Power Spectrum Of Image Research Articles

Blends of polypropylene with poly(cis‐butadiene) rubber. III. Study on the phase structure and morphology of incompatible blends of polypropylene with poly(cis‐butadiene) rubber

AbstractScanning electron microscopy (SEM) was used to study the structure and morphology of partly compatible binary blends of polypropylene with poly(cis‐butadiene) rubber. The SEM images were transformed by digital image process software designed by our group, and binarized images were obtained. The size (mean diameters dp and characteristic lengths L) of phases was calculated using binarized images. Small‐angle light scattering was employed to study the structure and morphology of phases in the blends. The structural parameters, including correlation distance ac, average chord lengths l, and mean diameter DS to describe the structure and morphology of phases in binary blends, were calculated based on the corresponding theory. The variation of correlation distance ac, average chord length l, and mean diameter DS were the same as that of mean diameters dp and characteristic length L. At the same time, the distribution of sizes of the dispersed phase in binary blends was calculated with graph transition technique, which possessed log‐normal distribution characterization. The power spectrum images corresponding to small‐angle light scattering images were obtained by two‐dimensional fourier transformation of binary images. The correlation distances acf and average chord length lf have been calculated by intensity of power spectrum images and that was the same as ac and l. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 4900–4909, 2006

Method of Processing Closed-Circuit Television Digital Images for Poor Visibility Identification

This study proposes a method for identifying poor visibility under adverse weather conditions by processing closed-circuit television (CCTV) digital images. The weighted intensity of the power spectrum (WIPS) was examined to determine its applicability as a value for the identification of poor visibility. The magnitude of WIPS represents the difference in spatial frequencies within the image on the basis of the human contrast sensitivity function. WIPS was calculated by the following image-processing procedure: the spatial frequency of the cutout image was calculated with a two-dimensional Fourier transform, and the power spectrum of the cutout image was calculated; WIPS was totaled at spatial frequencies that ranged from 1.5 to 18 cycles per degree. Two kinds of experiments were performed to determine whether WIPS represented the subjective visibility assessment values (SVAVs) given by the test subjects. Clear linear relationships between WIPS and SVAVs were found in both experiments. In addition, the two correlation lines overlapped within the whole range of WIPS. These results suggest that WIPS may be appropriate for identifying poor visibility by the use of digital images.

Method of Processing Closed-Circuit Television Digital Images for Poor Visibility Identification

This study proposes a method for identifying poor visibility under adverse weather conditions by processing closed-circuit television (CCTV) digital images. The weighted intensity of the power spectrum (WIPS) was examined to determine its applicability as a value for the identification of poor visibility. The magnitude of WIPS represents the difference in spatial frequencies within the image on the basis of the human contrast sensitivity function. WIPS was calculated by the following image-processing procedure: the spatial frequency of the cutout image was calculated with a two-dimensional Fourier transform, and the power spectrum of the cutout image was calculated; WIPS was totaled at spatial frequencies that ranged from 1.5 to 18 cycles per degree. Two kinds of experiments were performed to determine whether WIPS represented the subjective visibility assessment values (SVAVs) given by the test subjects. Clear linear relationships between WIPS and SVAVs were found in both experiments. In addition, the tw...

In-field evaluation of the modulation transfer function and the signal-to-noise ratio of electronic-display devices

