Fast, robust and efficient 2D pattern recognition for re-assembling fragmented images

4. Rotation invariance in exemplar-based image inpainting

“…2.2.3). These methods are inspired by the work in [FT05], where a mathematical approach to reorganize pieces of Italian frescoes, which were bombed in World War II, is presented. In the so called Progetto Mantegna, digital scans of around 80.000 fresco pieces were brought back to their original positions by the help of gray-scale images of the frescoes without knowledge of their mutual rotation with respect to these photographs [CCFF + 06], see also Fig.…”

“…10. As we will see in Section 2 the framework presented in [FT05] can fruitfully be extended for the comparison of patches, whenever their mutual rotation angle is unknown.…”

“…In particular, we introduce an efficient method for the comparison of two patches in a weighted L 2 -norm, whose weight function is rotation invariant. The computation of the matching coefficient in [FT05] is extended by the Circular Harmonic moments (see (2.12)), whose m = 0, and without much further computational cost the precise L 2 -scalar product between the two patches is computed for the best rotation angle. This allows the treatment of the so called patch non-local means scheme of exemplar-based inpainting (cf.…”

“…We shall start with an ideal method to understand properties of matching coefficients. Thereafter we shall describe a method for mutual angle detection based on CH-moments which was introduced in [FT05].…”

“…x , p y 2 one might not want to trust the detected angle as much as the one of more prominent terms [FT05].…”