The sub-block-based image retrieval method utilizes global and local image features to retrieve trademarks through separating individual an images into some blocks. This paper proposes a sub-block-based trademark image retrieval algorithm under the polar coordinate system. Experiment results show that our algorithm can keep excellent invariance in image translation, scaling and rotation and the...

This paper studies invariants of 3-manifolds derived from finite dimensional Hopf algebras. The invariants are based on right integrals for the Hopf algebras. In fact, it is shown that the defining property of the right integral is an algebraic translation of a necessary condition for invariance under handle slides in the Kirby calculus. The resulting class of invariants is distinct from the cl...

An atomic model of dislocations in face centered cubic crystals with a twoatom basis is proposed. This model has the standard cubic anisotropic elasticity as its continuum limit, and its main ingredients are the elastic stiffness constants and a dimensionless periodic function that restores the translation invariance of the crystal and influences the dislocation size. Possible applications incl...

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Tolerance to image variations (e.g. translation, scale, pose, illumination) is an important desired property of any object recognition system, be it human or machine. Moving towards increasingly bigger datasets has been trending in computer vision specially with the emergence of highly popular deep learning models. While being very useful for learning invariance to object interand intra-class s...

Most image encodings achieve orientation invariance by aligning the patches to their dominant orientations and translation invariance by completely ignoring patch position or by max-pooling. Albeit successful, such choices introduce too much invariance because they do not guarantee that the patches are rotated or translated consistently. In this paper, we propose a geometric-aware aggregation s...

(a) Mathematical modularization applies to a well-defined large class of fast transforms, which we refer to as FA4, standing for Fast Approximate Analytic-Algebraic Algorithms. (b) The decompositions of FA4 transform matrices are of a generic form, based on three mathematical properties of the transform kernels: invariance under translation, decay with spatial distance, and periodicity. (c) Mat...

Invariance is an attractive principle for specifying image processing algorithms. In this presentation, we promote affine invariance—more precisely, invariance with respect to translation, scaling and rotation. As starting point, we identify the corresponding class of invariant 2D operators: these are combinations of the (fractional) Laplacian and the complex gradient (or Wirtinger operator). W...

We study space-time symmetries in Non-Commutative (NC) gauge theory in the (constrained) Hamiltonian framework. The specific example of NC CP (1) model, posited in [9], has been considered. Subtle features of Lorentz invariance violation in NC field theory were pointed out in [13]. Out of the two Observer and Particle distinct types of Lorentz transformations, symmetry under the former, (due to...