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1. ASIFT simulates rotation and tilt on both compared images. Is it wise to perform these simulations only on one side (especially if the other image is in frontal view)? ?

To cover a transition tilt equal to t, one can simulate either a tilt of \sqrt{t} on both images, or a tilt of t on one of the two images. If one knows a priori in which image the object of interest is of higher resolution than in the other, then it is better to perform the simulations on that image. If one does not have access to that information, which is the case assumed in the paper, it is better to simulate rotation and tilt on both sides.

2. Do ASIFT descriptors have the same nature as the "normal" SIFT descriptors? Can I apply other matching algorithms to match ASIFT descriptors?

Although ASIFT descriptors are computed from the rotated and tilted images, they have exactly the same nature as "normal" SIFT descriptors. Indeed rotated and tilted images are images. Any descriptor matching algorithm that works for SIFT descriptors can be applied to match ASIFT descriptors as well.

3. Which descriptor matching algorithm is used in the ASIFT online demo?

In the ASIFT online demo, the descriptor matching consists in two steps. The first step follows the simple but powerful matching algorithm of David Lowe. More precisely, to see if a descriptor A in the left image matches with some descriptor in the right image or not, we compute first the Euclidean distance d(A, A') between the descriptor A in the left image with all the descriptors A' in right image. If the nearest distance, say d(A, A₁'), is smaller than k times the second nearest distance, say d(A, A₂'), then A and A₁' are considered as matched. We set k=0.6, the same as in Lowe's SIFT software. In the second step, we apply the Moisan-Stival ORSA (Optimized Random Sampling Algorithm) algorithm to filter out the false matches using the epipolar geometry constraint. As ASIFT produces many more descriptors than SIFT, without applying ORSA the former is expected to generate more false matches than the latter. Nevertheless, let us notice that even without ORSA, the number of ASIFT false matches is reasonably small and acceptable.