### Abstract

The formulation of afront-end orearly vision system is addressed, and its connection with scale-space is shown. A front-end vision system is designed to establish a convenient format of some sampled scalar field, which is suited for postprocessing by various dedicated routines. The emphasis is on the motivations and implications of symmetries of the environment; they pose natural, a priori constraints on the design of a front-end.
The focus is on static images, defined on a multidimensional spatial domain, for which it is assumed that there are no a priori preferred points, directions, or scales. In addition, the front-end is required to be linear. These requirements are independent of any particular image geometry and express the front-end's pure syntactical, bottom up nature.
It is shown that these symmetries suffice to establish the functionality properties of a front-end. For each location in the visual field and each inner scale it comprises a hierarchical family of tensorial apertures, known as the Gaussian family, the lowest order of which is the normalised Gaussian. The family can be truncated at any given order in a consistent way. The resulting set constitutes a basis for alocal jet bundle.
Note that scale-space theory shows up here without any call upon the prohibition of spurious detail, which, in some way or another, usually forms the basic starting point for diffusion-like scale-space theories.

Original language | English |
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Pages (from-to) | 325-351 |

Journal | Journal of Mathematical Imaging and Vision |

Volume | 4 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1994 |

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## Cite this

Florack, L. M. J., Haar Romenij, ter, B. M., Koenderink, J. J., & Viergever, M. A. (1994). Linear scale-space.

*Journal of Mathematical Imaging and Vision*,*4*(4), 325-351. https://doi.org/10.1007/BF01262401