## Filtering and Features

Image filtering and representation has a long tradition with CVL and its members. In 1974, while at MIT, Gösta Granlund worked out and published in 1978 what is probably the first documented use in Computer Vision of spatially local transforms, or Gabor functions, which later became known as Wavelets. It introduced a modular, similarity metric, first used for description of edge and line orientation, see article, and later extended to more complex objects, see book.

The double angle vector representation developed there, could be used for
predictive image coding
(1983) and for
adaptive image filtering
(1983), which later came to be termed
*steerable filters*
. The filtering and representation techniques were further developed using tensors, to allow filtering in 3-D and 4-D spaces. This is documented in the book
Signal Processing for Computer Vision. The representation in terms of a standard similarity metric allows all levels in a pyramid to have the same abstract representation, vectors or tensors, although they will have different `meanings' at different levels.

An important aspect is the signal/certainty principle. This says that the certainty or confidence of a measure must not be mixed up with its value. This is especially important when data is missing. Instead of setting the value to 0 at such points, which is often done carelessly or implicitly, one should let the value be unspecified and set the corresponding certainty to 0. Filtering of uncertain signals can be accomplished using the method of Normalized Convolution.

Filters are frequently designed in the frequency domain. To realize them as discrete, spatially localized, convolution kernels we use Filter Optimization.

Speed is a major concern when filtering images and other high-dimensional signals. An efficient approach is to use Filter Networks where components are built up and combined in a network.

Recent work in the filtering area has centered around Polynomial Expansion. Using quadratic polynomials as a local signal model leads to filters which automatically become Cartesian separable and can be computed in a hierarchical structure. Since the method is designed in the spatial domain using Normalized Convolution, it can also handle uncertain or irregularly sampled signals. Polynomial Expansion has successfully been used for e.g. Orientation and Velocity Estimation, Detection of Rotational Symmetries, and Disparity Estimation.

A tutorial on rotational symmetries and a Matlab software package for automatic detection are avaiable on a separate web-page.

Last updated: 2016-01-15