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In this paper, we propose a novel method for automatic hand gesture recognition from images based on shape context. Unlike conventional approaches, our method can robustly detect hand gestures rotated with arbitrary angle. Specifically, we improve the existing shape context to rotational invariant by creating a new log-polar space based on the tangent line of the boundary points. We first align the two hand gestures by solving a correspondence problem. The similarity of two hand gestures are obtained by calculating the shape distance based on our proposed rotational invariant shape context. Finally, the best matched result is identified by retrieving the gesture with the maximal shape similarity. Our method is evaluated using a standard simulated gesture dataset. Experimental results show that our method can accurately identify hand gestures, either with or without rotation. Comparison experiments also suggest that our method outperforms existing hand gesture recognition methods based on conventional shape context.

A computationally efficient method for the problem of estimating the parameters—the central direction of arrival (DOA) and angular spread of coherently distributed source is presented. The proposed method is based on Schur–Hadamard product which enables the estimation of the central DOA decoupled from that of angular spread of the source. So an underlying rotational invariance structure is exploited. Then the key idea is to apply the propagator method to estimate the central DOA, which only requires linear operations. The angular spread is estimated by a proposed second-order statistics sequently, from which the closed solution of angular spread is derived. An advantage of this method over the classical subspace-based algorithm, such as ESPRIT and MUSIC for distributed source, is that it does not apply any searching. Numerical examples illustrate the performance of the method.

An array signal processing method TLS-ESPRIT (total least squares-estimation of signal parameters via rotational invariance technique) is applied in parameter identification of synchronous machine in this paper. This method decomposes original signal into signal subspace in sigulai value decomposition and noise subspace and is processed by TLS(total least square), so it is a high precision method and improve the capacity of anti-noise. It can extract the transient and sub-transient parameters of synchronous machine accurately. The simulation example demonstrate that this method is capable of higher precision, stronger anti-noise capacity and easier than other identification methods. The dynamic simulation test proves that method is available and feasible.

The performance of ESPRIT (Estimated Signal Parameters via Rotational Invariance Technique) algorithm about frequency estimation is obviously declined, when the SNR of signal is relatively low. Aiming at this problem, an improved ESPRIT algorithm is presented. The algorithm is based on spectrum interception of noise suppression, and can narrow the selection area of β in the improved ESPRIT algorithm based on rotational transformation of autocorrelation matrix, using γ local maximum point of DFT spectrum. The algorithm not only reduces the computational complexity, but also weakens the impact of noise on frequency estimation of signal. Theoretical analysis and simulation results verify the effectiveness and feasibility of the proposed algorithm.

Local binary patterns [LBP][1] are popular texture descriptors in many image analysis tasks. One of the important aspects of this texture descriptor is their rotational invariance. Most work in LBP has focused on 2D images. Here, we present a three dimensional LBP with a rotational invariant operator using spherical harmonics. Unlike Fehr and Burkhardt [2], the invariance is constructed implicitly, without considering all possible combinations of the pattern. We demonstrate the 3D LBP on phantom data and a clinical CTA dataset.

In signal processing, a frequently encountered problem is harmonic retrieval in additive colored noise. Based on the theory of cross-power spectrum and higher order statistics, a modified cross-high-order spectral estimation approach based on rotational invariance technique is developed in this paper. In this approach the signal parameters are directly determined by eigenvalue without searching procedure inherent in all previous cross-high-order spectral estimation methods. Simulation results indicate that spectral density curve is smooth without false peaks existence. This approach is ideally suited for harmonic retrieval in additive colored noise and short data conditions, and is also accurate to estimate signal parameter in hybrid colored noises.

We define what it means for a learning algorithm to be kernelizable in the case when the instances are vectors, asymmetric matrices and symmetric matrices, respectively. We can characterize kernelizability in terms of an invariance of the algorithm to certain orthogonal transformations. If we assume that the algorithm's action relies on a linear prediction, then we can show that in each case the linear parameter vector must be a certain linear combination of the instances. We give a number of examples of how to apply our methods. In particular we show how to kernelize multiplicative updates for symmetric instance matrices.

An Hamiltonian formulation with complex fluxes and currents is proposed. This formulation is derived from a recent Lagrangian formulation with complex electrical quantities. The complexification process avoids the usual separation into real and imaginary parts and notably simplifies modeling issues. Simple modifications of the magnetic energy underlying standard (α,β) models yield new (α,β) models describing machines with magnetic saturation and saliency. We prove that the usual expression of the electro-mechanical torque (wedge product of fluxes and currents) is related to a rotational invariance characterizing sinusoidal machines.

Symmetry plays an important role in quantum mechanics. Closed solutions of quantum mechanical problems are mostly determined with help of symmetry properties of the underlying Schrodinger equation. This holds particularly for one-electron problems with rotationally symmetric potentials. In this case the solutions split into products of problem-dependent radial parts and angular parts that are built up from three-dimensional spherical harmonics. The most prominent example is the Schrodinger equation for hydrogen-like atoms. The knowledge about its solutions is basic for our understanding of chemistry. The solutions of the Schrodinger equation for a general system of N electrons moving in the field of a given number of clamped nuclei unfortunately do not attain such a simple form. The norms that we introduced to measure their mixed derivatives are however invariant to rotations of the coordinates of the single electrons.We therefore decompose the solutions of the N-particle equation in this chapter into tensor products of three-dimensional angular momentum eigenfunctions, the decomposition that reflects this rotational invariance.

