2D Cross-correlation Research Articles

Estimating drift velocity of polar cap patches with all‐sky airglow imager at Resolute Bay, Canada

Highly sensitive all‐sky airglow imager has been operative at Resolute Bay, Canada (74.73°N, 265.07°E; AACGM latitude 82.9°) since January 2005. We present, as a first result from the imager, an event of polar cap patches drifting anti‐sunward during the southward IMF conditions. Magnitude and direction of patch drift velocities are computed with a temporal resolution of 2 min by using the newly developed patch‐tracking algorithm based on 2D cross correlation analysis. It is well visualized that the patches change their moving speed and direction drastically in a short time scale (a few minutes). Speed of the patch is primally controlled by the IMF Bz. Dawn‐dusk component of the patch drift velocities is well correlated with the IMF By in agreement with published By dependence of the nightside polar cap convection. However, response of the patch drift direction to the IMF By is found to be much slower (≈20 min) than that of the drift speed to the IMF Bz (almost instantaneous).

Nucleated dwarf elliptical galaxies in the Virgo cluster

Using images from a charge-coupled device survey with the Wide Field Camera on the Isaac Newton Telescope, we performed B- and I-band photometry on 156 Virgo cluster dwarf elliptical (dE) galaxies, 25 candidate new cluster dwarfs, and nine candidate field dwarfs. Galaxies were modelled with Sérsic profiles, using both 1D χ2 and 2D cross-correlation methods, with nuclei modelled as point sources. The intensity profiles of 50 galaxies previously classified as dE, dE?, or ? are more accurately fitted if a nucleus is included, and this results in the majority of dwarfs now being classified as nucleated dwarf ellipticals (dE,N). Some faint galaxies with B magnitudes of 18–21 have particularly large relative nuclei, while a small number have apparent central dimmings. For cluster dE,N galaxies the nucleus magnitude is correlated with the magnitude of the host galaxy. The profile parameters of dE and dE,N galaxies are not significantly different, and there is no evident discontinuity in relative nucleus size between non-nucleated and nucleated dwarfs, suggesting that they may form a continuum. Nuclei are on average redder than their underlying galaxies, though a spread of relative colours was found, and two-fifths of nuclei are bluer. Formation mechanisms of nuclei are discussed: at least some appear to have formed in an already existing non-nucleated galaxy, though others may have formed simultaneously with their galaxies and subsequently evolved within them.

Estimation of cirrus and stratus cloud height using landsat data and 3D graphical representation

Cirrus and stratus cloud heights are estimated using LANDSAT MSS(MultiSpectral Scanner) and TM(Thematic mapper) data. Cloud heights are calculated from the sun elevation angle and the horizontal distance between cloud and its shadow templates. The matching of these templates is accomplished by the 2D cross-correlation function. Before accomplishing the matching, histogram equalization, inversion of shadow template, and Fourier Fast Transformation are applied to both templates. Then 2D cross-correlation function is calculated in the frequency domain. Correlation coefficients are 3D graphically displayed to check visually how sharply the templates match. The effects of the skew angle and the nonnadir observation angle are taken into consideration to modify the direction from the cloud template to its corresponding shadow template. The results show that this method is accurate within several pixels.

High-Precision Motion Estimate of Soft Tissue in the Physiologaical State Using Two-Dimensional Complex-Valued Wavelet Transform of Speckle Echo

In contrast with tissue elasticity imaging, a nonquantitative but high-resolution and real-time image of abdominal tissue strain could be a promising diagnostic tool for ultrasonic visualized palpation using a conventional array transducer. In order to realize the 2D strain imaging, accurate estimation of the lateral displacement perpendicular to the beam axis is required, which overcomes the limitation of the 2D cross-correlation method affected by the data window which determines the spatial resolution and computing efficiency of the estimation. The hierarchical 2D wavelet coefficients of successive complex-valued echo frames were applied to realize the excellent performance of the 2D motion estimate in accuracy, variance, spatial resolution and computational cost. The resultant total performance of this algorithm is evaluated on the basis of physiological free motion to obtain clinical data of hepatocellular carcinoma.

