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.

Application of higher order statistics/spectra in biomedical signals : a review

For many decades correlation and power spectrum have been primary tools for digital signal processing applications in the biomedical area. The information contained in the power spectrum is essentially that of the autocorrelation sequence; which is sufficient for complete statistical descriptions of Gaussian signals of known means. However, there are practical situations where one needs to look beyond autocorrelation of a signal to extract information regarding deviation from Gaussianity and the presence of phase relations. Higher order spectra, also known as polyspectra, are spectral representations of higher order statistics, i.e. moments and cumulants of third order and beyond. HOS (higher order statistics or higher order spectra) can detect deviations from linearity, stationarity or Gaussianity in the signal. Most of the biomedical signals are non-linear, non-stationary and non-Gaussian in nature and therefore it can be more advantageous to analyze them with HOS compared to the use of second order correlations and power spectra. In this paper we have discussed the application of HOS for different bio-signals. HOS methods of analysis are explained using a typical heart rate variability (HRV) signal and applications to other signals are reviewed.

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

Homo- and heteronuclear meso,meso-(E)-Ethene-1,2-diyl-Linked Diporphyrins : preparation, X-ray crystal structure, electronic absorption and emission spectra and density functional theory calculations

Homo-and heteronuclear meso,meso-(E)-ethene-1,2-diyl-linked diporphyrins have been prepared by the Suzuki coupling of porphyrinylboronates and iodovinylporphyrins. Combinations comprising 5,10,15-triphenylporphyrin (TriPP) on both ends of the ethene-1,2-diyl bridge M 210 (M 2=H 2/Ni, Ni 2, Ni/Zn, H 4, H 2Zn, Zn 2) and 5,15-bis(3,5-di-tert-butylphenyl)porphyrinato-nickel(II) on one end and H 2, Ni, and ZnTriPP on the other (M 211), enable the first studies of this class of compounds possessing intrinsic polarity. The compounds were characterized by electronic absorption and steady state emission spectra, 1H NMR spectra, and for the Ni 2 bis(TriPP) complex Ni 210, single crystal X-ray structure determination. The crystal structure shows ruffled distortions of the porphyrin rings, typical of Ni II porphyrins, and the (E)-C 2H 2 bridge makes a dihedral angle of 50° with the mean planes of the macrocycles. The result is a stepped parallel arrangement of the porphyrin rings. The dihedral angles in the solid state reflect the interplay of steric and electronic effects of the bridge on interporphyrin communication. The emission spectra in particular, suggest energy transfer across the bridge is fast in conformations in which the bridge is nearly coplanar with the rings. Comparisons of the fluorescence behaviour of H 410 and H 2Ni10 show strong quenching of the free base fluorescence when the complex is excited at the lower energy component of the Soret band, a feature associated in the literature with more planar conformations. TDDFT calculations on the gas-phase optimized geometry of Ni 210 reproduce the features of the experimental electronic absorption spectrum within 0.1 eV. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Robust image hash functions using higher order spectra

