Pattern recognition is an important aspect of image processing. Image features are computed from image objects and subsequently used by an object classificator to map (and therefore classify) image objects into their corresponding object classes. To avoid misclassification the image features used should be selected in such a way that they represent the image object similarity appropriately. Similarity however is a well known theoretical concept in physics, where similar phenomena are mathematically expressed as constant dimensionless numbers. These dimensionless numbers are determined from the dimensional representation of the relevant variables by means of a technique called dimensional analysis. In consequence, the concept of
dimensional analysis is applied for the derivation of dimensionless features of color images based on various color models. The properties such as color constancy of the resulting dimensionless numbers are studied using analytical and numerical examples. Also the similarity resulting from the different color models is analyzed
and discussed.
Feature extraction is a major processing step in pattern recognition. To classify similar objects into the correct object class the selected image features should represent the desired objects invariance. This means any two objects, which are similar according to the given similarity postulate, should have identical features so that the classificator maps them to the same object class. If the similarity postulate requires invariance under translation, scaling, and rotation, then geometric moments have been shown to exhibit appropriate properties. As an extension to the traditional use of geometric moments it is possible to assign physical dimensions to geometric moments. By this means the application of dimensional analysis becomes possible. For the case of color images the spectral power distribution can be used directly to derive dimensionless features for color objects. The construction of these dimensionless color features and their properties for color object classification will be discussed.
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.
Classification is a central task in pattern recognition. To classify objects into object classes, features are calculated from objects. Objects classes are determined by class boundaries. If it is thus possible to reconstruct objects from their features, variations of feature on their objects and on class boundaries can be studied explicitly. In this work the classical steps in pattern recognition form object space to feature space are extended by the concept of physical similarity and by a back-transform form feature space to object space. The analytic assumptions and numeric properties of this back-transformation from feature space into object space are investigated using gray scale images. Higher moments of these grey scale images are computed and later used for reconstruction. When a grey scale image is written as a discrete valued 2D function, the function lies in the Hilbert space of quadratic integrable functions. Quadratic integrable functions can be written as a series of orthonormal functions, where the coefficients of the series are calculated using a scalar product of the image and the orthonormal base functions. Using Legendre polynomials as base functions, the scalar products for the determination of the series' coefficients can be calculated from the moments and the polynomials coefficients only thus yielding the back-transformation.
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