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Spatial Filter Design

We use the spatial filter design framework of Moller et al. This is actually the first time the framework has been used to create second derivative filters.

Instead of controlling frequency domain properties like aliasing, leaking, and so forth, this works directly in the same spatial domain in which the filter is applied, analysing the Taylor series expansion of the convolution sum.

The main quality metric you control, called accuracy, is the degree of the polynomial that can be reconstructed exactly. You can also control the derivative, continuity and support characteristics

What you get out are piece-wise polynomial filters with symmetric support, which we like for their efficiency of evaluation.

Hoping to provide practical advice on choosing a set of filters for curvature measurement, we did a little experiment to find the optimal combination of filters, with 4x4x4 sample support, which is really the bare minimum for any kind of second derivative measurement. We tested filter combinations by rendering the mean curvature on the surface of the Marschner-Lobb test dataset.