Robust hashing is an emerging field that can be used to hash certain data types in applications unsuitable for traditional cryptographic hashing methods. Traditional hashing functions have been used extensively for data/message integrity, data/message authentication, efficient file identification and password verification. These applications are possible because the hashing process is compressive, allowing for efficient comparisons in the hash domain but non-invertible meaning hashes can be used without revealing the original data. These techniques were developed with deterministic (non-changing) inputs such as files and passwords. For such data types a 1-bit or one character change can be significant, as a result the hashing process is sensitive to any change in the input. Unfortunately, there are certain applications where input data are not perfectly deterministic and minor changes cannot be avoided. Digital images and biometric features are two types of data where such changes exist but do not alter the meaning or appearance of the input. For such data types cryptographic hash functions cannot be usefully applied. In light of this, robust hashing has been developed as an alternative to cryptographic hashing and is designed to be robust to minor changes in the input. Although similar in name, robust hashing is fundamentally different from cryptographic hashing. Current robust hashing techniques are not based on cryptographic methods, but instead on pattern recognition techniques. Modern robust hashing algorithms consist of feature extraction followed by a randomization stage that introduces non-invertibility and compression, followed by quantization and binary encoding to produce a binary hash output. In order to preserve robustness of the extracted features, most randomization methods are linear and this is detrimental to the security aspects required of hash functions. Furthermore, the quantization and encoding stages used to binarize real-valued features requires the learning of appropriate quantization thresholds. How these thresholds are learnt has an important effect on hashing accuracy and the mere presence of such thresholds are a source of information leakage that can reduce hashing security. This dissertation outlines a systematic investigation of the quantization and encoding stages of robust hash functions. While existing literature has focused on the importance of quantization scheme, this research is the first to emphasise the importance of the quantizer training on both hashing accuracy and hashing security. The quantizer training process is presented in a statistical framework which allows a theoretical analysis of the effects of quantizer training on hashing performance. This is experimentally verified using a number of baseline robust image hashing algorithms over a large database of real world images. This dissertation also proposes a new randomization method for robust image hashing based on Higher Order Spectra (HOS) and Radon projections. The method is non-linear and this is an essential requirement for non-invertibility. The method is also designed to produce features more suited for quantization and encoding. The system can operate without the need for quantizer training, is more easily encoded and displays improved hashing performance when compared to existing robust image hashing algorithms. The dissertation also shows how the HOS method can be adapted to work with biometric features obtained from 2D and 3D face images.

Application of higher-order spectra for automated grading of diabetic maculopathy

Diabetic macular edema (DME) is one of the most common causes of visual loss among diabetes mellitus patients. Early detection and successive treatment may improve the visual acuity. DME is mainly graded into non-clinically significant macular edema (NCSME) and clinically significant macular edema according to the location of hard exudates in the macula region. DME can be identified by manual examination of fundus images. It is laborious and resource intensive. Hence, in this work, automated grading of DME is proposed using higher-order spectra (HOS) of Radon transform projections of the fundus images. We have used third-order cumulants and bispectrum magnitude, in this work, as features, and compared their performance. They can capture subtle changes in the fundus image. Spectral regression discriminant analysis (SRDA) reduces feature dimension, and minimum redundancy maximum relevance method is used to rank the significant SRDA components. Ranked features are fed to various supervised classifiers, viz. Naive Bayes, AdaBoost and support vector machine, to discriminate No DME, NCSME and clinically significant macular edema classes. The performance of our system is evaluated using the publicly available MESSIDOR dataset (300 images) and also verified with a local dataset (300 images). Our results show that HOS cumulants and bispectrum magnitude obtained an average accuracy of 95.56 and 94.39 % for MESSIDOR dataset and 95.93 and 93.33 % for local dataset, respectively.

Electronic and vibrational spectra of gaspeite

Visible, near-infrared, IR and Raman spectra of magnesian gaspeite are presented. Nickel ion is the main source of the electronic bands as it is the principal component in the mineral where as the bands in IR and Raman spectra are due to the vibrational processes in the carbonate ion as an entity. The combination of electronic absorption and vibrational spectra (including near-infrared, FTIR and Raman) of magnesian gaspeite are explained in terms of the cation co-ordination and the behaviour of CO32– anion in the Ni–Mg carbonate. The electronic absorption spectrum consists of three broad and intense bands at 8130, 13160 and 22730 cm–1 due to spin-allowed transitions and two weak bands at 20410 and 30300 cm–1 are assigned to spin-forbidden transitions of Ni2+ in an octahedral symmetry. The crystal field parameters evaluated from the observed bands are Dq = 810; B = 800 and C = 3200 cm–1. The two bands in the near-infrared spectrum at 4330 and 5130 cm–1 are overtone and combination of CO32– vibrational modes. For the carbonate group, infrared bands are observed at 1020 cm–1(1 ), 870 cm–1 (2), 1418 cm–1 (3) and 750 cm–1 (4), of which3, the asymmetric stretching mode is most intense. Three well resolved Raman bands at 1571, 1088 and 331 cm–1 are assigned to 3, 1 and MO stretching vibrations.

