IMAGE DESCRIPTION WITH NONSEPARABLE TWO-DIMENSIONAL CHARLIER AND MEIXNER MOMENTS

2011 ◽  
Vol 25 (01) ◽  
pp. 37-55 ◽  
Author(s):  
HONGQING ZHU ◽  
MIN LIU ◽  
YU LI ◽  
HUAZHONG SHU ◽  
HUI ZHANG
Keyword(s):  
Recurrence Relations ◽  
Numerical Approximation ◽  
Dynamic Range ◽  
Reconstruction Error ◽  
Coordinate Space ◽  
Image Description ◽  
Meixner Polynomials ◽  
Discrete Orthogonal ◽  
Computational Aspects ◽  
Meixner Moments

This paper presents two new sets of nonseparable discrete orthogonal Charlier and Meixner moments describing the images with noise and that are noise-free. The basis functions used by the proposed nonseparable moments are bivariate Charlier or Meixner polynomials introduced by Tratnik et al. This study discusses the computational aspects of discrete orthogonal Charlier and Meixner polynomials, including the recurrence relations with respect to variable x and order n. The purpose is to avoid large variation in the dynamic range of polynomial values for higher order moments. The implementation of nonseparable Charlier and Meixner moments does not involve any numerical approximation, since the basis function of the proposed moments is orthogonal in the image coordinate space. The performances of Charlier and Meixner moments in describing images were investigated in terms of the image reconstruction error, and the results of the experiments on the noise sensitivity are given.

scholarly journals Bivariate Hahn moments for image reconstruction

2014 ◽  
Vol 24 (2) ◽  
pp. 417-428 ◽  
Author(s):  
Haiyong Wu ◽  
Senlin Yan
Keyword(s):  
Image Reconstruction ◽  
Numerical Stability ◽  
Parameter Selection ◽  
Experimental Results ◽  
Grayscale Image ◽  
Orthogonal Moments ◽  
Binary Images ◽  
Hahn Polynomials ◽  
Discrete Orthogonal ◽  
Computational Aspects

Abstract This paper presents a new set of bivariate discrete orthogonal moments which are based on bivariate Hahn polynomials with non-separable basis. The polynomials are scaled to ensure numerical stability. Their computational aspects are discussed in detail. The principle of parameter selection is established by analyzing several plots of polynomials with different kinds of parameters. Appropriate parameters of binary images and a grayscale image are obtained through experimental results. The performance of the proposed moments in describing images is investigated through several image reconstruction experiments, including noisy and noise-free conditions. Comparisons with existing discrete orthogonal moments are also presented. The experimental results show that the proposed moments outperform slightly separable Hahn moments for higher orders.

scholarly journals Bounds for zeros of Meixner and Kravchuk polynomials

2014 ◽  
Vol 17 (1) ◽  
pp. 47-57 ◽  
Author(s):  
A. Jooste ◽  
K. Jordaan
Keyword(s):  
Orthogonal Polynomials ◽  
Recurrence Relations ◽  
Discrete Orthogonal ◽  
Bounds For Zeros ◽  
Set Of Points ◽  
Kravchuk Polynomials

AbstractThe zeros of certain different sequences of orthogonal polynomials interlace in a well-defined way. The study of this phenomenon and the conditions under which it holds lead to a set of points that can be applied as bounds for the extreme zeros of the polynomials. We consider different sequences of the discrete orthogonal Meixner and Kravchuk polynomials and use mixed three-term recurrence relations, satisfied by the polynomials under consideration, to identify bounds for the extreme zeros of Meixner and Kravchuk polynomials.

Numerical Evaluation of the Green Function of Water-Wave Radiation and Diffraction

1986 ◽  
Vol 30 (02) ◽  
pp. 69-84 ◽  
Author(s):  
J. G. Telste ◽  
F. Noblesse
Keyword(s):  
Green Function ◽  
Power Series ◽  
Water Wave ◽  
Numerical Evaluation ◽  
Recurrence Relations ◽  
Numerical Approximation ◽  
Computing Time ◽  
Absolute Error ◽  
Wave Radiation ◽  
The Green Function

This study presents a simple, accurate, and efficient method for numerically evaluating the Green function, and its gradient, of the theory of water-wave radiation and diffraction. The method is based on five expressions for the Green function that are useful in complementary regions of the quadrant in which the Green function is defined. These expressions consist of asymptotic expansions, ascending series, two complementary Taylor series, and a numerical approximation based on a modified form of the Haskind integral representation. The four series representations are refinements of the series obtained previously in Noblesse [1].2 These series express the Green function and its gradient as sums of power series and terms involving functions of only one variable. The power series can be evaluated quickly by using recurrence relations; and the functions of one variable, by using rational approximations. The method permits the Green function and its gradient to be evaluated with an absolute error smaller than 10–6 very efficiently (with computing time less than 6 × 10–5 sec on a CDC CYBER 176 computer). A listing of the FORTRAN subroutine is included in the paper.

