Image Reconstruction from Geometric Moments via Cascaded Digital Filters

An important aspect of the real-time image processing applications using orthogonal moments is the speed of their computation. They can be computed directly or via geometric moments (GMs). One of the fast methods to generate GMs is the usage of the cascaded digital filter outputs. However, a concern of this design is that the outputs of the digital filters, which operate as accumulators, increase exponentially as the orders of moment increase. It is shown in previous works, for an N × N image, the digital filter outputs are sampled at N or later instances. In this paper, we propose a new formulation to solve this problem by using a set of lower digital filter output values as the order of moments increases. This is achieved by sampling the digital filter outputs at earlier instances, N, N - 1, N - 2,…,N - p, where p is the maximum moment order. This method enables the usage of the lower digital filter output values for higher-order moments. As the moment order approaches N, the number of additions is approximately 45% less for the proposed method when compared with the existing methods, resulting in a corresponding reduction in computation time.

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Learning based restoration of Gaussian blurred images using weighted geometric moments and cascaded digital filters

Applied Soft Computing ◽

10.1016/j.asoc.2017.11.021 ◽

2018 ◽

Vol 63 ◽

pp. 124-138 ◽

Cited By ~ 3

Author(s):

Ahlad Kumar ◽

Mohd Fikree Hassan ◽

P. Raveendran

Keyword(s):

Digital Filters ◽

Geometric Moments ◽

Blurred Images

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Fast Legendre Moments in Securing Digital Image

International Journal of Innovative Technology and Exploring Engineering - Special Issue ◽

10.35940/ijitee.k1278.10812s19 ◽

2019 ◽

Vol 8 (12S) ◽

pp. 1008-1011

Keyword(s):

Image Reconstruction ◽

Digital Image ◽

Digital Images ◽

Geometric Error ◽

Zernike Moments ◽

Experimental Results ◽

Geometric Moments ◽

Approximation Errors ◽

Legendre Moments

Moments are set of values used to describe the information contained in the image. In this paper the content of the image is represented with the help of fast legendre moments. Legendre moments has the advantage that these moments are calculated exactly without any loss in information while other moments like geometric moments, zernike moments etc suffer from approximation errors and geometric error when applied to digital images. Legendre moments are also more suitable for image reconstruction. Experimental results show that the proposed system is very efficient in computing moments at much faster time than the Zernike moments since fast legendre moments calculates the moments as two ID function rather as a 2D function of a digital image and the results of reconstruction in case of tampering is also shown

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Criteria and Methods for Reliable Three-Dimensional Image Reconstruction

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100051669 ◽

1974 ◽

Vol 32 ◽

pp. 330-331

Author(s):

R. A. Crowther

Keyword(s):

Image Reconstruction ◽

Finite Number ◽

Density Distribution ◽

Electron Micrographs ◽

Mathematical Problem ◽

Three Dimensional ◽

Ideal Case ◽

Dimensional Image ◽

General Object ◽

The Ideal

The reconstruction of a three-dimensional image of a specimen from a set of electron micrographs reduces, under certain assumptions about the imaging process in the microscope, to the mathematical problem of reconstructing a density distribution from a set of its plane projections.In the absence of noise we can formulate a purely geometrical criterion, which, for a general object, fixes the resolution attainable from a given finite number of views in terms of the size of the object. For simplicity we take the ideal case of projections collected by a series of m equally spaced tilts about a single axis.

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Three dimensional deblurring of transmitted-light brightfield micrographs

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100148654 ◽

1993 ◽

Vol 51 ◽

pp. 564-565

Author(s):

Santosh Bhattacharyya

Keyword(s):

Image Reconstruction ◽

Three Dimensional ◽

Transmitted Light ◽

Reconstruction Algorithms ◽

3D Image Reconstruction ◽

Structural Details ◽

Spread Function ◽

Early Testing ◽

Linearized Model ◽

Image Reconstruction Algorithms

Three dimensional microscopic structures play an important role in the understanding of various biological and physiological phenomena. Structural details of neurons, such as the density, caliber and volumes of dendrites, are important in understanding physiological and pathological functioning of nervous systems. Even so, many of the widely used stains in biology and neurophysiology are absorbing stains, such as horseradish peroxidase (HRP), and yet most of the iterative, constrained 3D optical image reconstruction research has concentrated on fluorescence microscopy. It is clear that iterative, constrained 3D image reconstruction methodologies are needed for transmitted light brightfield (TLB) imaging as well. One of the difficulties in doing so, in the past, has been in determining the point spread function of the system.We have been developing several variations of iterative, constrained image reconstruction algorithms for TLB imaging. Some of our early testing with one of them was reported previously. These algorithms are based on a linearized model of TLB imaging.

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