The SIFT Method

In this chapter and in the next one, we describe one of the most popular shape descriptors, Lowe's Scale-Invariant Feature Transform (SIFT) method [114]. In continuation we will perform a structural and practical comparison of the SIFTbased matching method with the Level Line Descriptor method (LLD) developed in this book. The LLD method in fact includes the features of the recent, also popular, MSER method. Comparing SIFT and LLD is not an easy task, since they are of different nature. On the one hand LLD is based on geometrical shape descriptors, rigorously invariant with respect to similarity or affine transformations. Moreover, the method comes with decision rules, either for matching or grouping. On the other hand, SIFT descriptors are local patches which are based on key points and which are just similarity-invariant. The comparison will be based on ad hoc experimental protocols, in the spirit of the SIFT method itself. These protocols check the robustness of local descriptors to all perturbations listed in Sect. 1.2 (Chap. 1).

We start with a comprehensive description of the SIFT shape encoding (Sect. 10.1). Then we compare robustness and stability of both shape descriptors (Sect. 10.2). Sect. 10.3 compares the matching performances of both algorithms on pair of images having similar shapes or obtained by photographing the same scene under different viewpoints. The main focus of the book is the computation of matching thresholds. In the SIFT method the thresholds are learned from the pair of images. We shall see that obvious matches can be missed when the query shape appears more than once in the searched image. In the next chapter a fusion of SIFT and of the a contrario techniques both for matching and grouping will be proposed.