For strongly directed anisotropic di usion ltering it is crucial to use numerical schemes with highly accurate directional behaviour. To this end, we introduce a novel algorithm for coherence-enhancing anisotropic di usion. It applies recently discovered di erentiation lters with optimal rotation invariance [11], and comes down to an explicit scheme on a 5 5 stencil. By comparing it with severa...

|A new formulation for coordinate system independent adaptation of arbitrary normal mutation distributions with zero mean is presented. This enables the evolution strategy (ES) to adapt the correct scaling of a given problem and also ensures invariance with respect to any rotation of the tness function (or the coordinate system). Especially rotation invariance, here resulting directly from the ...

This letter introduces the LOOP binary descriptor (local optimal oriented pattern) that encodes rotation invariance into the main formulation itself. This makes any post processing stage for rotation invariance redundant and improves on both accuracy and time complexity. We consider fine-grained lepidoptera (moth/butterfly) species recognition as the representative problem since it involves rep...

Neural network (connectionist) models are designed to encode image features and provide the building blocks for object and shape recognition. These models generally call for: a) initial diffuse connections from one neuron population to another, and b) training to bring about a functional change in those connections so that one or more high-tier neurons will selectively respond to a specific sha...

This paper shows how to extract dense optical flow from videos with a convolutional neural network (CNN). The proposed model constitutes a potential building block for deeper architectures to allow using motion without resorting to an external algorithm, e.g. for recognition in videos. We derive our network architecture from signal processing principles to provide desired invariances to image c...

For strongly directed anisotropic processes such as coherence-enhancing di usion ltering it is crucial to use numerical schemes with highly accurate directional behavior. We show that this is not possible in a satisfactory way when discretizations are limited to 3 3 stencils. As a consequence, we investigate a novel algorithm based on 5 5 stencils. It utilizes recently discovered di erentiation...

For D=4 theories of a single U(1) gauge field strength coupled to gravity and matters, we show that the electric-magnetic duality can be formulated as an invariance of the actions. The symmetry is associated with duality rotation acting directly on the gauge field. The rotation is constructed in flat space, and an extension to curved spaces is also given. It is non-local and non-covariant, yet ...

Partial differential equations have been successfully used for fibre tractography and for mapping connectivity indices in the brain. However, the current implementation of methods which require 3D orientation to be tracked can suffer from serious shortcomings when invariance to 3D rotation is desired. In this paper we focus on the 3D stochastic completion field and introduce a new methodology t...

We investigate a Lorentz invariant action which is quadratic in two rank-2 symmetric tensor fields Minkowski spacetime. apply scalar-vector-tensor decomposition to by virtue of 3-dimensional rotation-invariance spacetime and classify theories with seven degrees freedom based on the Hamiltonian analysis. find new theories, cannot be mapped from linearized Hassan-Rosen bigravity. In these mass in...

Abstract: Shift and stretch invariance lead to the exponential-Boltzmann probability distribution. Rotational invariance generates the Gaussian distribution. Particular scaling relations transform the canonical exponential and Gaussian patterns into the variety of commonly observed patterns. The scaling relations themselves arise from the fundamental invariances of shift, stretch and rotation, ...