The steerable pyramid decomposition [1] is an outgrowth of the Laplacian pyramid [2].
It decomposes an image into oriented, bandpass filtered components
at different (binary) scales. It is overcomplete by the factor 4k/3,
but it avoids aliasing in the downsampling process, and it has useful shiftability
properties in both translation and rotation [3].
The WiT igraph shown here implements one stage of the forward and inverse
steerable pyramid transform using the algorithm of Simoncelli et. al. [1].
Click to download the WiT igraph file
or the GIF image of the igraph (40K).
For k = 1, the decomposition uses a nondirectional bandpass filter, similar to the Laplacian pyramid [2].
Click to download the convolution kernels
or the MathCAD file that generates them
[PDF file].
For k = 2, the decomposition uses two directional derivative (vertical and horizontal) bandpass filters.
Click to download the convolution kernels
or the MathCAD file that generates them
[PDF file].
For k = 3, the decomposition uses three directional derivative bandpass filters (0, 60, 120 degrees).
Click to download the convolution kernels
or the MathCAD file that generates them
[PDF file].
For k = 4, the decomposition uses four directional derivative bandpass filters (0, 45, 90, 135 degrees).
Click to download the convolution kernels
or the MathCAD file that generates them
[PDF file].