Phase correlation and log-polar conversion are implemented in the frequency domain, both of these algorithms are obtained from the Fourier shift theorem that the two translated images will show a similar phase difference in the frequency domain. Phase correlation is only capable of detecting shear, while the log-polar transformation works in the log-polar region, which essentially converts changes in rotation and scale to linear translation. Thus, using the logarithmic-polar correspondence, you can register two images that are scaled, rotated and translated copies of each other. Both of these algorithms cannot register a deformable transformation. For a detailed analysis of the uncertainty and range of rotation and zooming, these algorithms can determine, you can refer to this article " http://ieeexplore.ieee.org/document/901003/ ".
Pattern matching essentially finds the known presence of the pattern in the base image using various similarity indicators (sum of squared differences, normalized cross-correlation, Hausdorff distance, etc.). Thus, a match can be applied either to a spatial feature (intensity image, edge map, HOG), or to a frequency attribute (phase). Phase correlation and log field matching can be implemented on images of the same size, therefore matching patterns based on phases will essentially correspond to detecting the same patch in the search space with the highest correlation value.
SIFT, SURF, etc. generate a large set of vector functions, depending on various parameters, so that it does not depend on zooming, noise and lighting. This is a very broad topic, and many documents are available on the Internet, comparing their functioning.
According to my experience with SIFT, SURF is a much more reliable classifier when localizing an object in one frame, but if you plan to find the object in a video where computational time is the limiting factor, then template comparison is better.