— This paper describes a charged-coupled device (CCD) camera, which was developed for in-field evaluation of the image quality of electronic-display devices [such as cathode-ray tubes (CRTs) and liquid-crystal displays (LCDs)] used for medical applications. Contrary to traditional cameras for display-image-quality evaluation, this CCD camera does not require a sophisticated x-y-z translation stage for mounting and adjustment. Instead, it is handheld and pressed by gentle pressure against the display screen. It is controlled by a software package which was originally developed for display calibration according to the DICOM 14 gray-scale standard display function (GSDF). This software package controls the camera gain when measurements are made at different display luminance, display test patterns, performs image analysis and displays the results of the measurements and calculations. The work concentrated on the measurement of modulation transfer function (MTF) and of signal-to-noise ratio (SNR) per display pixel. The MTF is derived from the Fourier transform of the line spread function (LSF). The single-display-pixel SNR is derived from the integration of the noise power spectrum (NPS) of a camera image taken of a display with a uniform luminance. It is demonstrated that the device can produce repeatable results in terms of MTF and SNR. MTFs were measured on three monochrome CRTs and five monochrome LCDs in order to study repeatability and similar quantities. The MTF was measured on a 5-Mpixel LCD yielding values that lie within 3.5% of the average MTF at the Nyquist frequency and 4.0% of the maximum total sharpness (∫ MTF2 df). The MTF was also measured on a 9-Mpixel LCD, yielding values that lie within 9.0% of the average MTF at the Nyquist frequency and 8.0% of the maximum total sharpness. The SNR was measured eight times on a 3-Mpixel monochrome LCD at nine digital driving levels (DDLs). At a DDL of 185, the mean SNR was 15.694 and the standard deviation (Stdv) was 0.587. At a DDL of 65, the mean SNR was 5.675 and Stdv was 0.120.

Study on Phase Formation and Evolution of High Impact Polystyrene with Poly(Cis‐Butadiene) Rubber Blends

Phase formation and evolution of high‐impact polystyrene with poly(cis‐butadiene) rubber blends was studied. The characteristic length, L, was defined to describe the size of particles, and the graph‐estimation method was introduced to determine the width of the distribution of L. Based on the method, the distribution of L proved to be a log‐normal distribution and the distribution width of L was calculated. The phase structure was also discussed in the wave‐number space. The correlation distance, a c , was defined and computed, applying light‐scattering theory to power spectrum images obtained by 2‐dimensional Fourier transformation (2DFT). The change of a c was in accord with that of L, which meant 2DFT was valid to study the phase structure. A fractal dimension, D c , was introduced to describe the uniformity of the spatial distribution. The result showed that D c was an effective parameter to study the distribution of particles of the dispersed phase.

MO-D-I-609-07: Combined Scatter Subtraction and Digital Restoration of Ho-166 Images for Quantification

Purpose: Ho-166-DOTMP used as targeted radiotherapy to the skeleton has shown great potential for treating multiple myeloma with improved therapeutic index. Potential kidney toxicity has suggested quantification of kidney activity in treatment planning. This has been limited by poor image quality, due to low abundance of imaging photons and relatively high septal penetration of 1.4-MeV photons. Scatter subtraction techniques have been limited because of poor counting statistics after subtraction. We explored the combination of digital restoration and scatter subtraction for Ho-166 image. Method and Materials: A medium-energy collimator was used as a compromise to maximize sensitivity and reduce septal penetration. One photon-window (81-keV) and 2 scatter-windows (lower: 57–73 keV, upper: 89–105 keV) were acquired on a Philips camera with a ¾inch crystal. Images were first subtracted with upper-scatters as energy spectrum from 1.4-MeV photons was flat. Digital restoration was used instead of further subtracting lower scatters. The line-spread function (LSF) was obtained from a subtracted image to determine the modulation transfer function (MTF) at 10-cm depth. Object power spectrum of the Wiener filter was estimated from image power spectrum of Tc-99m-DTPA and Ho-166-DOTMP of the same patient. Results: An upper-scatter subtraction-fraction of 1.0 was confirmed by assessing LSF in air. Subtraction of upper-scatter before Wiener filtering is necessary to remove various image artifacts due to 1.4-MeV photon penetration. The maximum response of the Wiener filter was 2 at 0.08 cycle/pixel and response was decreased to 0.1 at 0.25 cycle/pixel. Image degradation (FWTM) was reduced from 80-mm to 50-mm. Image counting statistics were improved as the total image counts were increased 30% after scatter subtraction and wiener filtering for kidney image 4–6 hour post injection. Conclusion: Combined upper-scatter subtraction and digital restoration improves image quality, allowing quantification of kidney activity with adequate counting statistics to obtain reliable data.