This work presents new ideas in multidimensional signal theory: an isotropic quadrature filter approach for extracting local features of arbitrary curved signals without the use of any steering techniques. We unify scale space, local amplitude, orientation, phase and curvature in one framework. The main idea is to lift up signals by a conformal mapping to the higher dimensional conformal space where the local signal features can be analyzed with more degrees of freedom compared to the flat space of the original signal domain. The philosophy is based on the idea to make use of the relation of the conformal signal to geometric entities such as hyper-planes and hyper-spheres. Furthermore, the conformal signal can not only be applied to 2D and 3D signals but also to signals of any dimension. The main advantages in practical applications are the rotational invariance, the low computational time complexity, the easy implementation into existing Computer Vision software packages, and the numerical robustness of calculating exact local curvature of signals without the need of any derivatives. Applications can be optical flow and object tracking not only limited to constant velocities but detecting also arbitrary accelerations which correspond to the local curvature.

Differential Evolution (DE) is a powerful optimization procedure that self-adapts to the search space, although DE lacks diversity and sufficient bias in the mutation step to make efficient progress on non-separable problems. We present an enhancement to Differential Evolution that introduces greater diversity. The new DE approach demonstrates fast convergence towards the global optimum and is highly scalable in the decision space.

This paper describes a neural-based technique for detecting upright persons in low-resolution beach imagery in order to predict trends of tourist activities at beach sites. The proposed system uses a structural feature extraction technique to represent objects of interest for training a selection of neural classifiers. A number of neural-based classifiers are compared in this study and a direction-based feature extraction technique is investigated in conjunction with a rotationally invariant procedure for the purpose of beach object classification. Encouraging results are presented for person detection using video imagery collected from a beach site on the coast of Australia.

Neural networks have been used in the development of intelligent recognition systems that simulate our ability recognize patterns. However, rotated objects may cause incorrect identification by recognition systems. Our quick glance provides an overall approximation of a pattern regardless of noise or rotations. This paper proposes that the overall approximation of a pattern can be achieved via pattern averaging prior to training a neural network to recognize that pattern in various rotations. Pattern averaging provides the neural network with “fuzzy” rather than “crisp” representations of the rotated objects, thus, minimizing computational costs and providing the neural network with meaningful learning of various rotations of an object. The proposed method will be used to recognize rotated coins and is implemented to solve an existing problem where slot machines in Europe accept the new Turkish 1 Lira coin as a 2 Euro coin.

A family of spatio-temporal scale-spaces suitable for a moving observer is developed. The scale-spaces are required to be time causal for being usable for real time measurements, and to be "velocity adapted", i.e. to have Galilean covariance to avoid favoring any particular motion. Furthermore standard scale-space axioms: linearity, positivity, continuity, translation invariance, scaling covariance in space and time, rotational invariance in space and recursivity are used. An infinitesimal criterion for scale-spaces is developed, which simplifies calculations and makes it possible to define scale spaces on bounded regions. We show that there are no temporally causal Galilean scale-spaces that are semigroups acting on space and time, but that there are such scale-spaces that are semigroups acting on space and memory (where the memory is the scale-space). The temporally causal scale-space is a time-recursive process using current input and the scale-space as state, i.e. there is no need for storing earlier input. The diffusion equation acting on the memory with the input signal as boundary condition, is a member of this family of scale spaces and is special in the sense that its generator is local.

Accurate and stable identification of feature points is a requirement for such varied applications as wide-baseline stereo, object recognition and simultaneous localisation and mapping. Although a wide variety of feature extraction methods exist, certain aspects remain active areas of research. In this paper, a feature model is proposed which makes use of the summed area images in achieving scale invariance at the loss of theoretical rotational invariance. By making use of approximations to first and second derivatives, as well as the Laplacian, a wide variety of features may be obtained. Additionally, the stability of this method is increased by an improved approach to ordering of features. Evaluation is performed versus other common approaches using tests on precision, recall and information content of the extracted points.

Weighted averaging filters and nonlinear partial differential equations (PDEs) are two popular concepts for discontinuity-preserving denoising. In this paper we investigate novel relations between these filter classes: We deduce new PDEs as the scaling limit of the spatial step size of discrete weighted averaging methods. In the one-dimensional setting, a simple weighted averaging of both neighbouring pixels leads to a modified Perona-Malik-type PDE with an additional acceleration factor that provides sharper edges. A similar approach in the two-dimensional setting yields PDEs that lack rotation invariance. This explains a typical shortcoming of many averaging filters in 2-D. We propose a modification leading to a novel, anisotropic PDE that is invariant under rotations. By means of the example of the bilateral filter, we show that involving a larger number of neighbouring pixels improves rotational invariance in a natural way and leads to the same PDE formulation. Numerical examples are presented that illustrate the usefulness of these processes.

