Edges In Scale Space Research Articles

Early diagnosis of cirrhosis via automatic location and geometric description of liver capsule

We propose in this paper an automatic method for early diagnosis of cirrhosis using high-frequency ultrasound images. Instead of analyzing image texture, our method exploits image characteristics of liver capsule. To this end, we first propose a novel spatial context-constrained multi-scale method to accurately extract the boundaries of the liver capsule. Our approach detects all the possible edges in scale space, and the irrelevant edges are then filtered out with a spatial context-based energy function. Secondly on this basis, two novel descriptors are proposed to characterize the geometric properties of liver capsule and the changes of liver capsule with the aggravation of liver cirrhosis. These two descriptors are used as features fed into a support vector machine classifier for quantitative analysis in automatic diagnosis. Experiment results show that the proposed method can reliably localize liver capsule and accurately classify ultrasound liver images into normal and cirrhosis classes automatically.

A snake for CT image segmentation integrating region and edge information

Abstract The 3D representation and solid modeling of knee bone structures taken from computed tomography (CT) scans are necessary processes in many medical applications. The construction of the 3D model is generally carried out by stacking the contours obtained from a 2D segmentation of each CT slice, so the quality of the 3D model strongly depends on the precision of this segmentation process. In this work we present a deformable contour method for the problem of automatically delineating the external bone (tibia and fibula) contours from a set of CT scan images. We have introduced a new region potential term and an edge focusing strategy that diminish the problems that the classical snake method presents when it is applied to the segmentation of CT images. We introduce knowledge about the location of the object of interest and knowledge about the behavior of edges in scale space, in order to enhance edge information. We also introduce a region information aimed at complementing edge information. The novelty in that is that the new region potential does not rely on prior knowledge about image statistics; the desired features are derived from the segmentation in the previous slice of the 3D sequence. Finally, we show examples of 3D reconstruction demonstrating the validity of our model. The performance of our method was visually and quantitatively validated by experts.

Edge Detection and Ridge Detection with Automatic Scale Selection

When computing descriptors of image data, the type of information that can be extracted may be strongly dependent on the scales at which the image operators 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 image features, such as edges and ridges. A novel 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 consequence of this definition is that it allows the scale levels to vary along the edge. Two specific measures of edge strength are analyzed in detail, the gradient magnitude and a differential expression derived from the third-order derivative in the gradient direction. For a certain way of normalizing these differential descriptors, by expressing them in terms of so-called γ-normalized derivatives, an immediate consequence of this definition is that the edge detector will adapt its scale levels to the local image structure. Specifically, sharp edges will be detected at fine scales so as to reduce the shape distortions due to scale-space smoothing, whereas sufficiently coarse scales will be selected at diffuse edges, such that an edge model is a valid abstraction of the intensity profile across the edge. Since the scale-space edge is defined from the intersection of two zero-crossing surfaces in scale-space, the edges will by definition form closed curves. This simplifies selection of salient edges, and a novel significance measure is proposed, by integrating the edge strength along the edge. Moreover, the scale information associated with each edge provides useful clues to the physical nature of the edge. With just slight modifications, similar ideas can be used for formulating ridge detectors with automatic selection, having the characteristic property that the selected scales on a scale-space ridge instead reflect the width of the ridge. It is shown how the methodology can be implemented in terms of straightforward visual front-end operations, and the validity of the approach is supported by theoretical analysis as well as experiments on real-world and synthetic data.

A multi-scale edge detector

A multi-scale edge detector with subpixel accuracy is described. A subpixel Laplacian edge detector, recursively implemented, is run at different scales and the recovered edge information is combined. The multi-scale edge detection is based on the behavior of edges in scale space and takes into account their physical phenomena. With this purpose in mind, four-step edge models are considered: the ideal, the blurred, the pulse and the staircase. It is emphasized that the use of two scales (the larger and the smaller) is sufficient for good edge detection. Furthermore, a set of rules is derived for combining edge information obtained from a Laplacian detector which has some special properties. However, this type of edge detector gives at least two classes of false edges, one of which cannot be eliminated by the usual thresholding methods. An appropriate thresholding algorithm is given taking into account the origin of the false edges and their behavior in scale space.

Reasoning about edges in scale space

Explores the role of reasoning in early vision processing. In particular, the problem of detecting edges is addressed. The authors do not try to develop another edge detector, but rather, they study an edge detector rigorously to understand its behavior well enough to formulate a reasoning process that allow appliance of the detector judiciously to recover useful information. They present a multiscale reasoning algorithm for edge recovery: reasoning about edges in scale space (RESS). The knowledge in RESS is acquired from the theory of edge behavior in scale space and represented by a number of procedures. RESS recovers desired edge curves through a number of reasoning processes on zero crossing images at various scales. The knowledge of edge behavior in scale space enables RESS to select proper scale parameters, recover missing edges, eliminate noise or false edges, and correct the locations of edges. A brief evaluation of RESS is performed by comparing it with two well-known multistage edge detection algorithms.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Behavior of edges in scale space

An analysis is presented of the behavior of edges in scale space for deriving rules useful in reasoning. This analysis of liner edges at different scales in images includes the mutual influence of edges and identifies at what scale neighboring edges start influencing the response of a Laplacian or Gaussian operator. Dislocation of edges, false edges, and merging of edges in the scale space are examined to formulate rules for reasoning in the scale space. The theorems, corollaries, and assertions presented can be used to recover edges, and related features, in complex images. The results reported include one lemma, three theorems, a number of corollaries and six assertions. The rigorous mathematical proofs for the theorems and corollaries are presented. These theorems and corollaries are further applied to more general situations, and the results are summarized in six assertions. A qualitative description as well as some experimental results are presented for each assertion.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Singularity theory and phantom edges in scale space

The process of detecting edges in a one-dimensional signal by finding the zeros of the second derivative of the signal can be interpreted as the process of detecting the critical points of a general class of contrast functions that are applied to the signal. It is shown that the second derivative of the contrast function at the critical point is related to the classification of the associated edge as being phantom or authentic. The contrast of authentic edges decreases with filter scale, while the contrast of phantom edges are shown to increase with scale. As the filter scale increases, an authentic edge must either turn into a phantom edge or join with a phantom edge and vanish. The points in the scale space at which these events occur are seen to be singular points of the contrast function. Using ideas from singularity, or catastrophy theory, the scale map contours near these singular points are found to be either vertical or parabolic. >