A standard prerequisite for object recognition in image processing is the computation of features. The features are subsequently employed by a classificator to classify objects into classes. As feature candidates geometrical invariants are often used to classify objects in binary images. Objects in grey scale images however have an additional contrast property. In order to classify objects correctly which are geometrically similar, but possess different contrast into the same class, geometrically as well as contrast invariant features are required. In this paper the concept of physical similarity is used to compute geometrically and contrast invariant features from objects in grey scale images. The images are represented by a two-dimensional intensity function. The introduction of a third variable which represents the grey-scale leads to a three-dimensional image function. Furthermore, physical dimensions are assigned to the intensity function consistently and lead to dimensional higher order moments. By the use of dimensional analysis dimensionless moments can be computed, which are invariant against geometric transformations and changes in contrast. The three-dimensional intensity function lies in the Hilbert Space of quadratic integrable functions and can thus be expanded into a general Fourier Series. As shown in previous work, it is therefore possible to recompute objects from their features. This back transform from feature space to object space can be used to examine and visualize the class-boundaries through the construction of a feature-editor for image features. By this means the use of dimensionless moments for geometrically and contrast invariant classification will be investigated.
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