First Implementation Of Phase Diversity At Themis

Phase diversity techniques are robust post-processing tools for image enhancement and correction of telescopic and atmospheric induced aberrations. We present results obtained applying the Partitioned Phase-Diverse Speckle (PPDS) technique to images acquired at THEMIS. We also present an image quality estimator based on image power spectrum content we developed in order to automatically evaluate the results of large amount of data.

Spatial Structure of Complex Cell Receptive Fields Measured with Natural Images

Neuronal receptive fields (RFs) play crucial roles in visual processing. While the linear RFs of early neurons have been well studied, RFs of cortical complex cells are nonlinear and therefore difficult to characterize, especially in the context of natural stimuli. In this study, we used a nonlinear technique to compute the RFs of complex cells from their responses to natural images. We found that each RF is well described by a small number of subunits, which are oriented, localized, and bandpass. These subunits contribute to neuronal responses in a contrast-dependent, polarity-invariant manner, and they can largely predict the orientation and spatial frequency tuning of the cell. Although the RF structures measured with natural images were similar to those measured with random stimuli, natural images were more effective for driving complex cells, thus facilitating rapid identification of the subunits. The subunit RF model provides a useful basis for understanding cortical processing of natural stimuli.

The ACS Virgo Cluster Survey. IV. Data Reduction Procedures for Surface Brightness Fluctuation Measurements with the Advanced Camera for Surveys

The Advanced Camera for Surveys (ACS) Virgo Cluster Survey is a large program to image 100 early-type Virgo galaxies using the F475W and F850LP bandpasses of the Wide Field Channel of the ACS instrument on the Hubble Space Telescope (HST). The scientific goals of this survey include an exploration of the three-dimensional structure of the Virgo Cluster and a critical examination of the usefulness of the globular cluster luminosity function as a distance indicator. Both of these issues require accurate distances for the full sample of 100 program galaxies. In this paper, we describe our data reduction procedures and examine the feasibility of accurate distance measurements using the method of surface brightness fluctuations (SBF) applied to the ACS Virgo Cluster Survey F850LP imaging. The ACS exhibits significant geometrical distortions owing to its off-axis location in the HST focal plane; correcting for these distortions by resampling the pixel values onto an undistorted frame results in pixel correlations that depend on the nature of the interpolation kernel used for the resampling. This poses a major challenge for the SBF technique, which normally assumes a flat power spectrum for the noise. We investigate a number of different interpolation kernels and show through an analysis of simulated galaxy images having realistic noise properties that it is possible, depending on the kernel, to measure SBF distances using distortion-corrected ACS images without introducing significant additional error from the resampling. We conclude by showing examples of real image power spectra from our survey.

Invariant texture retrieval using modified Zernike moments

This paper presents an effective texture descriptor invariant to translation, scaling, and rotation for texture-based image retrieval applications. In order to find the minimal matching distance between two descriptors, existing frequency-layout descriptors require a lot of distance calculations with every possible combination of scaling and rotation values because they are not invariant to geometrical transformation. To cope with this problem, a new compact descriptor is proposed that is theoretically invariant to such transformations. The proposed descriptor is obtained by first calculating the power spectrum of an original texture image for translation invariance and then the power spectrum image is normalized for scale invariance. Finally, modified Zernike moments are calculated for rotation invariance. The proposed algorithm is simpler and lower than conventional algorithms in terms of the computational complexity. The effectiveness of the proposed descriptor for invariant texture retrieval is shown with various texture datasets by comparing the retrieval accuracy, the descriptor size, and the matching complexity of the proposed descriptor with those of conventional descriptors.

