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Tell & Carlsson ECCV 2002

7
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05-01-2012
09:55 PM ET (US)
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6
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05-01-2012
09:52 PM ET (US)
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Edited 05-01-2012 09:53 PM
5
sandwichmaker
10-03-2002
01:19 PM ET (US)
The heuristic comment in Tell and Carlson's paper refers to the idea of a shape context. The shape context and the similarly related idea of order structure are both ways of capturing a description of a point in an image which is relational, i.e. it describes each point in terms of its relationship to the those around it, and then the task of recognition or matching boils down to the task of matching these local descriptions. The advantage being that these local descriptions are richer compared to just matching image patches.

This however does not change the fact that both these descriptors while capturing weighted local statistics about the arrangements of feature points around a given point, do not really have any theory behind them. There is some justification but no analysis of the exact analytical properties of either of them.
Edited 10-03-2002 01:21 PM
4
Josh Wills
10-03-2002
12:46 PM ET (US)
Kristin: in response to your questions
(1) Similarity transforms are a subset of the affine transforms. They allow for rotation, translation, and a scale change, but they do not allow the shear that affine transforms allow.

(2) I discussed the "heuristic" comment with Serge and I seem to have forgotten exactly what he said (I will get back to you), but it is funny since Carlsson, Tell's Advisor, worked on a project called "Order Structure" that is very similar in approach to shape contexts.

(3) As Satya explained, the profiles are related by scale if the patches containing them are affine. This doesn't however, cause them to break down under perspective conditions. In the ladder case that you discribed, you are correct in thinking that profiles spanning the entire length of the ladder will likely not match very well. However, for many projections (especially in small regions) affine is a fairly good approximation to a homography. So while you wouldn't get matches for the long profiles that span the ladder, you would get a good deal of matches that break that profile into smaller steps so that the affine approximation is close.

(4) The distance in (1) is the Mahalanobis distance and the covariance matrix is that of the feature vectors as a whole. In his thesis, Tell actually says that this approach didn't work very well so they used L2 distances (I don't know why this wasn't spelled out in the paper). The difference between eqs 1 and 2 is that in 1 there is no limit on the number of matches that will be deemed acceptable since it is only a threshold on distance and common profiles will likely be "close" to many other profiles. Equation (2) defines matches according to rank in a sorted list of the profiles by distance. This would allow you define the number of profiles that may be cosidered "close" to any given profile.
3
Kristin BransonPerson was signed in when posted
10-03-2002
11:24 AM ET (US)
What is meant by "if the viewing conditions are affine"? It seems to me that the examples in Figures 1 and 2 are not related by only affine transformations, but also have projective transformations. Does profile matching work in these examples because of an approximation that the relationship between the images is only affine?

I agree with Satya that the contributions of this paper are great additions to this algorithm -- a very simple idea that can immensely improve the performance of profile matching.
2
Satya
10-03-2002
05:38 AM ET (US)
Kristin : this is with reference to (3). I think what you say is correct, however let me quote the paper:

" if an intensity profile lies along a planar surface, and if the viewing conditions are affine or if the images are related by an affine transformation, then corresponding intensity pro├┐les are related by only one parameter - a scale change."

In your ladder example, the two images would be related by a projective trasform as opposed to an affine one.

These are a few things I really like about the paper:
1) It recognizes the fact that texture alone cannot be used for reliable correspondence match and advocates the use of relation between the feature points for solving correspondence along with texture.

2) The idea of using string matching seems great.

3) The results in fig 6 look very impressive.

However, the amount of time it takes for solving correspondence seems prohibitive.
Edited 10-03-2002 05:41 AM
1
Kristin BransonPerson was signed in when posted
10-03-2002
01:38 AM ET (US)
My main complaint about this paper is that parts of it are very vague, indescript, and narrative and other parts, while maybe specific, lack critical details and narrative explanation. I'm sure a lot of this has to do with my unfamiliarity with the subject matter, but I think I am often misinterpreting the aim of the authors.

Some questions I had while reading through:

1) What is a similarity transform? Image plane translations and rotations are described to be similarity transformations, but aren't these affine transformations? Are affine and similarity transformations disjoint sets?

2) What makes the Belongie et al. [10] approach heuristic?

3) I don't see that the intensity profiles are related by only a scale change -- or at least not a constant scale change. I'm thinking of a ladder viewed straight on so that the distance between each rung is constant compared to the ladder viewed upward from close to the bottom rung, where the 2D projected distance between the rungs gets smaller the farther up the ladder you go. The intensity profile perpendicular to the rungs is not just uniformly scaled from one image to the other.

4) What's the covariance matrix C the covariance of? The profile feature vectors? What's the intuition behind equation (1)? Are (1) and (2) voting function that are improvements on the original algorithm, even without the cyclic string matching stuff? How do these two functions compare and which is better?
Edited 10-03-2002 01:38 AM

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