In the past decades linear scale-space theory was derived on the basis of various axiomatics. In this paper we revisit these axioms and show that they merely coincide with the following physical principles, namely that the image domain is a Galilean space, that the total energy exchange between a region and its surrounding is preserved under linear filtering and that the physical observables should be invariant under the group of similarity transformations. These observables are elements of the similarity jet spanned by natural coordinates and differential energies read out by a vision system. Furthermore, linear scale-space theory is extended to spatio-temporal images on bounded and curved domains. Our theory permits a delay-operation at the present moment which is in agreement with the motion detection model of Reichardt. In this respect our theory deviates from that of Koenderink which requires additional syntactical operators to realise such a delay-operation. Finally, the semi-d...

This paper has been completely written in Mathematica version 4 as a notebook. The advantage is that this paper can be read as an interactive paper: the high level code of any function is directly visible, and can be operated directly, as well as modified or templated for own use. Students can now use the exact code rather then pseudocode. With these high level programming tools most programs can be expressed in very few lines, so it keeps the reader at a highly intuitive but practical level. Mathematica notebooks are portable, and run on any system equivalently.Previous speed limitationsare now well overcome. The main focus of the paper is twofold: to provide a rehearsal of the derivation of the Gaussian kernel and its derivatives as an essential class of front-end vision aperture functions, and to provide a practical tutorial for a broad audience to be able to do geometric reasoning with robust multiscale differential operators on dis-