Power spectra and distribution of contrasts of natural images from different habitats

Some theories for visual receptive fields postulate that they depend on the image statistics of the natural habitat. Consequently, different habitats may lead to different receptive fields. We thus decided to study how some of the most relevant statistics vary across habitats. In particular, atmospheric and underwater habitats were compared. For these habitats, we looked at two measures of the power spectrum and one of the distributions of contrasts. From power spectra, we analyzed the log–log slope of the fall and the degree of isotropy. From the distribution of contrasts, we analyzed the fall in a semi-log scale. Past studies found that the spatial power spectra of natural atmospheric images fall linearly in logarithmic axes with a slope of about −2 and that their distribution of contrasts shows an approximate linear fall in semi-logarithmic axes. Here, we show that the power spectrum of underwater images have statistically significantly steeper slopes (≈−2.5 in log–log axes) than atmospheric images. The vast majority of power spectra are non-isotropic, but their degree of anisotropy is extremely low, especially in atmospheric images. There are also statistical differences across habitats for the distribution of contrasts, with it falling faster for underwater images than for atmospheric ones. We will argue that these differences are due to the optical properties of water and that the differences have relevance for theories of visual receptive fields. These theories would predict larger receptive fields for aquatic animals compared to land animals.

Mathematical extrapolation of image spectrum for constraint-set design and set-theoretic superresolution.

Several powerful iterative algorithms are being developed for the restoration and superresolution of diffraction-limited imagery data by use of diverse mathematical techniques. Notwithstanding the mathematical sophistication of the approaches used in their development and the potential for resolution enhancement possible with their implementation, the spectrum extrapolation that is central to superresolution comes in these algorithms only as a by-product and needs to be checked only after the completion of the processing steps to ensure that an expansion of the image bandwidth has indeed occurred. To overcome this limitation, a new approach of mathematically extrapolating the image spectrum and employing it to design constraint sets for implementing set-theoretic estimation procedures is described. Performance evaluation of a specific projection-onto-convex-sets algorithm by using this approach for the restoration and superresolution of degraded images is outlined. The primary goal of the method presented is to expand the power spectrum of the input image beyond the range of the sensor that captured the image.

Analysis of the Diffuse Near‐Infrared Emission from Two‐Micron All‐Sky Survey Deep Integration Data: Foregrounds versus the Cosmic Infrared Background

This is one of two papers in which we report the detection of structure in the cosmic infrared background (CIB) between 1.25 and 2.2 μm through the use of data from the Two-Micron All-Sky Survey (2MASS). This paper concentrates on data assembly, analysis, and the estimate of the various foreground contributions; the companion Letter presents the cosmological results for the CIB fluctuations and their implications. By using repeated observations of a specific calibration star field, we were able to achieve integration times in excess of 3900 s, compared to the 7.8 s in the standard 2MASS data product. This yielded a point-source detection limit (3 σ) of +18.5 mag in the Ks band. The resulting co-added images were processed to remove point sources to a limiting surface brightness of +20 mag arcsec-2 or 40 nW m-2 sr-1. The remaining maps contained over 90% of the pixels and were Fourier transformed to study the spatial structure of the diffuse background light. After removing resolved sources and other artifacts, we find that the power spectrum of the final images has a power-law distribution consistent with clustering by distant galaxies. We estimate here the contributions to this signal from Galactic foregrounds, atmospheric OH-glow, zodiacal light, and instrument noise, all of which are small and of different slopes. This supports the identification offered in the companion Letter of the signal as coming from the CIB fluctuations produced by distant clustered galaxies.

Spectral analysis of full field digital mammography data.

