Improving Deriche-style recursive Gaussian filters

Gaussian smoothing filters and Gaussian derivative filters can be estimated by recursive IIR filters, as shown by Deriche [3, 4]. The design of those filters does, however, not enforce the important property that derivative filters should have an exactly zero DC-response. This article extends the theory in [4] to take this constraint into account without loss of performance and also gives new compact closed form expressions for the normalization factors required for proper scaling of the filter responses.