home   |<<   <--   -->   >>|

Spatial Filter Design Experiment

For comparison, here's the analyical result, and here's what you can do if you can afford an 8x8x8 sample support, with degree six polynomials. These are actually the best filters available in the current implementation of the framework.

This image, though, is really the result of our experiment, showing the best possible filter combination with a 4x4x4 sample support. These have polynomial degrees 7, 4, and 1.

But we were curious about how more familiar cubic filters and their derivatives would compare. These are the results of using Catmull-Rom for reconstruction, and the first and second derivative of the cubic B-spline. Its pretty close!

So a secondary result of this experiment is that these familiar cubic polynomials, and their derivatives, do a very respectable job of measuring curvature.

If want some smoothing built into your reconstruction, replace Catmull-Rom ...