The spectral content of mammograms acquired from using a full field digital mammography (FFDM) system are analyzed. Fourier methods are used to show that the FFDM image power spectra obey an inverse power law; in an average sense, the images may be considered as 1/f fields. Two data representations are analyzed and compared (1) the raw data, and (2) the logarithm of the raw data. Two methods are employed to analyze the power spectra (1) a technique based on integrating the Fourier plane with octave ring sectioning developed previously, and (2) an approach based on integrating the Fourier plane using rings of constant width developed for this work. Both methods allow theoretical modeling. Numerical analysis indicates that the effects due to the transformation influence the power spectra measurements in a statistically significant manner in the high frequency range. However, this effect has little influence on the inverse power law estimation for a given image regardless of the data representation or the theoretical analysis approach. The analysis is presented from two points of view (1) each image is treated independently with the results presented as distributions, and (2) for a given representation, the entire image collection is treated as an ensemble with the results presented as expected values. In general, the constant ring width analysis forms the foundation for a spectral comparison method for finding spectral differences, from an image distribution sense, after applying a nonlinear transformation to the data. The work also shows that power law estimation may be influenced due to the presence of noise in the higher frequency range, which is consistent with the known attributes of the detector efficiency. The spectral modeling and inverse power law determinations obtained here are in agreement with that obtained from the analysis of digitized film-screen images presented previously. The form of the power spectrum for a given image is approximately l/f2beta with beta approximately 1.4-1.5.

Application of image processing techniques for analysis of nano- and micro-spaces in carbon materials

Transmission electron microscopy (TEM) is one of the most useful methods to clarify the structure in carbon materials. We developed quantitative analysis methods for the texture and structure of carbon materials containing the micro- and nano-spaces by using electron microscopy combined with image processing technique. The relations between phase transfer functions and TEM images of amorphous carbon films which consist of random arrangement of carbon layers were investigated using image processing. The similar patterns as the laser diffraction are obtained by the two-dimensional (2D) fast Fourier transform (FFT) of the digitized TEM images. The details of frequency distribution can be analyzed by integration around the central point of the power spectrum images. We applied this new technique to the study of microtexture and structure of graphite intercalation compounds (GICs). As a result of application of the frequency analysis using 2D FFT to the CuCl 2-GIC, a characteristic power spectrum pattern called streak, which was similar to the electron diffraction pattern, was obtained. The images corresponding to the specific frequencies were reconstructed by 2D inverse FFT (IFFT). The stage structure of CuCl 2-GICs was discussed by using this technique.

The near-surface current velocity determined from image sequences of the sea surface

A method to measure the ocean's near-surface current velocity vector based on the analysis of remote sea-surface image sequences was developed. The spatial and temporal records were transformed to the wavenumber-frequency domain, resulting in a three-dimensional (3-D) image power spectrum. In the spectrum, the signal energy of the waves is localized on a shell defined by the dispersion relation of surface waves. The sum of the sensor's velocity and the near-surface current profile deforms the dispersion shell due to the Doppler-frequency shift. An iterative least-squares fitting technique and an error-estimation model was implemented. To improve the method's accuracy, spectral wave energy found in higher harmonics of the dispersion shell and aliasing effects are taken into account. The most important nonlinear mechanism leading to higher harmonics is explained as resulting from wave shadowing due to the low grazing angles typical for ground- or ship-based radars. The improved method is examined analytically and is tested with Monte Carlo simulations. The variation of the shape of the measured or simulated 3-D image spectra, especially the peak wavenumber, the directional spread, and the main travel direction, controls the behavior and accuracy of the technique. A comparison of velocities acquired by nautical radar and independent Doppler log current measurements is presented. The technique's accuracy, its limits, and its adaptability are discussed. Additional improvements are proposed.

Beats, kurtosis and visual coding

Techniques adapted from standard higher-order statistical methods are applied to natural-image data in an attempt to discover exactly what makes `wavelet' representations of natural scenes sparse. Specifically, this paper describes a measure known as the phase-only second spectrum, a fourth-order statistic which quantifies harmonic beat interactions in data, and uses it to show that there are statistical consistencies in the phase spectra of natural scenes. The orientation-averaged phase-only second spectra of natural images appear to show power-law behaviour rather like image power spectra, but with a spectral exponent of approximately -1 instead of -2. They also appear to display a similar form of scale-invariance. Further experimental results indicate that the form of these spectra can account for the observed sparseness of bandpass-filtered natural scenes. This implies an intimate relationship between the merits of sparse neural coding and the exploitation of non-Gaussian `beats' structures by the visual system.