Computational Aspects of Three-Term Recurrence Relations

SIAM Review ◽  
1967 ◽  
Vol 9 (1) ◽  
pp. 24-82 ◽  
Author(s):  
Walter Gautschi
Keyword(s):  
Recurrence Relations ◽  
Computational Aspects

scholarly journals On Computational Aspects of Krawtchouk Polynomials for High Orders

2020 ◽  
Vol 6 (8) ◽  
pp. 81 ◽  
Author(s):  
Basheera M. Mahmmod ◽  
Alaa M. Abdul-Hadi ◽  
Sadiq H. Abdulhussain ◽  
Aseel Hussien
Keyword(s):  
Recurrence Relations ◽  
Computational Cost ◽  
Maximum Size ◽  
Reconstruction Error ◽  
Feature Descriptor ◽  
Large Signal ◽  
Krawtchouk Polynomials ◽  
Localization Property ◽  
Polynomial Coefficients ◽  
Polynomial Size

Discrete Krawtchouk polynomials are widely utilized in different fields for their remarkable characteristics, specifically, the localization property. Discrete orthogonal moments are utilized as a feature descriptor for images and video frames in computer vision applications. In this paper, we present a new method for computing discrete Krawtchouk polynomial coefficients swiftly and efficiently. The presented method proposes a new initial value that does not tend to be zero as the polynomial size increases. In addition, a combination of the existing recurrence relations is presented which are in the n- and x-directions. The utilized recurrence relations are developed to reduce the computational cost. The proposed method computes approximately 12.5% of the polynomial coefficients, and then symmetry relations are employed to compute the rest of the polynomial coefficients. The proposed method is evaluated against existing methods in terms of computational cost and maximum size can be generated. In addition, a reconstruction error analysis for image is performed using the proposed method for large signal sizes. The evaluation shows that the proposed method outperforms other existing methods.

Slow-Scan CCD Observation of Backscattering Patterns in SEM

1992 ◽  
Vol 50 (2) ◽  
pp. 1308-1309
Author(s):  
F. Ouyang ◽  
D. A. Ray ◽  
O. L. Krivanek
Keyword(s):  
Electron Beam ◽  
Electron Microscope ◽  
Scanning Electron Microscope ◽  
Dynamic Range ◽  
High Sensitivity ◽  
Lens System ◽  
Wide Dynamic Range ◽  
Peltier Cooler ◽  
Diffraction Patterns ◽  
Scanning Electron

Electron backscattering Kikuchi diffraction patterns (BKDP) reveal useful information about the structure and orientation of crystals under study. With the well focused electron beam in a scanning electron microscope (SEM), one can use BKDP as a microanalysis tool. BKDPs have been recorded in SEMs using a phosphor screen coupled to an intensified TV camera through a lens system, and by photographic negatives. With the development of fiber-optically coupled slow scan CCD (SSC) cameras for electron beam imaging, one can take advantage of their high sensitivity and wide dynamic range for observing BKDP in SEM.We have used the Gatan 690 SSC camera to observe backscattering patterns in a JEOL JSM-840A SEM. The CCD sensor has an active area of 13.25 mm × 8.83 mm and 576 × 384 pixels. The camera head, which consists of a single crystal YAG scintillator fiber optically coupled to the CCD chip, is located inside the SEM specimen chamber. The whole camera head is cooled to about -30°C by a Peltier cooler, which permits long integration times (up to 100 seconds).

