requirements as the linear Gaussian scale-space concept. Hence, unexpected artifacts may sometimes occur and one should be very careful of not using the term "scale-space" for just any type of one-parameter family of images. A first-order extension of the isotropic Gaussian scale space is provided by the affine (Gaussian) scale space. One motivation for this extension originates from the common need for computing image descriptors subject for real-world objects that are viewed under a perspective camera model. To handle such non-linear deformations locally, partial invariance (or more correctly covariance) to local affine deformations can be achieved by considering affine Gaussian kernels with their shapes determined by the local image structure, see the article on affine shape adaptation for theory and algorithms. Indeed, this affine scale space can also be expressed from a non-isotropic extension of the linear (isotropic) diffusion equation, while still being within the class of linear partial differential equations. There exists a more general extension of the Gaussian scale-space model to affine and spatio-temporal scale-spaces. In addition to variabilities over scale, which original scale-space theory was designed to handle, this generalized scale-space theory also comprises other types of variabilities caused by geometric transformations in the image formation process, including variations in viewing direction approximated by local affine transformations, and relative motions between objects in the world and the observer, approximated by local Galilean transformations. This generalized scale-space theory leads to predictions about receptive field profiles in good qualitative agreement with receptive field profiles measured by cell recordings in biological vision. There are strong relations between scale-space theory and wavelet theory, although these two notions of multi-scale representation have been developed from somewhat different premises. There has also been work on other multi-scale approaches, such as pyramids and a variety of other kernels, that do not exploit or require the same requirements as true scale-space descriptions do. Relations to biological vision and hearing There are interesting relations between scale-space representation and biological vision and hearing. Neurophysiological studies of biological vision have shown that there are receptive field profiles in the mammalian retina and visual cortex, that can be well modelled by linear Gaussian derivative operators, in some cases also complemented by a non-isotropic affine scale-space model, a spatio-temporal scale-space model and/or non-linear combinations of such linear operators. Regarding biological hearing there are receptive field profiles in the inferior colliculus and the primary auditory cortex that can be well modelled