The complex wave representation (CWR) converts unsigned 2D distance transforms into their corresponding wave functions. The underlying motivation for performing this maneuver is as follows: the normalized power spectrum of the wave function is an excellent approximation (at small values of Planck’s constant—here a free parameter τ) to the density function of the distance transform gradients. Or...

We present an analysis of the representation of images as the magnitudes of their transform with complex-valued Gabor wavelets. Such a representation is a model for complex cells in the early stage of visual processing and of high technical usefulness for image understanding, because it makes the representation insensitive to small local shifts. We show that if the images are band limited and o...

The quest for a vision system capable of representing and recognizing arbitrary motions benefits from a low dimensional, non-specific representation of flow fields, to be used in high level classification tasks. We present Zernike polynomials as an ideal candidate for such a representation. The basis of Zernike polynomials is complete and orthogonal, and can be used for describing many types of...

We present an Initial Value Representation for the semiclassical coherent state propagator based on complex trajectories. We map the complex phase space into a real phase space with twice as many dimensions and use a simple procedure to automatically eliminate non-contributing trajectories. The resulting semiclassical formulas do not show divergences due to caustics and provide accurate results.

This paperconsiders the problem of representing complex systems that evolve stochastically over time. Dynamic Bayesian networks provide a compact representation for stochastic processes. Unfortunately, they are often unwieldy since they cannot explicitly model the complex organizational structure of many real life systems: the fact that processes are typically composed of several interacting su...

In this paper we present a method for representing complex façades. For this purpose we developed a hierarchical decomposition for the façade. The steps of the decomposition are represented as nodes in a typed graph where the leaves are the atomic façade elements. Every node includes necessary attributes for its façade structure. The edges in the graph depict adjacent façade elements providing ...

Representation theory. Let us try to study a given object X through vector spaces V associated naturally to it. The symmetries S of X can form a group or more generally some kind of an algebra usually related to a group (Lie algebra, quantum group,...). The Vector space V inherits the symmetries of X, and they act on V by linear operators. This is what one means by “V is a representation of the...

This paper proposes a layered graph model for representing the internal structure of complex plane regions, where each node represents the closure of a connected component of the interior or exterior of a complex region. The model provides a complete representation in the sense that the (global) nineintersections between the interiors, the boundaries, and the exteriors of two complex regions ca...

Researchers are often perplexed when their machine learning algorithms are required to deal with complex number. Various strategies are commonly employed to project complex number into real number, although it is frequently sacrificing the information contained in the complex number. This paper proposes a new method and four techniques to represent complex number as real number, without having ...

Climate networks have proven to be a valuable method to investigate spatial connectivity patterns of the climate system. However, so far such networks have mostly been applied to scalar observables. In this study, we propose a new method for constructing networks from atmospheric wind fields on two-dimensional isobaric surfaces. By connecting nodes along a spatial environment based on the local...