Tensor and Vector Approaches to Objects Recognition by Inverse Feature Filters

Abstract

The investigation of the extraction of image objects features by filters based on tensor and vector data presentation is considered. The tensor data is obtained as a sum of rank-one tensors, given by the tensor product of the vector of lexicographic representation of image fragments pixels with itself. The accumulated tensor is approximated by one rank tensor obtained using singular values decomposition. It has been shown that the main vector of the decomposition can be considered as the object feature vector. The vector data is obtained by accumulating analogous vectors of image fragments pixels. The accumulated vector is also considered as an object feature. The filter banks of a set of objects are obtained by regularized inversion of the matrices compiled by object features vectors. Optimized regularization of the inversion is used to expand the regions of object features capture with minimal error. The object fragments and corresponding feature vectors are selected through a training iterative process. The tensor and vector approaches create two channels for recognition. High efficiency of object recognition can be achieved by choosing the filter capture band and creating filter branches according to the given bands. The filters create a convolutional network to recognize a set of objects. It has been shown that the obtained filters have an advantage over known correlation filters when recognizing objects with small fragments.