Pattern recognition using invariants defined from higher order spectra : 2-D image inputs

A new algorithm for extracting features from images for object recognition is described. The algorithm uses higher order spectra to provide desirable invariance properties, to provide noise immunity, and to incorporate nonlinearity into the feature extraction procedure thereby allowing the use of simple classifiers. An image can be reduced to a set of 1D functions via the Radon transform, or alternatively, the Fourier transform of each 1D projection can be obtained from a radial slice of the 2D Fourier transform of the image according to the Fourier slice theorem. A triple product of Fourier coefficients, referred to as the deterministic bispectrum, is computed for each 1D function and is integrated along radial lines in bifrequency space. Phases of the integrated bispectra are shown to be translation- and scale-invariant. Rotation invariance is achieved by a regrouping of these invariants at a constant radius followed by a second stage of invariant extraction. Rotation invariance is thus converted to translation invariance in the second step. Results using synthetic and actual images show that isolated, compact clusters are formed in feature space. These clusters are linearly separable, indicating that the nonlinearity required in the mapping from the input space to the classification space is incorporated well into the feature extraction stage. The use of higher order spectra results in good noise immunity, as verified with synthetic and real images. Classification of images using the higher order spectra-based algorithm compares favorably to classification using the method of moment invariants

Shape discrimination using invariants defined from higher-order spectra

An approach to pattern recognition using invariant parameters based on higher-order spectra is presented. In particular, bispectral invariants are used to classify one-dimensional shapes. The bispectrum, which is translation invariant, is integrated along straight lines passing through the origin in bifrequency space. The phase of the integrated bispectrum is shown to be scale- and amplification-invariant. A minimal set of these invariants is selected as the feature vector for pattern classification. Pattern recognition using higher-order spectral invariants is fast, suited for parallel implementation, and works for signals corrupted by Gaussian noise. The classification technique is shown to distinguish two similar but different bolts given their one-dimensional profiles

Pattern recognition using invariants defined from higher order spectra - one-dimensional inputs

A new approach to pattern recognition using invariant parameters based on higher order spectra is presented. In particular, invariant parameters derived from the bispectrum are used to classify one-dimensional shapes. The bispectrum, which is translation invariant, is integrated along straight lines passing through the origin in bifrequency space. The phase of the integrated bispectrum is shown to be scale and amplification invariant, as well. A minimal set of these invariants is selected as the feature vector for pattern classification, and a minimum distance classifier using a statistical distance measure is used to classify test patterns. The classification technique is shown to distinguish two similar, but different bolts given their one-dimensional profiles. Pattern recognition using higher order spectral invariants is fast, suited for parallel implementation, and has high immunity to additive Gaussian noise. Simulation results show very high classification accuracy, even for low signal-to-noise ratios.

Watson-Crick pairing, the Heisenberg group and Milnor invariants

We study the secondary structure of RNA determined by Watson-Crick pairing without pseudo-knots using Milnor invariants of links. We focus on the first non-trivial invariant, which we call the Heisenber invariant. The Heisenberg invariant, which is an integer, can be interpreted in terms of the Heisenberg group as well as in terms of lattice paths. We show that the Heisenberg invariant gives a lower bound on the number of unpaired bases in an RNA secondary structure. We also show that the Heisenberg invariant can predict allosteric structures for RNA. Namely, if the Heisenberg invariant is large, then there are widely separated local maxima (i.e., allosteric structures) for the number of Watson-Crick pairs found.

On the invariants of coloured Petri Nets

In this paper, we develop a theorem that enables computation of the place invariants of the union of a finite collection of coloured Petri Nets when the individual nets satisfy certain conditions and their invariants are known. We consider the illustrative examples of the Readers-Writers problem, a resource sharing system, and a network of databases and show how this theorem is a valuable tool in the analysis of concurrent systems.