OCT elastography: imaging microscopic deformation and strain of tissue

Optical coherence tomography (OCT) has been applied to the study of the microscopic deformation of biological tissue under compressive stress. We describe the hardware and theory of operation of an OCT elastography system that measures internal displacements as small as a few micrometers by using 2D cross-correlation speckle tracking. Results obtained from gelatin scattering models, pork meat, and intact skin suggest possible medical applications of the technique.

HST Planetary Camera images of quasar host galaxies

We present Hubble Space Telescope (HST) images of seven low-redshift quasars (six taken with the Planetary Camera, one with the Wide Field Camera). These complete the sample of 14 quasars observed by the Faint Object Camera Investigation Definition Team (FOC IDT). Following subtraction of the quasar nuclear light, host galaxies can be seen in all seven cases. A combination of the optical morphology and luminosity profiles of the residual host galaxies and the results of 2D cross-correlation model fitting implies that five of the objects have elliptical host galaxies and two have disc host galaxies. The luminosities vary from slightly fainter than L* to about 1.3 mag brighter than L*. We discuss the properties of the complete sample of 14 quasars. Nine of the objects appear to have elliptical host galaxies (all six of the radio-loud quasars in the sample as well as three radio-quiet quasars). Two further radio-quiet quasars appear to lie in disc galaxies. The other three objects (radio-quiet, ultraluminous infrared quasars) all lie in violently interacting systems. The sample as a whole has an average luminosity about 0.8 mag brighter than L*, although the radio-loud objects have hosts on average 0.7 mag brighter than the radio-quiet objects. We compare our results with those from HST imaging of quasars by other authors. Taken together, our observations are in broad agreement with those of Bahcall et al. Radio-loud quasars appear to lie in luminous elliptical galaxies whereas radio-quiet quasars are found to lie in either elliptical or spiral hosts. Host galaxy luminosities (of radio-quiet and radio-loud quasars) are much brighter than would be expected if they followed a Schechter luminosity function.

Three-dimensional distortion correction applied to tomographic reconstructions of sectioned crystals

Unaveraged tomograms of embedded and sectioned insect flight muscle show not only structural variation within the individual unit cells but also defects in the filament lattice such as lack of straightness of the filaments and wrinkling of the sections. Adaptation of conventional 2D crystal image processing methods usually average out these structural variations and lattice defects thereby reducing the resolution and information content of the 3D reconstructions. We present here a computational method to correct the reconstructed 3D object for these distortions to make it suitable for further analysis. The correction is an extension of conventional 2D cross-correlation techniques applied to a 3D image. These procedures determine the unit cell positions of the distorted crystal and use a spline-fitting approach to calculate a mapping function from the observed positions that is subsequently used to reinterpolate the image onto a regular grid. The resulting reinterpolated image is corrected for both filament straightening as well as section wrinkling.

Two-Dimensional Correlation of Fourier Transform Near-Infrared and Fourier Transform Raman Spectra I: Mixtures of Sugar and Protein

Two-dimensional (2D) correlation of near-infrared (NIR) and Raman spectra was carried out for mixtures of protein (lysozyme) and sugar (sucrose) to investigate the potential of this technique for qualitative NIR spectral interpretation. Cross-correlation by least-squares was employed to assess changes in both sets of spectra which result from changes in the set of sample spectra. Fourier transform (FT) NIR and NIR-excited FT-Raman spectra were measured for each of the samples under the same conditions, and point-for-point 2D cross-correlation was calculated. In this technique, each wavenumber in the NIR region gives rise to a sliced Raman spectrum where each data point is correlated to the NIR wavenumber, while each wavenumber in a Raman spectrum provides a sliced NIR spectrum in which each data point is correlated to the Raman wavenumber. For example, choosing NIR wavenumbers 7272, 6960, 6324, and 4812 cm−1gives sliced Raman spectra with features attributable to sucrose, while choosing NIR wavenumbers at 8424, 5148, 5052, and 4584 cm−1provides slices with distinct lysozyme features. Therefore, the technique permits the determination of the most probable origin of NIR signals by connecting NIR spectra, which have rather broad and overlapped bands, to Raman spectra consisting of sharp and clearly separated bands. It is also possible to produce sliced NIR spectra of lysozyme and sucrose by properly selecting wavenumbers in their Raman spectra. The NIR slices explain which wavenumbers in the NIR region are correlated to lysozyme or to sucrose. Thus, 2D correlation spectroscopy helps explain the reasons why certain wavenumbers are selected in a chemometric calibration model.

