Edge Focusing

Bergholm, Fredrik

doi:10.1109/tpami.1987.4767980

Cited by 443 publications

(201 citation statements)

References 11 publications

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“…This analysis can be used for stating a formal description of the edge focusing method developed by Bergholm (1987), in which edges are detected at a coarse scale and then tracked to ner scales see also Clark (1988) and Lu and Jain (1989) concerning the behaviour of edges in scale-space. Note the qualitative di erence between linking across scales in the scale-space representation of a signal and the corresponding problem in a pyramid.…”

Section: Feature B Ased Linking (Di Erential Singularities)mentioning

confidence: 99%

Scale-space theory: a basic tool for analyzing structures at different scales

Lindeberg

1994

Journal of Applied Statistics

982

564

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An inherent property of objects in the world is that they only exist as meaningful entities over certain ranges of scale. If one aims at describing the structure of unknown real-world signals, then a multi-scale representation of data is of crucial importance.This chapter gives a tutorial review of a special type of multi-scale representation, linear scale-space r epresentation, w h i c h has been developed by t h e c o mputer vision community in order to handle image structures at di erent scales in a consistent manner. The basic idea is to embed the original signal into a oneparameter family of gradually smoothed signals, in which the ne scale details are successively suppressed.Under rather general conditions on the type of computations that are to performed at the rst stages of visual processing, in what can be termed the visual front end, it can be shown that the Gaussian kernel and its derivatives are singled out as the only possible smoothing kernels. The conditions that specify the Gaussian kernel are, basically, linearity and shift-invariance combined with di erent w ays of formalizing the notion that structures at coarse scales should correspond to simpli cations of corresponding structures at ne scales | they should not be accidental phenomena created by the smoothing method. Notably, s e v eral di erent w ays of choosing scale-space axioms give rise to the same conclusion.The output from the scale-space representation can be used for a variety o f early visual tasks operations like feature detection, feature classi cation and shape computation can be expressed directly in terms of (possibly non-linear) combinations of Gaussian derivatives at multiple scales. In this sense, the scalespace representation can serve as a basis for early vision.During the last few decades a number of other approaches to multi-scale representations have been developed, which are more or less related to scalespace theory, notably the theories of pyramids, wavelets and multi-grid methods. Despite their qualitative di erences, the increasing popularity o f e a c h o f t h e s e approaches indicates that the crucial notion of scale is increasingly appreciated by the computer vision community and by researchers in other related elds.An interesting similarity with biological vision is that the scale-space operators closely resemble receptive eld pro les registered in neurophysiological studies of the mammalian retina and visual cortex.

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Section: Feature B Ased Linking (Di Erential Singularities)mentioning

confidence: 99%

Scale-space theory: a basic tool for analyzing structures at different scales

Lindeberg

1994

Journal of Applied Statistics

982

564

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“…A smaller amount of smoothing, on the other hand, can be expected to improve the localization properties at the cost of a lower signal-tonoise ratio. To circumvent this problem, (Bergholm 1987) proposed to detect edges at coarse scales, and to follow these to finer scales using edge focusing. He did, however, not present any method for determining the scale level for the detection step, or to what scales the edges should be localized.…”

Section: Introductionmentioning

confidence: 99%

Edge detection and ridge detection with automatic scale selection

Lindeberg

1996

Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition

937

1,360

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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 analysed 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.

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“…Because of the coarse scales used to detect the lung edges, their location has shifted. In principle, one could use edge focusing techniques [19] to trace the edges back to a finer scale. In practice, this procedure introduces new scale parameters and does not easily lead to improved results, especially not if the edges are curved or connected.…”

Section: Discussionmentioning

confidence: 99%