Comparison of Image Decompositions Through Inverse Difference and Laplacian Pyramids

2015 ◽  
Vol 6 (1) ◽  
pp. 19-38 ◽  
Author(s):  
Roumen Kountchev ◽  
Stuart Rubin ◽  
Mariofanna Milanova ◽  
Roumiana Kountcheva
Keyword(s):  
Image Processing ◽  
Fourier Transform ◽  
Computational Complexity ◽  
Image Representation ◽  
Quantization Noise ◽  
Laplacian Pyramid ◽  
Image Transfer ◽  
Multi Level ◽  
Real Time Applications ◽  
The Fourier Transform

In this work, the Inverse Difference Pyramid (IDP) and its modification – the Reduced IDP (RIDP), are compared and evaluated with the famous Laplacian Pyramid (LP) for multi-level decomposition of digital images. The comparison comprises: the structures of LP and IDP, the image representation through LP and IDP in the pixel space and in the spectrum space of the Fourier transform, the efficiency of both transforms for the aims of the progressive image transfer, the LP and the IDP computation graphs and the evaluation of the computational complexity of the algorithms for the 3-level reduced LP and the 3-level reduced IDP. The influence of the quantization noise on both decompositions is also analyzed. On the basis of the comparison are outlined the basic advantages of the RIDP for pipeline image processing. The results obtained could be used for the design of coders for image compression, aimed at real-time applications, etc.

Filterbank and DFT Based Fast Parallel Discrete Gabor Transform for Image Representation

2012 ◽  
Vol 461 ◽  
pp. 444-447 ◽  
Author(s):  
Juan Juan Gu ◽  
Liang Tao
Keyword(s):  
Image Processing ◽  
Fourier Transform ◽  
Computational Complexity ◽  
Parallel Algorithm ◽  
Image Representation ◽  
Gabor Transform ◽  
Parallel Channel ◽  
Real Time Image ◽  
Parallel Channels ◽  
Time Image

Fast parallel algorithm for the 2-D discrete Gabor transform (DGT) is presented based on 2-D filterbank. A 2-D analysis filterbank is designed for the 2-D DGT. The parallel channels in the filterbank have a unified structure and can apply the 2-D inverse fast discrete Fourier transform (IFFT) algorithm to reduce the computational load. The computational complexity of each parallel channel is very low and is independent of the oversampling rate. Thus, the proposed parallel algorithm is attractive for real time image processing.

The role of amplitude and phase of the Fourier transform in the digital image processing

1991 ◽  
Vol 59 (8) ◽  
pp. 744-748 ◽  
Author(s):  
I. Juvells ◽  
S. Vallmitjana ◽  
A. Carnicer ◽  
J. Campos
Keyword(s):  
Image Processing ◽  
Fourier Transform ◽  
Digital Image Processing ◽  
Digital Image ◽  
The Fourier Transform

scholarly journals Implementation of FFT Architecture using Various Adders

2019 ◽  
Vol 8 (10) ◽  
pp. 3750-3755
Keyword(s):  
Image Processing ◽  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Orthogonal Frequency Division Multiplex ◽  
Cell Phones ◽  
Frequency Division ◽  
Ripple Carry Adder ◽  
Significant Area ◽  
Area Optimization ◽  
The Fourier Transform

In 1965 a technique called Fast Fourier Transform (FFT) was invented to find the Fourier Transform. This paper compares three architectures, the basic architecture/ non-reduced architecture of FFT, decomposed FFT architecture without retiming and decomposed FFT architecture with retiming. In each case, the adder used will be Ripple Carry Adder (RCA) and Carry Save Adder (CSA). A fast Fourier transform (FFT) calculates the discrete Fourier transform (DFT) or the inverse (IDFT) of a sequence. Fourier analysis transforms a signal from time to frequency domain or vice versa. One of the most burgeoning use of FFT is in Orthogonal Frequency Division Multiplex (OFDM) used by most cell phones, followed by the use in image processing. The synthesis has been carried out on Xilinx ISE Design Suite 14.7. There is a decrease in delay of 0.824% in Ripple Carry Adder and 6.869% in Carry Save Adder, further the reduced architecture for both the RCA and CSA architectures shows significant area optimization (approximately 20%) from the non-reduced counterparts of the FFT implementation.

scholarly journals Microstructural analysis of non-woven fabrics using scanning electron microscopy and image processing. Part 1: Development and verification of the methods

