mfinegan@uceng.UC.EDU (michael k finegan) (02/03/89)
Is it possible to translate an MxN convolution (MxN mask (window)) into several 3x3, or 4x4 convolutions? Are there any appropriate references, whether algorithms exist, or not ? Thanks, Mike Finegan mfinegan@uceng.uc.edu
tomg@hpcvlx.HP.COM (Thomas J. Gilg) (02/06/89)
> Is it possible to translate an MxN convolution (MxN mask (window)) into > several 3x3, or 4x4 convolutions? Are there any appropriate references, > whether algorithms exist, or not ? Had this stuff in college one year ago, and can't remember much of it now ( sound familar :-) ). As a reference, I would point you to "Digital Image Processing" by 'Rafael C. Gonzalez / Paul Wintz', second edition. In particular Section 4.6 : generation of Spatial Masks from frequency-Domain Specifications - basically, the idea is that some filters are best described in the frequency domain, but that spatial domain masks are easier to apply. Therefore it is nice to convert frequency domain solutions to arbitrarly sized spatial masks ( obviously approximations - least square error approximations are popular ). This section would provide you with the "conversion" algorithms or ideas needed. I would assume you could approximate both ways ( spat <=> freq ) your filter masks. Note : nasty stuff if you ask me. # * -1 * C = (C C) C H Moore-Penrose generalized inverse Section 5.6 : Constrained least-squares restoration Section 5.8 : Restoration in the Spatial Domain Thomas Gilg tomg%hp-pcd@hplabs.hp.com