A more suitable class of ECPSs for artistic imaging is the value and criterion fi lter structure  that stems from the early work of Kuwahara  and its subsequent generaliza- tions. These nonlinear fi lters are able to smooth out texture while enhancing, not only preserving, edges and corners, and they produce images quite similar to paintings. However, we showed in this paper that such fi lters are not mathematically well de fi ned operators and give rise to instability in presence of shadowed areas. In this contribution, we proposed a new EPCS that does not suffer the mentioned limitations. The proposed operator is based on similar principles as the Kuwahara fi lter but it is mathemati- cally well de fi ned. The chosen form of the weighting functions is particularly suitable for preserving edges and sharp corners and, at the same time, for achieving the same texture rejection level as the Gaussian fi ltering on edgeless areas. It is worth pointing out that that our operator, introduced in (11), has some similarity to bilateral fi ltering , de fi ned as (14) In , is the Gaussian kernel (6) and the range distance is proportional to , where is an input pa- rameter. Thus, in the weighted average (14), the major contribu- tion is given by those pixels which are spatially closer to point and whose gray levels are closer to . The proposed operator has a similar structure: in (11), the weighted sum is over the regions instead over the pixels, and the weighting coef fi cients are determined by the degree of homogeneity of each re- gion, instead of the range distance between each gray level and the central value . The spatial term does not appear explicitly in (11), but is taken into account by the convolutions (5). The novelty of bilateral fi ltering was that the local average (14) is mainly determined by those pixels for which the range distance is suf fi ciently high. This fact makes the fi lter an ECPS. However, its main limitation is that the pixels for which the term is high are spatially unrelated to each other. The factor only limits the average (14) on a local neighborhood of . The proposed approach overcomes this limitation by averaging over regions instead over pixels. From the computational point of view, the proposed oper- ator is more demanding than the VCFS because the weighting windows , are not shifted versions of the same window . Therefore, the number of required convolutions is instead of 2. To summarize, the most signi fi cant differences of our ap- proach to previous approaches are: 1) new weighting windows for computing local averages and local standard deviations, 2) a new combination rule which overcomes the ill-posedness of the Kuwahara fi lter, and 3) adaptive and automatic selection of the of sectors that give a non negligible contribution to the weighted average (11), according to the local pattern around each pixel.
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- Spring '15
- Dr Mahmoud Khalil