This paper discusses the Elliptically Weighted Average (EWA) filtering algorithm along with enhancements that further increase image quality. We derive all the mathematical results that are needed in the algorithm and generalize the algorithm as follows. First, we allow filters with varying radii of support. Second, we propose a technique to embed differing filters for the minification and magnification. This enhances the image quality by allowing to use those filters in reconstruction that do not create excessive blurring on magnification. The transition between these filters is made invisible by linearly interpolating between the filters. The original EWA algorithm is recovered by setting both filters to a Gaussian filter with radius 1. Third, our derivations are coordinate-free which we believe is the best representation for the formulae in the algorithm. This also enables generalizing the algorithm to higher dimensions (e.g. filtering voxel data in 3d), although this would be very costly. We shall demonstrate that using a filter radius of 1 for the gaussian filter as in the original EWA filtering algorithm leads to artifacts when magnifying.

This paper is still a work in progress. For example, it is missing the description of “Enhanced Ewa” algorithm. Meanwhile, what isn’t said in the paper can be deduced from the source code.

Since it can be hard to see from the paper which pixels are there in purpose and which are due to Adobe Acrobat resizing, I have included all the images in a separate webpage in their original size.

The implementation of the Enhanced EWA algorithm can be found from the Pastel library in PastelGfx -> Textures.