification error and in overall classification error given by the scale space classifier for classification applications where object scale is important. In both visual and objective comparisons, the scale space approach outperforms the traditional fixed scale clustering algorithms and the parametric Bayesian classifier for classification tasks that depend on object scale.

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This paper shows how the performance of feature trackers can be improved by building a hierarchical view-based object representation consisting of qualitative relations between image structures at di#erent scales. The idea is to track all image features individually, and to use the qualitative feature relations for avoiding mismatches, resolving ambiguous matches and for introducing feature hypotheses whenever image features are lost. Compared to more traditional work on view-based object tracking, this methodology has the ability to handle semi-rigid objects and partial occlusions. Compared to trackers based on threedimensional object models, this approach is much simpler and of a more generic nature. A hands-on example is presented showing how an integrated application system can be constructed from conceptually very simple operations.

A fundamental goal of research in molecular biology is to understand protein structure. Protein crystallography is currently the most successful method for determining the threedimensional (3D) conformation of a protein, yet it remains labor intensive and relies on an expert's ability to derive and evaluate a protein scene model. In this paper, the problem of protein structure determination is formulated as an exercise in scene analysis. A computational methodology is presented in which a 3D image of a protein is segmented into a graph of critical points. Bayesian and certainty factor approaches are described and used to analyze critical point graphs and identify meaningful substructures, such as ff-helices and fi-sheets. Results of applying the methodologies to protein images at low and medium resolution are reported. The research is related to approaches to representation, segmentation and classification in vision, as well as to top-down approaches to protein structure prediction. 1...

An image representation in terms of local centers is developed and motivated in the context of natural object recognition. Local centers are visually compact regions that have significant internal-external value contrast in some measurement. Existing computational models of the concept are compared, and a particular model, the appropriate-scale ridge, is developed. In this model, local centers are defined as smoothed image extrema that are also extrema, with respect to scale, in the second spatial derivatives. The usefulness of the model is analyzed via 1D scale-space behavior and demonstrated on 2D natural images. The basic concept of a local center is also extended to color and oriented texture data. The stability of the texture model is demonstrated on images of a moving face under varying illumination and tested via a face detection task. Keywords: Shape and image representation, automatic scale selection, ridge detection, oriented texture features, human face detection The autho...