Talk:Ridge detection

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[edit] Edges and Ridges

Would it be possible to include a discussion on the difference/similarities between ridges and edges. Maybe an example which demonstrates the conceptual differences? --KYN 21:01, 24 September 2006 (UTC)

Well, in terms of object representation, the intention with a ridge descriptor can be to capture the axis of symmetry of the object, while the purpose of an edge is to capture the boundary of the object. This notion is particularly useful for tasks such as road extraction in aerial images and blood vessel segmentation in medical images. Tpl 18:24, 25 September 2006 (UTC)

Some authors discuss "line features" in terms of local structures which are constant in one direction and have local maximum or minimum in the orthogonal direction. How close does this come to ridges? I get the feeling that ridges relate to more global structures like objects? --KYN 19:53, 25 September 2006 (UTC)

Yes, there is a close connection between line features and ridge features. Unfortunately, a few authors also refer to line features as edge features, which complicates the matter. I have had plans to include more precise definitions of ridge features in this article. However, I'm also a bit hesitant, since it is algorithmically much harder to extract robust ridge features from images than edge, corner or blob features. There are also more alternatives to ridge extraction, and personally I'm convinced that current algorithms can be improved substantially. Tpl 05:35, 26 September 2006 (UTC)

For example the structure tensor can be used to detect lines, possibly in combination with a local phase descriptor to distinguish lines from edges. Would this qualify as a ridge detector? --KYN 22:14, 26 September 2006 (UTC)

With this terminology, the notion of ridges should include explicit extraction of one-dimensional curves that represent the ridges. Actually, there have been a number of alternative approaches to how to precisely define the notion of a ridge. With this terminology, however, I would not see just a measure of ridge strength as a ridge detector. Moreover, a ridge detector is more than an extractor thin lines. Ridges may occur at different scales and should be allow to extend to ridge widths comparable to the image size. Tpl 09:46, 27 September 2006 (UTC)

[edit] The first paragraph

In a 2-D function, a ridge is a connected set of points that are maximal in at least one dimension. In 2D, "maximal in at least one dimension" would include singular point maximas are ridges. Is this correct? When extended to N dimensions, a ridge is a connected sequence of points that are maximal in N-1 dimensions. In both sentences the word "maximal" is used, but I would guess that "minimal" may also be applicable? Or is the concept of ridges restricted to bright structures on dark background? --KYN 07:54, 27 September 2006 (UTC)

Of course the important word "bright" is missing here. I have corrected that. Tpl 09:47, 27 September 2006 (UTC)

"In a 2-D function, a (bright) ridge is a connected set of points that are maximal in at least one dimension". This definition includes also isolated point maximas. Is this correct? --KYN 16:08, 28 September 2006 (UTC)

Some of the ridge points will also be local maxima. Whether to include or exclude them is to me a matter of definition. Tpl 05:46, 29 September 2006 (UTC)

This could then be mentioned as a possible distinction between ridges and lines. --KYN 18:33, 30 September 2006 (UTC)

[edit] Second paragraph

In the scale space of an image, ridges provide an invariant description of elongated structures invariant relative to what? , and thus provide a complement to natural interest points (local extremal points) I take it that local extremal points are an example of what here is called natural interest points. There are other natural interest points in the form of corners or crossings. Are ridges complements also of these interest points? . In image scale space, a ridge is a connected set of points that are maximal in one of the spatial dimensions as well as in the scale dimension. 1) Is this an alternative definition relative to the one provided in the first paragraph, or a more precise formulation? 2) This definition is interesting since it suggests that a ridge can be a curve in the 3D scale space of a 2D image. Is this correct? Is the resulting ridge then the projection of this curve onto the 2D image? Ridges occur along the center of elongated structures since "elongated structures" is a rather vaguely defined concept maybe "in general occur along..." is better since it promises less? , and thus provide a form of scale invariant skeleton for organizing spatial constraints on local appearance. These three concepts need to be explained, perhaps in terms of examples: 1) Scale invariant skeleton 2) spatial constraints (which constraints?) 3) Local appearance --KYN 18:33, 30 September 2006 (UTC)

I'm not the first author of the text in this paragraph. Since I may have modified the text somewhat and know about the field, I'll answer your questions.

• Concerning invariance, the invariance properties depend a bit upon precisely which ridge definition you use, but as a general statement a reasonable ridge definition should be covariant with respect to translations, rotations and rescalings in the image domain as well as affine stretchnings of the intensity domain. In addition, some definitions are also covariant with monotone intensity transformations, but the latter property is hard to maintain on noisy data.
• Concerning complement to interest point, the word "natural" is not essential here. Ridge features in the form of curves serve as a complement to interest points in terms of corners, blobs and local maxima and minima. Also point-like features that respond to ridges have been defined and been used in simplified systems for tracking and recognition.
• For ridges defined in a scale-space representation, a reasonable definition of a scale-space ridge will for a two-dimensional image be a one-dimensional curve embedded in the three-dimensional scale-space, which in turn can be projected onto the two-dimensional image domain. This is really an important aspect of the definition and can be seen as an extension of the way in which certain interest point features are defined from scale-space extrema, which are local maxima in the 3-D scale-space of a 2-D image, and then projected down to 2-D image space.
• Concerning elongated structures, the underlying motivation for extracting ridge features is in most cases to capture the axes of symmetry of an elongated object.
• Concerning the sentence "[ridges] thus provide a form of scale invariant skeleton for organizing spatial constraints on local appearance", I agree that this sentence is somewhat condensed. However, it is not at all incorrect, and agrees with the intention of ridge descriptors by a few authors in the area. To develop this notion in more detail in Wikipedia, however, there is more work that one could do in terms of research articles first. (Some people may have some work to do here :-)

Tpl 17:40, 3 October 2006 (UTC)