Estimation of Cirrus and Stratus Cloud Heights Using Landsat Imagery

Abstract A new method based upon high-spatial-resolution imagery is presented that matches cloud and shadow regions to estimate cirrus and stratus cloud heights. The distance between the cloud and the matching shadow pattern is accomplished using the 2D cross-correlation function from which the cloud height is derived. The distance between the matching cloud-shadow patterns is verified manually. The derived heights also are validated through comparison with a temperature-based retrieval of cloud height. It is also demonstrated that an estimate of cloud thickness can be retrieved if both the sunside and antisunside of the cloud-shadow pair are apparent. The technique requires some intepretation to determine the cloud height level retrieved (i.e., the top, base, or mid-level). It is concluded that the method is accurate to within several pixels, equivalent to cloud height variations of about ±250 m. The results show that precise placement of the templates is unnecessary, so that the development of a semiaut...

Two-Dimensional Vibrational Spectroscopy II: Correlation of the Absorptions of Lignins in the Mid- and Near-Infrared

Two-dimensional (2D) statistical correlation of mid- and near-infrared spectra was used as a means to assist with qualitative spectral interpretation of the lignin carbohydrate fractions from plant materials. Cross-correlation by least-squares is used to assess changes in both regions that result from changes in the set of sample spectra. The technique has been applied to a set of specially prepared “lignin” samples that differ in lignin content, species of origin, and method of preparation. Dispersive near-infrared (NIR) and Fourier transformed mid-infrared (FT-IR) diffuse reflectance spectra (DRIFTS) were obtained on each of the samples, and point-for-point 2D cross-correlation was obtained. The technique permits the correlation of the combination and overtone bands of the NIR region with the fundamental vibrations in the mid-infrared (MIR) region. The results show a broad correlation of aromatic C-H stretch at 3022 cm−1 in the MIR to 1666-nm location in the NIR region and other locations to a lesser extent all across the NIR from 1400 to 2500 nm. A narrower region of correlation was found for the phenolic O-H stretch in the MIR at 3663 cm−1 to 1428 nm and 1938 nm in the MIR. Multiple narrow correlations occur in the area of the summation bands from 1450 to 1650 cm−1, indicative of substitution patterns and correlated areas of C-H and O-H stretch in the NIR.

Two-Dimensional Vibration Spectroscopy: Correlation of Mid- and Near-Infrared Regions

A novel approach, utilizing a two-dimensional (2D) statistical correlation of mid- and near-infrared spectra, is presented as a means to assist with qualitative spectral interpretation. The method utilizes cross-correlation by least-squares to assess changes in both regions that result from changes in sample composition. The technique has been applied to complex agricultural samples that differ in wax (cuticle), carbohydrate, protein, and lignin content. Dispersive near-infrared (NIR) and interferometric mid-infrared (FT-IR) diffuse reflectance spectra were obtained on each of the samples, and point-for-point 2D cross-correlation was obtained. The technique permits the correlation of the combination and overtone region of the NIR to the fundamental vibrations in the mid-infrared (MIR) region. This allows the determination of the most probable source of NIR signals and verification of the “real” information content of the purely statistically derived signals whose intensities currently are used for quantitative analysis in this spectral region.

Stochastic time resolved CIDNP spectroscopy

A method to obtain time-resolved CIDNP N.M.R. spectra at low excitation powers and high time resolution is proposed. With binary modulation of light and r.f. input signals a 2D time domain function is computed on-line from analog 2D cross-correlation of input and response signals. This function transforms into a stack of one-dimensional CIDNP spectra, which follow the time evolution of the stimulated chemical reaction.