Rotation-Invariant Categorization of Colour Images using the Radon Transform

Abstract—We have derived a novel rotation-invariant feature vector, or signature, for two-variable functions like images. The feature vector is calculated as an angular integral of the Radon transform of the function. Three such feature vectors are calculated for each colour image. Subsequently, these feature vectors are used to categorize colour images in a network of 3+1 self-organizing modules. The 3-D ‘labels ’ produced by the first level modules are used by the second level modules and can be thought of as a “universal neuronal code”. The network is trained for un-rotated images and then tested for rotated images. It has been demonstrated that rotation of images by the angles included in calculation of the Radon transform results in the perfect categorization. For the angles in between, that is, those not included in the Radon transform, a small shift in categorization might occur, keeping, however, the objects well inside their clusters. Since calculation of the rotation-invariant feature vectors is very simple and involves only summations of signals (pixel values), hence very fast, it is postulated that such a mechanism might be included in the biological vision systems