Position, rotation, and scale invariant recognition of images using higher-order spectra

A new approach to recognition of images using invariant features based on higher-order spectra is presented. Higher-order spectra are translation invariant because translation produces linear phase shifts which cancel. Scale and amplification invariance are satisfied by the phase of the integral of a higher-order spectrum along a radial line in higher-order frequency space because the contour of integration maps onto itself and both the real and imaginary parts are affected equally by the transformation. Rotation invariance is introduced by deriving invariants from the Radon transform of the image and using the cyclic-shift invariance property of the discrete Fourier transform magnitude. Results on synthetic and actual images show isolated, compact clusters in feature space and high classification accuracies

Digit recognition using trispectral features

Features derived from the trispectra of DFT magnitude slices are used for multi-font digit recognition. These features are insensitive to translation, rotation, or scaling of the input. They are also robust to noise. Classification accuracy tests were conducted on a common data base of 256× 256 pixel bilevel images of digits in 9 fonts. Randomly rotated and translated noisy versions were used for training and testing. The results indicate that the trispectral features are better than moment invariants and affine moment invariants. They achieve a classification accuracy of 95% compared to about 81% for Hu's (1962) moment invariants and 39% for the Flusser and Suk (1994) affine moment invariants on the same data in the presence of 1% impulse noise using a 1-NN classifier. For comparison, a multilayer perceptron with no normalization for rotations and translations yields 34% accuracy on 16× 16 pixel low-pass filtered and decimated versions of the same data.

Reduction of amplitude equations by the renormalization group approach

This article elucidates and analyzes the fundamental underlying structure of the renormalization group (RG) approach as it applies to the solution of any differential equation involving multiple scales. The amplitude equation derived through the elimination of secular terms arising from a naive perturbation expansion of the solution to these equations by the RG approach is reduced to an algebraic equation which is expressed in terms of the Thiele semi-invariants or cumulants of the eliminant sequence { Zi } i=1 . Its use is illustrated through the solution of both linear and nonlinear perturbation problems and certain results from the literature are recovered as special cases. The fundamental structure that emerges from the application of the RG approach is not the amplitude equation but the aforementioned algebraic equation. © 2008 The American Physical Society.

Generalized azimuthal shear deformations in compressible isotropic elastic materials

In this article we study the azimuthal shear deformations in a compressible Isotropic elastic material. This class of deformations involves an azimuthal displacement as a function of the radial and axial coordinates. The equilibrium equations are formulated in terms of the Cauchy-Green strain tensors, which form an overdetermined system of partial differential equations for which solutions do not exist in general. By means of a Legendre transformation, necessary and sufficient conditions for the material to support this deformation are obtained explicitly, in the sense that every solution to the azimuthal equilibrium equation will satisfy the remaining two equations. Additionally, we show how these conditions are sufficient to support all currently known deformations that locally reduce to simple shear. These conditions are then expressed both in terms of the invariants of the Cauchy-Green strain and stretch tensors. Several classes of strain energy functions for which this deformation can be supported are studied. For certain boundary conditions, exact solutions to the equilibrium equations are obtained. © 2005 Society for Industrial and Applied Mathematics.

The eight variable homogeneous degree three bent functions

We determine the affine equivalence classes of the eight variable degree three homogeneous bent functions using a new algorithm. Our algorithm applies to general bent functions and can systematically determine the automorphism groups. We provide a partial verification of the enumeration of eight variable degree three homogeneous bent functions obtained by Meng et al. We determine the affine equivalence classes of these functions.

Safety envelope for security

We present an approach for detecting sensor spoofing attacks on a cyber-physical system. Our approach consists of two steps. In the first step, we construct a safety envelope of the system. Under nominal conditions (that is, when there are no attacks), the system always stays inside its safety envelope. In the second step, we build an attack detector: a monitor that executes synchronously with the system and raises an alarm whenever the system state falls outside the safety envelope. We synthesize safety envelopes using a modified machine learning procedure applied on data collected from the system when it is not under attack. We present experimental results that show effectiveness of our approach, and also validate the several novel features that we introduced in our learning procedure.

