Steerable Gaussian Mixed-Derivative Convolution - Separable?

1. Feb 28, 2012

Rhob

It's well-known that Gaussian convolutions are separable. So are convolutions of first-order and second-order Gaussian derivatives. The former can be made steerable by multiplying ∂G/∂x by cos($\theta$), multiplying ∂G/∂y by sin($\theta$), and subtracting the result (please correct me if my math is wrong). I'm wondering if it's possible to perform a steerable convolution of a second-order mixed Gaussian derivative, i.e. ∂2G/∂x∂y. A non-steerable convolution of that form is definitely separable - first convolve the input by ∂G/∂x and then convolve the result by ∂G/∂y.

This is not a homework assignment. I'm researching computer vision and image processing in my spare time. Second-order mixed Gaussian derivatives are apparently useful in determining saddle points in images. Thanks in advance for your help!