The Steerable Pyramid is a
linear multi-
scale, multi-
orientation image decomposition that provides a useful front-end for many computer
vision and
image processing applications. The basis
functions are
directional derivative operators, that come in different sizes and orientations. The
transformation is a type of overcomplete
wavelet transform (specifically, it is an approximation to a "tight frame").
The steerable pyramid performs a polar-separable decomposition in the frequency domain, thus allowing independent representation of scale and orientation. Since it is a tight frame, it obeys the generalized form of Parseval's Equality: The vector-length (L2-norm) of the coefficients equals that of the original signal.
More importantly, the representation is translation-invariant (i.e., the subbands are aliasing-free, or equivariant with respect to translation) and rotation-invariant (i.e., the subbands are steerable, or equivariant with respect to rotation).
The Steerable Pyramid has been used successfully in a number of areas. Applications include noise reduction and enhancement, transient detection and texture synthesis (e.g. it can "generalize" a texture, and synthesize more of it in a seamless manner).