A good size measurement method should meet at least three criteria. These are rotational invariance, reproducibility and embody overall shape description (elongation / flakiness or angularity). According to these three criteria, this paper analyzes and evaluates several existing methods of solid particle measurement, such as Chord sizing, (multiple) Ferret diameter, equivalent circle, maximum diameter and equivalent ellipse etc. in image analysis. Based on the analyses and evaluations of the existing methods, we propose a new method – best-fit rectangle for size measurement that satisfactorily meets the criteria of rotational invariance, reproducibility and shape description.

This work presents a new approach to texture classification, in which orientation histograms and multiscale analysis have been combined to achieve a reliable method. From the outputs of a set of filters, the orientation and magnitude of the gradient in every point of a texture are estimated. By combining the orientations and relative magnitudes of the gradient, we build an orientation histogram for each texture. We have used Fourier analysis to measure the similarity between the histograms of different textures, considering the effects of a change in the size or orientation of the image to make our method invariant under these phenomena. Since different textures may generate very similar histograms, we have analyzed the evolution of these histograms at different scales, extracting a scale factor for each couple of compared textures to adjust the filters which are applied to them when the multiscale analysis is carried out.

This paper addresses the issue of a higher dimensional discrete scale-space (DSS) formulation. The continuous linear scale-space theory provides a unique framework for visual front-end processes. In practice, a higher dimensional DSS formulation is necessary since higher dimensional discrete signals must be dealt with. In this paper, first we examine the approximation fidelity of the commonly used sampled Gaussian. Second, we propose a generalized DSS formulation for 2-D and 3-D signals. The DSS theory has been presented at first by Lindeberg. While his 1-D DSS formulation is complete, the formulation as related to the extension to higher dimensions has not been fully derived. Furthermore, we investigate the properties of our derived DSS kernels and present the results of a validation study with respect to both smoothing and differentiation performance.

We describe a nonlinear system capable of use as a recognition system. This system is composed of a set of coupled oscillators, connected by linear springs. Images are overlaid on the system by altering the masses and spring constants of the oscillators, thereby modifying the detailed behavior of the system. Signatures extracted from the system using FFT of the individual oscillator positions show coherance, relative continuity, and translational and rotational invariance. These properties are discussed in the context of the eventual use of this system as a general identification system.

The paper describes the architecture of a real-time invariant object recognition machine. The machine has been implemented on five XC4010 reconfigurable Xilinx Field Programmable Gate Array (FPGA) devices, operate with a PC host. The employment of FPGAs allowed compact implementation of a highly complex design with accelerated speed performance. Rotational invariance of the image is achieved by first performing projection process, and then a 32-point fast feature extractor, the Rapid Transform, is adopted. The machine can operate at up to 50 frames/sec using images received from a 128x128 camera.

Recently, low-lying (Ex = 3 MeV) M1-collective states in deformed nuclei have been discovered [1] experimentally. We would like to mention that probably for the first time collective M1-transitions in the energy region of 2 ÷ 4 MeV in deformed nuclei were predicted in our work [2]. We treated them in a microscopic model with pairing and residual spin-spin interactions in the framework of RPA. In particular, for Kπ = 1+ state in 168Er the calculated energy was Ex = 3.18 MeV and B(M1, 0+ → 1+) ≃ 1.8μ N 2 . Later it was derived using a modified model in which the broken rotational invariance of the deformed self-consistent field was restored. These calculations have confirmed in general the predicted characteristics of the 1+ — states in Ref. [2]. In Ref. [3] the calculations, for example, for 154Sm and 166Er clearly indicated the appearance of collective 1+ -excitations within the energy range Ex = 2.5 ÷ 4 MeV and with a typical value of B(M1, 0+ → 1+) ≃ 1 ÷ 2 μμ N 2 . But one should stress that the main strength of the M1-transitions is concentrated in the region of Ex ≈ 7 ÷ 10 MeV. The low-lying 1+ states exhausted no more than 10% of the energy weighted sum-rule.

When the idea that incommensurability problems might exist in smectics was first put forward [1], the wealth of consequences was not guessed. The possibility of incommensurate smectics and the connection with reentrance was soon realized [2], but the understanding that antiphases were also a natural consequence of incommensurability [3] had to await their experimental discovery [4]. A total of at least seven different phases results from the simple introduction of two order parameters with two incommensurate preferred wave vectors [5]. In most cases, the stability domains of the different phases which can be obtained from the mean field agree well with experimental findings [6–8]. In the following we concentrate on those cases which cannot be simply described by the mean field approach. Curiously they seem a priori simpler since they do not involve phases other than nematics and smectics. However, rotational invariance and dislocation statistics provide enough input to bring novelty into the statistical physics of these problems. In this short note we outline the main features of the smectic A-smectic A transition [9,10] and its alternative, the “nematic island”, and discuss the degree of universality of the related phase diagrams.

One-dimensional antiferromagnets, and quantum fluids in general, have ground-state properties resembling itinerant fermion systems. An approach to the Heisenberg antiferromagnet based on referring it back to an itinerant spin-1/2 fermion system is outlined. One advantage of this description is that full spin rotational invariance can be retained at all stages of a calculation.