Comparative Electrochemical Study of Unsubstituted and Substituted Bis(phthalocyaninato) Rare Earth(III) Complexes

The electrochemistry of homoleptic substituted phthalocyaninato rare earth double-decker complexes M(TBPc)2 and M(OOPc)2 [M = Y, La...Lu except Pm; H2TBPc = 3(4),12(13),21(22),30(31)-tetra-tert-butylphthalocyanine, H2OOPc = 3,4,12,13,21,22,30,31-octakis(octyloxy)phthalocyanine] has been comparatively studied by cyclic voltammetry (CV) and differential pulse voltammetry (DPV) in CH2Cl2 containing 0.1 M tetra-n-butylammonium perchlorate (TBAP). Two quasi-reversible one-electron oxidations and three or four quasi-reversible one-electron reductions have been revealed for these neutral double-deckers of two series of substituted complexes, respectively. For comparison, unsubstituted bis(phthalocyaninato) rare earth analogues M(Pc)2 (M = Y, La...Lu except Pm; H2Pc = phthalocyanine) have also been electrochemically investigated. Two quasi-reversible one-electron oxidations and up to five quasi-reversible one-electron reductions have been revealed for these neutral double-decker compounds. The three bis(phthalocyaninato)cerium compounds display one cerium-centered redox wave between the first ligand-based oxidation and reduction. The half-wave potentials of the first and second oxidations and first reduction for double-deckers of the tervalent rare earths depend on the size of the metal center. The difference between the redox potentials of the second and third reductions for MIII(Pc)2, which represents the potential difference between the first oxidation and first reduction of [MIII(Pc)2]−, lies in the range 1.08−1.37 V and also gradually diminishes along with the lanthanide contraction, indicating enhanced π−π interactions in the double-deckers connected by the smaller, lanthanides. This corresponds well with the red-shift of the lowest energy band observed in the electronic absorption spectra of reduced double-decker [MIII(Pc′)2]− (Pc′ = Pc, TBPc, OOPc).

Time-Dependent Density Functional Molecular Orbital and Excited State Calculations on Bis(porphyrinyl)butadiynes in the Monocationic, Neutral, Monoanionic, and Dianionic Oxidation States

We report a theoretical study of the multiple oxidation states (1+, 0, 1−, and 2−) of a meso,meso-linked diporphyrin, namely bis[10,15,20-triphenylporphyrinatozinc(II)-5-yl]butadiyne (4), using Time-Dependent Density Functional Theory (TDDFT). The origin of electronic transitions of singlet excited states is discussed in comparison to experimental spectra for the corresponding oxidation states of the close analogue bis{10,15,20-tris[3‘,5‘-di-tert-butylphenyl]porphyrinatozinc(II)-5-yl}butadiyne (3). The latter were measured in previous work under in situ spectroelectrochemical conditions. Excitation energies and orbital compositions of the excited states were obtained for these large delocalized aromatic radicals, which are unique examples of organic mixed-valence systems. The radical cations and anions of butadiyne-bridged diporphyrins such as 3 display characteristic electronic absorption bands in the near-IR region, which have been successfully predicted with use of these computational methods. The radicals are clearly of the “fully delocalized” or Class III type. The key spectral features of the neutral and dianionic states were also reproduced, although due to the large size of these molecules, quantitative agreement of energies with observations is not as good in the blue end of the visible region. The TDDFT calculations are largely in accord with a previous empirical model for the spectra, which was based simplistically on one-electron transitions among the eight key frontier orbitals of the C4 (1,4-butadiyne) linked diporphyrins.