Rotationally invariant similarity measures for nonlocal image denoising

Many natural or texture images contain structures that appear several times in the image. One of the denoising filters that successfully take advantage of such repetitive regions is NL means. Unfortunately, the block matching of NL means cannot handle rotation or mirroring. In this paper, we analyse two natural approaches for a rotationally invariant similarity measure that will be used as an alternative to, respectively a modification of the well-known block matching algorithm in nonlocal means denoising. The first approach is based on moment invariants whereas the second one estimates the rotation angle, rotates the block via interpolation and then uses a standard block matching. In contrast to the standard method, the presented algorithms can find similar regions or patches in an image even if they appear in several rotated or mirrored instances. Hence, one can find more suitable regions for the weighted average and yield improved results.

Research highlights
► We present different approaches for rotationally invariant NL means denoising.
► First approach deals with a moment-based similarity measure.
► Second method modifies traditional block matching (RIBM).
► We use the structure tensor for a better estimation of rotation angles (RIBM+ST).
► Large experimental section including comparisons of the proposed methods with classic NL means.