A new approach is proposed to constructing a classifier of two dimensional (2D) objects in a space of multiresolution object representations. The approach is based on constructing tree structured covers (TSCs) of clusters of a training set by spheres in the space of the object representations taken at the maximum resolution level. The covering spheres and their projections of all resolution levels generate a multilevel net work of templates in which the sphere centers yield the templates, while the spheres themselves form the influence regions of the templates at the corresponding resolution levels. Using the multilevel structure of the template network, a hierarchical search algorithm is proposed for making a decision group of the templates by a given voting criterion. A computational complexity of this algorithm is evaluated. An efficiency of the proposed TSC classifier is demonstrated by estimates of error rates in experiments on signature, hand gesture and face recognition, as well as by the comparative error rates obtained for these sources using the known SVM classifier.