Fourier Amplitude Decay of Electron Cryomicroscopic Images of Single Particles and Effects on Structure Determination

Several factors, including spatial and temporal coherence of the electron microscope, specimen movement, recording medium, and scanner optics, contribute to the decay of the measured Fourier amplitude in electron image intensities. We approximate the combination of these factors as a single Gaussian envelope function, the width of which is described by a single experimental B-factor. We present an improved method for estimating this B-factor from individual micrographs by combining the use of X-ray solution scattering and numerical fitting to the average power spectrum of particle images. A statistical estimation from over 200 micrographs of herpes simplex virus type-1 capsids was used to estimate the spread in the experimental B-factor of the data set. The B-factor is experimentally shown to be dependent on the objective lens defocus setting of the microscope. The average B-factor, the X-ray scattering intensity of the specimen, and the number of particles required to determine the structure at a lower resolution can be used to estimate the minimum fold increase in the number of particles that would be required to extend a single particle reconstruction to a specified higher resolution. We conclude that microscope and imaging improvements to reduce the experimental B-factor will be critical for obtaining an atomic resolution structure.

Woven Fabric Quality Evaluation Using Image Analysis

As a factor important to fabric quality, reed marks are studied by theoretical and experimental methods. In order to analyze their appearance, the power spectrum of a fabric's image is simulated in terms of that fabric's geometry. These power spectra offer peaks of wavelength coincident with the reed spacing. Further, they are used as an indicator to explain reed marks in terms of packed warps. At this same wavelength in experimental power spectra, there is also a peak that exhibits dependence on fabric quality. This peak adequately describes the appearance of the reed marks and thus can be used as a quality indicator for a woven fabric.

Cool dust and gas in the Small Magellanic Cloud

We present high-angular-resolution, far-infrared images of the Small Magellanic Cloud (SMC). The images were reconstructed from data obtained with the Infrared Astronomical Satellite (IRAS), using the Pyramid Maximum Entropy algorithm. The angular resolutions of the images are 1 arcmin at 12, 25 and 60 mu m, and 1.7 arcmin at 100 mu m, which provides an excellent complement to the recent neutral hydrogen (H I) survey from the Australia Telescope Compact Array, which has a resolution of 1.6 arcmin. We use the 60- and 100-mu m data, together with a standard dust model, to derive a temperature map and a dust column density distribution. Dust temperatures range from 23 to 45 K, which is, on average, warmer than for the Galaxy, although there is a deficit of warm, very small dust grains in the SMC. The total amount of cool dust in the SMC is 1.8(-0.2)(+1.3) x 10(4) M.. There is a significant variation of the observed dust-to-gas ratio across the SMC. This may be caused by corresponding variations in metallicity, but this explanation is not supported by the limited available data in the literature. Alternatively, there may be a large amount of molecular hydrogen (H(2)) in the SMC, similar to 8 x 10(8) M., and/or a large amount (similar to 10(6) M.) of cold dust (less than or equal to 15 K) not seen by IRAS or COBE/DIRBE. The average dust-to-atomic gas ratio is, by mass, 8.2 x 10(-5), which is a factor of similar to 30 below the Galactic value. The spatial power spectrum of the dust column density image can be approximated by P(d)(k) proportional to k(-3.1), which shows that, as with the H I power spectrum, there is no preferred scale size for dust clouds. A spatial coherence analysis shows that, over a wide range of spatial scales (greater than or similar to 50 pc), H I and dust are well correlated (> 60 per cent).