Three-dimensional nth derivative of Gaussian separable steerable filters

This paper details the construction of three-dimensional separable steerable filters. The approach presented is an extension of the construction of two-dimensional separable steerable filters outlined in W.T. Freeman and E.H. Adelson (1991). Additionally, three-dimensional separable steerable filters, both continuous and discrete versions, for the second derivative of the Gaussian and its Hilbert transform are reported. Experimental evaluation demonstrates that the errors in the constructed separable filters are negligible.