Quantitative energy-filtered electron diffraction

1994 ◽  
Vol 52 ◽  
pp. 992-993
Author(s):  
R. Vincent
Keyword(s):  
Electron Diffraction ◽  
Inelastic Scattering ◽  
Dynamic Range ◽  
Electron Optics ◽  
Surface Layers ◽  
High Brightness ◽  
Inclined Surfaces ◽  
Perfect Symmetry ◽  
Amorphous Surface ◽  
The Ideal

Microanalysis and diffraction on a sub-nanometre scale have become practical in modern TEMs due to the high brightness of field emission sources combined with the short mean free paths associated with both elastic and inelastic scattering of incident electrons by the specimen. However, development of electron diffraction as a quantitative discipline has been limited by the absence of any generalised theory for dynamical inelastic scattering. These problems have been simplified by recent innovations, principally the introduction of spectrometers such as the Gatan imaging filter (GIF) and the Zeiss omega filter, which remove the inelastic electrons, combined with annual improvements in the speed of computer workstations and the availability of solid-state detectors with high resolution, sensitivity and dynamic range.Comparison of experimental data with dynamical calculations imposes stringent requirements on the specimen and the electron optics, even when the inelastic component has been removed. For example, no experimental CBED pattern ever has perfect symmetry, departures from the ideal being attributable to residual strain, thickness averaging, inclined surfaces, incomplete cells and amorphous surface layers.

Direct measurement of electron-diffraction-pattern intensities using an energy loss spectrometer

1989 ◽  
Vol 47 ◽  
pp. 668-669
Author(s):  
A. G. Jackson ◽  
M. Rowe
Keyword(s):  
Thermal Effects ◽  
Dynamic Range ◽  
Scattering Amplitude ◽  
Dynamical Theory ◽  
Site Symmetry ◽  
Proof Of Concept ◽  
Parallel Acquisition ◽  
Kinematic Approximation ◽  
Speed Up ◽  
Structure Calculations

Diffraction intensities from intermetallic compounds are, in the kinematic approximation, proportional to the scattering amplitude from the element doing the scattering. More detailed calculations have shown that site symmetry and occupation by various atom species also affects the intensity in a diffracted beam. [1] Hence, by measuring the intensities of beams, or their ratios, the occupancy can be estimated. Measurement of the intensity values also allows structure calculations to be made to determine the spatial distribution of the potentials doing the scattering. Thermal effects are also present as a background contribution. Inelastic effects such as loss or absorption/excitation complicate the intensity behavior, and dynamical theory is required to estimate the intensity value.The dynamic range of currents in diffracted beams can be 104or 105:1. Hence, detection of such information requires a means for collecting the intensity over a signal-to-noise range beyond that obtainable with a single film plate, which has a S/N of about 103:1. Although such a collection system is not available currently, a simple system consisting of instrumentation on an existing STEM can be used as a proof of concept which has a S/N of about 255:1, limited by the 8 bit pixel attributes used in the electronics. Use of 24 bit pixel attributes would easily allowthe desired noise range to be attained in the processing instrumentation. The S/N of the scintillator used by the photoelectron sensor is about 106 to 1, well beyond the S/N goal. The trade-off that must be made is the time for acquiring the signal, since the pattern can be obtained in seconds using film plates, compared to 10 to 20 minutes for a pattern to be acquired using the digital scan. Parallel acquisition would, of course, speed up this process immensely.

Development of imaging plate for a TEM and its characteristics

1989 ◽  
Vol 47 ◽  
pp. 100-101
Author(s):  
N. Mori ◽  
T. Oikawa ◽  
Y. Harada ◽  
J. Miyahara ◽  
T. Matsuo
Keyword(s):  
Dynamic Range ◽  
Protective Layer ◽  
High Sensitivity ◽  
Imaging Plate ◽  
Phosphor Layer ◽  
Imaging Device ◽  
X Ray Imaging ◽  
New Type ◽  
Basic Characteristics ◽  
Reading System

The Imaging Plate (IP) is a new type imaging device, which was developed for diagnostic x ray imaging. We have reported that usage of the IP for a TEM has many merits; those are high sensitivity, wide dynamic range, and good linearity. However in the previous report the reading system was prototype drum-type-scanner, and IP was also experimentally made, which phosphor layer was 50μm thick with no protective layer. So special care was needed to handle them, and they were used only to make sure the basic characteristics. In this article we report the result of newly developed reading, printing system and high resolution IP for practical use. We mainly discuss the characteristics of the IP here. (Precise performance concerned with the reader and other system are reported in the other article.)Fig.1 shows the schematic cross section of the IP. The IP consists of three parts; protective layer, phosphor layer and support.

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