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I have a question regarding the Harris-Laplacian-Detector introduced by Mikolajczyk et al. With the Harris you search maximas of "cornerness" within each particular scale and then with the Laplacian you search maximas of "blobness" over the scales that are one larger and one smaller than the scale of a found Harris-point.

Why does the maximization of the "blobness" over scale have such a good effect on corner-points? I would assume, that it is much better to search for maximum "cornerness" (e.g. find maximum of Harris over scales) to find good corner-points.

Ehsan
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steckl
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1 Answers1

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The inclusion of the laplacian is needed to ensure scale invariance.

While the scale adapted Harris detector did have very good repeatability (in terms of location of the detection), the scale selection remained a problem. They noticed that

during our experiments we noticed that the adapted Harris function rarely attains maxima in 3D space. Therefore, we propose to use a different function, the Laplacian, for scale maxima detection.

(From Indexing based on scale invariant interest points)

This is explained in better detail in his thesis:

In our experiments (cf. section 3.2.4) we noticed that the scale adapted Harris function rarely attains maxima over scales in a scale-space representation. If too few interest points are detected, the image is not reliably represented. Therefore, we abandoned the idea of searching 3D maxima of the Harris function. Furthermore, the experiments showed that LoG function enables the highest percentage of correct characteristic scales to be found. Therefore, we propose to use the Laplacian to select the scales for points extracted with the Harris detector. Harris-Laplace detector uses the Harris function (cf. equation 4.1) to localize points in each level of the scale-space representation. Next, it selects the points, for which the Laplacian-of-Gaussian (cf. equation 4.2) attains a maximum over scale. In this way we combine these two methods to obtain a reliable interest point detector invariant to signicant scale changes.

I don't have any intuitive explanation for why the Harris function doesn't give many maxima over scales, but empirically, they found this to be the case. Looks like nothing's stopping you from using the Harris scale space maximum, but you'd probably just get many fewer detections.