Histogram of directions by the structure tensor

Many low-level features, as well as varying methods of extraction and interpretation rely on directionality analysis (for example the Hough transform, Gabor filters, SIFT descriptors and the structure tensor). The theory of the gradient based structure tensor (a.k.a. the second moment matrix) is a very well suited theoretical platform in which to analyze and explain the similarities and connections (indeed often equivalence) of supposedly different methods and features that deal with image directionality. Of special interest to this study is the SIFT descriptors (histogram of oriented gradients, HOGs). Our analysis of interrelationships of prominent directionality analysis tools offers the possibility of computation of HOGs without binning, in an algorithm of comparative time complexity