Depth of anaesthesia monitoring during procedural sedation and analgesia: A systematic review protocol

Background Procedural sedation and analgesia (PSA) is used to attenuate the pain and distress that may otherwise be experienced during diagnostic and interventional medical or dental procedures. As the risk of adverse events increases with the depth of sedation induced, frequent monitoring of level of consciousness is recommended. Level of consciousness is usually monitored during PSA with clinical observation. Processed electroencephalogram-based depth of anaesthesia (DoA) monitoring devices provide an alternative method to monitor level of consciousness that can be used in addition to clinical observation. However, there is uncertainty as to whether their routine use in PSA would be justified. Rigorous evaluation of the clinical benefits of DoA monitors during PSA, including comprehensive syntheses of the available evidence, is therefore required. One potential clinical benefit of using DoA monitoring during PSA is that the technology could improve patient safety by reducing sedation-related adverse events, such as death or permanent neurological disability. We hypothesise that earlier identification of lapses into deeper than intended levels of sedation using DoA monitoring leads to more effective titration of sedative and analgesic medications, and results in a reduction in the risk of adverse events caused by the consequences of over-sedation, such as hypoxaemia. The primary objective of this review is to determine whether using DoA monitoring during PSA in the hospital setting improves patient safety by reducing the risk of hypoxaemia (defined as an arterial partial pressure of oxygen below 60 mmHg or percentage of haemoglobin that is saturated with oxygen [SpO2] less than 90 %). Other potential clinical benefits of using DoA monitoring devices during sedation will be assessed as secondary outcomes. Methods/design Electronic databases will be systematically searched for randomized controlled trials comparing the use of depth of anaesthesia monitoring devices with clinical observation of level of consciousness during PSA. Language restrictions will not be imposed. Screening, study selection and data extraction will be performed by two independent reviewers. Disagreements will be resolved by discussion. Meta-analyses will be performed if suitable. Discussion This review will synthesise the evidence on an important potential clinical benefit of DoA monitoring during PSA within hospital settings.

Visualization tools for high angular resolution diffusion imaging

There is a major effort in medical imaging to develop algorithms to extract information from DTI and HARDI, which provide detailed information on brain integrity and connectivity. As the images have recently advanced to provide extraordinarily high angular resolution and spatial detail, including an entire manifold of information at each point in the 3D images, there has been no readily available means to view the results. This impedes developments in HARDI research, which need some method to check the plausibility and validity of image processing operations on HARDI data or to appreciate data features or invariants that might serve as a basis for new directions in image segmentation, registration, and statistics. We present a set of tools to provide interactive display of HARDI data, including both a local rendering application and an off-screen renderer that works with a web-based viewer. Visualizations are presented after registration and averaging of HARDI data from 90 human subjects, revealing important details for which there would be no direct way to appreciate using conventional display of scalar images.

Equivariant Birch-Swinnerton-Dyer Conjecture for the Base Change of Elliptic Curves: An Example

Let E be an elliptic curve defined over Q and let K/Q be a finite Galois extension with Galois group G. The equivariant Birch-Swinnerton-Dyer conjecture for h(1)(E x(Q) K)(1) viewed as amotive over Q with coefficients in Q[G] relates the twisted L-values associated with E with the arithmetic invariants of the same. In this paper I prescribe an approach to verify this conjecture for a given data. Using this approach, we verify the conjecture for an elliptic curve of conductor 11 and an S-3-extension of Q.

