[Reading] Lecture 03 - Scale & Affine Invariant Interest Point Detectors

Unlike Lowe's paper trying to address on each component (from point detection, descryption, indexing, to matching) of a feature point matching system, this paper mainly focus on the part of interesting point detection.

In Lowe's paper, Lowe has claimed that none of previous approaches are yet fully affine invariant, as they start with initial featurescales and locations selected in a non-affine-invariant manner due to the prohibitive cost of exploring the full affine space. Although this paper use affine-variant method to choose candidate positions in the very beginning, it uses affine-invariant method to refine the point position and the shape of its neighborhood. Therefore, the feature is very close to an Affine Invariant Detectors according to Lowe's argument.

The authors first introduce a scale invariant interesting point detection method called Harris-Laplace detector. This detector uses Harris detector and Laplacian-of-Gaussians (LoG) interchangeably to find the best position for a candidate point in 3D space. And the 3D space is composed of image space (x, y) and scale space. In other words, this detector is similar to the interesting point detector used in SIFT since they both are scale-invariant. In addition to the iterative approach, the author give a simplified Harris-Laplace detector to reduce the computation complexity.

And then, the affine invariant interest point detector is introduced. In essential, affine transformation can be viewed as different scale change in each direction. The second moment matrix is used to estimate the anisotropic shape of a local image structure. The author gives several examples to compare the results using scale invariant detectors and affine invariant detectors. From those figures, it can be seem easily that the regions covered by each interesting point are much less variant to the viewpoint.

An experiment is given to test the repeatability of different detectors. Not surprisely, their affine detector performs much better than other detectors in the case of strong affine deformations. A picture matching application is given in the end of the paper.

Reference:

K. Mikolajczyk and C. Schmid, “Scale & Affine InvariantInterest Point Detectors,” Int’l J. Computer Vision, vol. 1, no. 60,pp. 63-86, 2004.