Algorithms and Parallel Computing

13.3 2-D RECURSIVE FILTERS

A first-quadrant 2-D recursive filter can be represented by the equation

(13.1)

where X ≡ X (z₁, z₂), Y ≡ Y (z₁, z₂), and b(0, 0) = 0. The term represents one time step delay along a line. This delay could be implemented as memory address locators for use by the software threads or it could be implemented as actual hardware buffer for use by the software systolic array processing elements. The term represents one sample delay along a column. For progressive raster-scanned images, this is equivalent to W time-step delays where W is the image width. The above equation can also be written in a hierarchical way as

(13.2)

where the terms F(k₂) and G(k₂) are two one-dimensional (1-D) infinite impulse response (IIR) filter operators given by

(13.3)

(13.4)

From Eq. 13.2, it can be seen that a 2-D recursive filter can be treated as a combination of 1-D ...