Renormalization of the axial-vector current in QCD

Following the method of Ioffe and Smilga, the propagation of the baryon current in an external constant axial-vector field is considered. The close similarity of the operator-product expansion with and without an external field is shown to arise from the chiral invariance of gauge interactions in perturbation theory. Several sum rules corresponding to various invariants both for the nucleon and the hyperons are derived. The analysis of the sum rules is carried out by two independent methods, one called the ratio method and the other called the continuum method, paying special attention to the nondiagonal transitions induced by the external field between the ground state and excited states. Up to operators of dimension six, two new external-field-induced vacuum expectation values enter the calculations. Previous work determining these expectation values from PCAC (partial conservation of axial-vector current) are utilized. Our determination from the sum rules of the nucleon axial-vector renormalization constant GA, as well as the Cabibbo coupling constants in the SU3-symmetric limit (ms=0), is in reasonable accord with the experimental values. Uncertainties in the analysis are pointed out. The case of broken flavor SU3 symmetry is also considered. While in the ratio method, the results are stable for variation of the fiducial interval of the Borel mass parameter over which the left-hand side and the right-hand side of the sum rules are matched, in the continuum method the results are less stable. Another set of sum rules determines the value of the linear combination 7F-5D to be ≊0, or D/(F+D)≊(7/12). .AE

Cross polarization in laser beams

Polarization properties of Gaussian laser beams are analyzed in a manner consistent with the Maxwell equations, and expressions are developed for all components of the electric and magnetic field vectors in the beam. It is shown that the transverse nature of the free electromagnetic field demands a nonzero transverse cross-polarization component in addition to the well-known component of the field vectors along the beam axis. The strength of these components in relation to the strength of the principal polarization component is established. It is further shown that the integrated strengths of these components over a transverse plane are invariants of the propagation process. It is suggested that cross- polarization measurement using a null detector can serve as a new method for accurate determination of the center of Gaussian laser beams.

The curvature invariant for a class of homogeneous operators

For an operator T in the class B-n(), introduced by Cowen and Douglas, the simultaneous unitary equivalence class of the curvature and the covariant derivatives up to a certain order of the corresponding bundle E-T determine the unitary equivalence class of the operator T. In a subsequent paper, the authors ask if the simultaneous unitary equivalence class of the curvature and these covariant derivatives are necessary to determine the unitary equivalence class of the operator T is an element of B-n(). Here we show that some of the covariant derivatives are necessary. Our examples consist of homogeneous operators in B-n(). For homogeneous operators, the simultaneous unitary equivalence class of the curvature and all its covariant derivatives at any point w in the unit disc are determined from the simultaneous unitary equivalence class at 0. This shows that it is enough to calculate all the invariants and compare them at just one point, say 0. These calculations are then carried out in number of examples. One of our main results is that the curvature along with its covariant derivative of order (0, 1) at 0 determines the equivalence class of generic homogeneous Hermitian holomorphic vector bundles over the unit disc.

Studies on the assessment of the adequacy of anesthesia

Several hypnosis monitoring systems based on the processed electroencephalogram (EEG) have been developed for use during general anesthesia. The assessment of the analgesic component (antinociception) of general anesthesia is an emerging field of research. This study investigated the interaction of hypnosis and antinociception, the association of several physiological variables with the degree of intraoperative nociception, and aspects of EEG Bispectral Index Scale (BIS) monitoring during general anesthesia. In addition, EEG features and heart rate (HR) responses during desflurane and sevoflurane anesthesia were compared. A propofol bolus of 0.7 mg/kg was more effective than an alfentanil bolus of 0.5 mg in preventing the recurrence of movement responses during uterine dilatation and curettage (D C) after a propofol-alfentanil induction, combined with nitrous oxide (N2O). HR and several HR variability-, frontal electromyography (fEMG)-, pulse plethysmography (PPG)-, and EEG-derived variables were associated with surgery-induced movement responses. Movers were discriminated from non-movers mostly by the post-stimulus values per se or normalized with respect to the pre-stimulus values. In logistic regression analysis, the best classification performance was achieved with the combination of normalized fEMG power and HR during D C (overall accuracy 81%, sensitivity 53%, specificity 95%), and with the combination of normalized fEMG-related response entropy, electrocardiography (ECG) R-to-R interval (RRI), and PPG dicrotic notch amplitude during sevoflurane anesthesia (overall accuracy 96%, sensitivity 90%, specificity 100%). ECG electrode impedances after alcohol swab skin pretreatment alone were higher than impedances of designated EEG electrodes. The BIS values registered with ECG electrodes were higher than those registered simultaneously with EEG electrodes. No significant difference in the time to home-readiness after isoflurane-N2O or sevoflurane-N2O anesthesia was found, when the administration of the volatile agent was guided by BIS monitoring. All other early and intermediate recovery parameters were also similar. Transient epileptiform EEG activity was detected in eight of 15 sevoflurane patients during a rapid increase in the inspired volatile concentration, and in none of the 16 desflurane patients. The observed transient EEG changes did not adversely affect the recovery of the patients. Following the rapid increase in the inhaled desflurane concentration, HR increased transiently, reaching its maximum in two minutes. In the sevoflurane group, the increase was slower and more subtle. In conclusion, desflurane may be a safer volatile agent than sevoflurane in patients with a lowered seizure threshold. The tachycardia induced by a rapid increase in the inspired desflurane concentration may present a risk for patients with heart disease. Designated EEG electrodes may be superior to ECG electrodes in EEG BIS monitoring. When the administration of isoflurane or sevoflurane is adjusted to maintain BIS values at 50-60 in healthy ambulatory surgery patients, the speed and quality of recovery are similar after both isoflurane-N2O and sevoflurane-N2O anesthesia. When anesthesia is maintained by the inhalation of N2O and bolus doses of propofol and alfentanil in healthy unparalyzed patients, movement responses may be best avoided by ensuring a relatively deep hypnotic level with propofol. HR/RRI, fEMG, and PPG dicrotic notch amplitude are potential indicators of nociception during anesthesia, but their performance needs to be validated in future studies. Combining information from different sources may improve the discrimination of the level of nociception.