Anisotropic Gaussian Schell-model beams: Passage through optical systems and associated invariants

Anisotropic Gaussian Schell-model (AGSM) fields and their transformation by first-order optical systems (FOS’s) forming Sp(4,R) are studied using the generalized pencils of rays. The fact that Sp(4,R), rather than the larger group SL(4,R), is the relevant group is emphasized. A convenient geometrical picture wherein AGSM fields and FOS’s are represented, respectively, by antisymmetric second-rank tensors and de Sitter transformations in a (3+2)-dimensional space is developed. These fields are shown to separate into two qualitatively different families of orbits and the invariants over each orbit, two in number, are worked out. We also develop another geometrical picture in a (2+1)-dimensional Minkowski space suitable for the description of the action of axially symmetric FOS’s on AGSM fields, and the invariants, now seven in number, are derived. Interesting limiting cases forming coherent and quasihomogeneous fields are analyzed.

Localization of handwritten text in documents using moment invariants and Delaunay triangulation

This paper describes an approach based on Zernike moments and Delaunay triangulation for localization of hand-written text in machine printed text documents. The Zernike moments of the image are first evaluated and we classify the text as hand-written using the nearest neighbor classifier. These features are independent of size, slant, orientation, translation and other variations in handwritten text. We then use Delaunay triangulation to reclassify the misclassified text regions. When imposing Delaunay triangulation on the centroid points of the connected components, we extract features based on the triangles and reclassify the text. We remove the noise components in the document as part of the preprocessing step so this method works well on noisy documents. The success rate of the method is found to be 86%. Also for specific hand-written elements such as signatures or similar text the accuracy is found to be even higher at 93%.

Open manifolds, Ozsvath-Szabo invariants and exotic R-4 ` S

We construct an invariant of certain open four-manifolds using the Heegaard Floer theory of Ozsvath and Szabo. We show that there is a manifold X homeomorphic to R-4 for which the invariant is non-trivial,showing that X is an exotic R-4. This is the first invariant that detects exotic R-4' s. (C) 2009 Published by Elsevier GmbH.

On Application Of The Method Of Kinetic Invariants To The Description Of Dissolution Accompanied By A Chemical Reaction

The dissolution, accompanied by chemical reaction, of monodisperse solid particles has been analysed. The resulting model, which accounts for the variation of mass transfer coefficient with the size of the dissolving particles, yields an approximate analytical form of a kinetic function. Rigorous numerical and approximate analytical solutions have been obtained for the governing system of nonlinear ordinary differential equations. The transient nature of the dissolution process as well as the accuracy of the analytical solution is brought out by the rigorous numerical solution. The analytical solution is fairly accurate for the major part of the range of operational times encountered in practice.

Attitude estimation using moment invariants

The problem of estimating the three-dimensional rotational parameters of a rigid body from its monocular image data has been considered using the method of moment invariants. Second- and third-order moment invariants are used to construct the feature vector for the scale and orientation independent identification of the camera view axis direction in the body-fixed reference frame. The camera rotation angle about the view axis is derived from second-order central moments. The relative attitude of the rigid body is then expressed in terms of quaternion parameters to model the outputs of a video sensor in attitude control simulations. Experimental results and simulation outputs are presented using the mathematical model of a spacecraft.

Flat connections, geometric invariants and the symplectic nature of the fundamental group of surfaces

In this paper we associate a new geometric invariant to the space of fiat connections on a G (= SU(2))-bundle on a compact Riemann surface M and relate it tcr the symplectic structure on the space Hom(pi(1)(M), G)/G consisting of representations of the fundamental group pi(1)(M) Of M into G module the conjugate action of G on representations.

On some geometric invariants associated to the space of flat connections on an open space

A geometric invariant is associated to the parabolic moduli space on a marked surface and is related to the symplectic structure of the moduli space.

Flat connections, geometric invariants and energy of harmonic functions on compact Riemann surfaces

A geometric invariant is associated to the space of fiat connections on a G-bundle over a compact Riemann surface and is related to the energy of harmonic functions.