Scale-invariant feature transform

The last years show encouraging resirlts for the extraction of those features, which are commonly referred to as salient points, key points or points of interest. The algorithms designed to extract these points of interest are commonly referred to as interest operators. Mikolajczyk and Schmid (2004) evaluated a variety of interest operators and identified the scale-invariant feature transform (SIFT) algorithm as being the most resistant to common image deformations. SIFT transforms image data into scale-invariant coordinates relative to local features. 

In this work we employ the SIFT (scale invariant-feature transform) descriptor, which has been shown to perform better than other local descriptors (Mikolajczyk and Schmid, 2003). The SIFT descriptor is invariant to scale, rotation, intensity and contrast changes and, to a small degree, affine transformations. SIFT divides the region into a set of bins. For each bin, it computes a histogram of the intensity gradient orientation at each pixel. The result is a 128-dimensional real-valued vector. Once each detected region has been converted to a SIFT vector, the input image is discarded, and only the bag of SIFT vectors is retained for further analysis. 

Because moments are extensive, non-local, objects, their use in quantizing the energy and wavefunction will implicitly be of a multiscale nature, proceeding from large through small scales, as more moments are used. In addition, since moments transform linearly under affine maps, any moment based analysis will incorporate some degree of space-scale invariance, which can be an efficient feature for quantizing systems. 

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