An algebraic formulation of static isotropy and design of statically isotropic 6-6 Stewart platform manipulators

In this paper, we present an algebraic method to study and design spatial parallel manipulators that demonstrate isotropy in the force and moment distributions. We use the force and moment transformation matrices separately, and derive conditions for their isotropy individually as well as in combination. The isotropy conditions are derived in closed-form in terms of the invariants of the quadratic forms associated with these matrices. The formulation is applied to a class of Stewart platform manipulator, and a multi-parameter family of isotropic manipulators is identified analytically. We show that it is impossible to obtain a spatially isotropic configuration within this family. We also compute the isotropic configurations of an existing manipulator and demonstrate a procedure for designing the manipulator for isotropy at a given configuration. (C) 2008 Elsevier Ltd. All rights reserved.

Measurements of adequacy of anesthesia and level of consciousness during surgery and intensive care

The adequacy of anesthesia has been studied since the introduction of balanced general anesthesia. Commercial monitors based on electroencephalographic (EEG) signal analysis have been available for monitoring the hypnotic component of anesthesia from the beginning of the 1990s. Monitors measuring the depth of anesthesia assess the cortical function of the brain, and have gained acceptance during surgical anesthesia with most of the anesthetic agents used. However, due to frequent artifacts, they are considered unsuitable for monitoring consciousness in intensive care patients. The assessment of analgesia is one of the cornerstones of general anesthesia. Prolonged surgical stress may lead to increased morbidity and delayed postoperative recovery. However, no validated monitoring method is currently available for evaluating analgesia during general anesthesia. Awareness during anesthesia is caused by an inadequate level of hypnosis. This rare but severe complication of general anesthesia may lead to marked emotional stress and possibly posttraumatic stress disorder. In the present series of studies, the incidence of awareness and recall during outpatient anesthesia was evaluated and compared with that of in inpatient anesthesia. A total of 1500 outpatients and 2343 inpatients underwent a structured interview. Clear intraoperative recollections were rare the incidence being 0.07% in outpatients and 0.13% in inpatients. No significant differences emerged between outpatients and inpatients. However, significantly smaller doses of sevoflurane were administered to outpatients with awareness than those without recollections (p<0.05). EEG artifacts in 16 brain-dead organ donors were evaluated during organ harvest surgery in a prospective, open, nonselective study. The source of the frontotemporal biosignals in brain-dead subjects was studied, and the resistance of bispectral index (BIS) and Entropy to the signal artifacts was compared. The hypothesis was that in brain-dead subjects, most of the biosignals recorded from the forehead would consist of artifacts. The original EEG was recorded and State Entropy (SE), Response Entropy (RE), and BIS were calculated and monitored during solid organ harvest. SE differed from zero (inactive EEG) in 28%, RE in 29%, and BIS in 68% of the total recording time (p<0.0001 for all). The median values during the operation were SE 0.0, RE 0.0, and BIS 3.0. In four of the 16 organ donors, EEG was not inactive, and unphysiologically distributed, nonreactive rhythmic theta activity was present in the original EEG signal. After the results from subjects with persistent residual EEG activity were excluded, SE, RE, and BIS differed from zero in 17%, 18%, and 62% of the recorded time, respectively (p<0.0001 for all). Due to