2002 ◽  
Vol 216 (3) ◽  
pp. 199-207 ◽  
Author(s):  
E Ghassemieh ◽  
M Acar ◽  
H Versteeg
Keyword(s):  
Image Processing ◽  
Fourier Transform ◽  
Microstructural Analysis ◽  
Orientation Distribution ◽  
Woven Fabrics ◽  
Computational Time ◽  
Sem Images ◽  
The Fourier Transform ◽  
Processing Techniques ◽  
Scanning Electron

This paper reports image analysis methods that have been developed to study the microstructural changes of non-wovens made by the hydroentanglement process. The validity of the image processing techniques has been ascertained by applying them to test images with known properties. The parameters in preprocessing of the scanning electron microscope (SEM) images used in image processing have been tested and optimized. The fibre orientation distribution is estimated using fast Fourier transform (FFT) and Hough transform (HT) methods. The results obtained using these two methods are in good agreement. The HT method is more demanding in computational time compared with the Fourier transform (FT) method. However, the advantage of the HT method is that the actual orientation of the lines can be concluded directly from the result of the transform without the need for any further computation. The distribution of the length of the straight fibre segments of the fabrics is evaluated by the HT method. The effect of curl of the fibres on the result of this evaluation is shown.

scholarly journals A Comparison of Quantum and Traditional Fourier Transform Computations

2020 ◽  
Author(s):  
Damian Musk
Keyword(s):  
Fourier Transform ◽  
Computational Complexity ◽  
Time Complexity ◽  
Quantum Algorithms ◽  
Quantum Fourier Transform ◽  
Initial State ◽  
Output Vector ◽  
Output State ◽  
The Fourier Transform

The quantum Fourier transform (QFT) can calculate the Fourier transform of a vector of size N with time complexity 𝒪(log2N) as compared to the classical complexity of 𝒪(NlogN). However, if one wanted to measure the full output state, then the QFT complexity becomes 𝒪(Nlog2N), thus losing its apparent advantage, indicating that the advantage is fully exploited for algorithms when only a limited number of samples is required from the output vector, as is the case in many quantum algorithms. Moreover, the computational complexity worsens if one considers the complexity of constructing the initial state. In this paper, this issue is better illustrated by providing a concrete implementation of these algorithms and discussing their complexities as well as the complexity of the simulation of the QFT in MATLAB.

scholarly journals WAVELET TRANSFORM AND LIP MODEL

2011 ◽  
Vol 21 (2) ◽  
pp. 121 ◽  
Author(s):  
Guy Courbebaisse ◽  
Frederic Trunde ◽  
Michel Jourlin
Keyword(s):  
Image Processing ◽  
Fourier Transform ◽  
Wavelet Transform ◽  
The Other ◽  
Mathematical Framework ◽  
Fast Computation ◽  
Microscope Images ◽  
Computation Algorithm ◽  
Logarithmic Image Processing ◽  
The Fourier Transform

The Fourier transform is well suited to the study of stationary functions. Yet, it is superseded by the Wavelet transform for the powerful characterizations of function features such as singularities. On the other hand, the LIP (Logarithmic Image Processing) model is a mathematical framework developed by Jourlin and Pinoli, dedicated to the representation and processing of gray tones images called hereafter logarithmic images. This mathematically well defined model, comprising a Fourier Transform "of its own", provides an effective tool for the representation of images obtained by transmitted light, such as microscope images. This paper presents a Wavelet transform within the LIP framework, with preservation of the classical Wavelet Transform properties. We show that the fast computation algorithm due to Mallat can be easily used. An application is given for the detection of crests.

Multirate and DFT Based Fast Parallel Algorithm for 2-D Inverse Discrete Gabor Transform

2013 ◽  
Vol 411-414 ◽  
pp. 1377-1380
Author(s):  
Juan Juan Gu ◽  
Liang Tao
Keyword(s):  
Image Processing ◽  
Fourier Transform ◽  
Computational Complexity ◽  
Parallel Algorithm ◽  
Gabor Transform ◽  
Parallel Channel ◽  
Inverse Discrete Fourier Transform ◽  
Real Time Image ◽  
Parallel Channels ◽  
Time Image

Multirate and DFT based fast parallel algorithm for the 2-D inverse discrete Gabor transform (IDGT) is presented. A 2-D synthesis filterbank is designed for the 2-D IDGT. The parallel channels in the filterbank have a unified structure and can apply the 2-D fast inverse discrete Fourier transform (IFFT) algorithm to reduce the computational load. The computational complexity of each parallel channel is very low and is independent of the oversampling rate. Thus, the proposed parallel algorithm is attractive for real time image processing.

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