various artifacts, the highest readings in all indices were recorded without neuromuscular blockade. The main sources of artifacts were electrocauterization, electromyography (EMG), 50-Hz artifact, handling of the donor, ballistocardiography, and electrocardiography. In a prospective, randomized study of 26 patients, the ability of Surgical Stress Index (SSI) to differentiate patients with two clinically different analgesic levels during shoulder surgery was evaluated. SSI values were lower in patients with an interscalene brachial plexus block than in patients without an additional plexus block. In all patients, anesthesia was maintained with desflurane, the concentration of which was targeted to maintain SE at 50. Increased blood pressure or heart rate (HR), movement, and coughing were considered signs of intraoperative nociception and treated with alfentanil. Photoplethysmographic waveforms were collected from the contralateral arm to the operated side, and SSI was calculated offline. Two minutes after skin incision, SSI was not increased in the brachial plexus block group and was lower (38 ± 13) than in the control group (58 ± 13, p<0.005). Among the controls, one minute prior to alfentanil administration, SSI value was higher than during periods of adequate antinociception, 59 ± 11 vs. 39 ± 12 (p<0.01). The total cumulative need for alfentanil was higher in controls (2.7 ± 1.2 mg) than in the brachial plexus block group (1.6 ± 0.5 mg, p=0.008). Tetanic stimulation to the ulnar region of the hand increased SSI significantly only among patients with a brachial plexus block not covering the site of stimulation. Prognostic value of EEG-derived indices was evaluated and compared with Transcranial Doppler Ultrasonography (TCD), serum neuron-specific enolase (NSE) and S-100B after cardiac arrest. Thirty patients resuscitated from out-of-hospital arrest and treated with induced mild hypothermia for 24 h were included. Original EEG signal was recorded, and burst suppression ratio (BSR), RE, SE, and wavelet subband entropy (WSE) were calculated. Neurological outcome during the six-month period after arrest was assessed with the Glasgow-Pittsburgh Cerebral Performance Categories (CPC). Twenty patients had a CPC of 1-2, one patient had a CPC of 3, and nine patients died (CPC 5). BSR, RE, and SE differed between good (CPC 1-2) and poor (CPC 3-5) outcome groups (p=0.011, p=0.011, p=0.008, respectively) during the first 24 h after arrest. WSE was borderline higher in the good outcome group between 24 and 48 h after arrest (p=0.050). All patients with status epilepticus died, and their WSE values were lower (p=0.022). S-100B was lower in the good outcome group upon arrival at the intensive care unit (p=0.010). After hypothermia treatment, NSE and S-100B values were lower (p=0.002 for both) in the good outcome group. The pulsatile index was also lower in the good outcome group (p=0.004). In conclusion, the incidence of awareness in outpatient anesthesia did not differ from that in inpatient anesthesia. Outpatients are not at increased risk for intraoperative awareness relative to inpatients undergoing general anesthesia. SE, RE, and BIS showed non-zero values that normally indicate cortical neuronal function, but were in these subjects mostly due to artifacts after clinical brain death diagnosis. Entropy was more resistant to artifacts than BIS. During general anesthesia and surgery, SSI values were lower in patients with interscalene brachial plexus block covering the sites of nociceptive stimuli. In detecting nociceptive stimuli, SSI performed better than HR, blood pressure, or RE. BSR, RE, and SE differed between the good and poor neurological outcome groups during the first 24 h after cardiac arrest, and they may be an aid in differentiating patients with good neurological outcomes from those with poor outcomes after out-of-hospital cardiac arrest.