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High-speed algorithm for hypercomplex number Fourier transform and hypercomplex number cross correlation of color image

A color image and Fourier transform technology, applied in image communication, color signal processing circuits, electrical components, etc., can solve the problems of inability to apply complex fast Fourier transform and inconvenience

Inactive Publication Date: 2008-03-12
上海龙东光电子有限公司
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Problems solved by technology

Because of some special mathematical properties of hypercomplex numbers (such as: not satisfying the commutative law of multiplication), in the past, when using hypercomplex Fourier transform to quickly calculate hypercomplex cross correlation, it is necessary to apply hypercomplex arithmetic rules to perform hypercomplex Fu It is very inconvenient to apply the traditional complex fast Fourier transform (FFT) tool

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  • High-speed algorithm for hypercomplex number Fourier transform and hypercomplex number cross correlation of color image
  • High-speed algorithm for hypercomplex number Fourier transform and hypercomplex number cross correlation of color image
  • High-speed algorithm for hypercomplex number Fourier transform and hypercomplex number cross correlation of color image

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Embodiment Construction

[0050] We describe an embodiment of the invention in terms of image registration of two color images.

[0051] 1. Let x=(x, y) be the coordinates of pixels in the color image, and the RGB model of each pixel in the two color images f and g is expressed as a pure hypercomplex number form: f(x, y)=f R (x,y)i+f G (x,y)j+f B (x,y)k and g(x,y)=g R (x,y)i+g G (x,y)j+g B (x,y)k.

[0052] 2. Find the real Fourier transform of each color of the color images f and g respectively: f RRFT , f GRFT , f BRFT , g RRFT , g GRFT and g BRFT .

[0053] 3. Calculate f and g hypercomplex cross-correlation. We use g to match f, assuming that the image to be matched is g(χ+ξ), where ξ=(m, n) represents the relative movement of the matching point in the image, then the hypercomplex number of the two images in (m, n) The cross-correlation cr(m, n), as shown in (4), is expanded according to R, G, B (red, green, blue) three colors as shown in (6), so that it can be quickly calculated by RFT...

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Abstract

The present invention belongs to the technical field of image signal processing, in particular to a hyper-complex Fourier transformation and a rapid algorithm correlated with the hyper-complex of a colorful image. The colorful image is disposed as a vector entity by the hyper-complex, compared with the traditional algorithm, the color association of the image can be described better, and the hyper-complex cross correlation is widely applied on multiple field of the colorful image disposition. At present, the ''decomposing and transforming method'' and the ''decomposing vertical and parallel vector method'' are mainly applied in the colorful image disposition to make the rapid calculation of the hyper-complex Fourier transformation and the hyper-complex cross correlation. The present invention expands the signal disposition of the hyper-complex according to the real part and each imaginary part, and separately calculates by utilizing the traditional rapid Fourier transformation FFT tool, and restores the relative unit vector, and provides a new rapid algorithm for the hyper-complex Fourier transformation and the hyper-complex cross correlation of the colorful image. The analysis shows that compared with the existing rapid method, the algorithm is simple and convenient, and the amount of calculation is smaller.

Description

technical field [0001] The invention belongs to the technical field of image signal processing, and in particular relates to a fast algorithm for super-complex Fourier transform and super-complex cross-correlation of color images. Background technique [0002] Over the past century, cross-correlation, as a signal matching technique, has been applied to almost all digital signal processing fields, but most of them are limited to scalar signal processing. However, many signal processing applications involve multi-dimensional vectors. In the past, algorithms used to perform scalar processing on signals of various dimensions, and then simply synthesize them, which often failed to achieve good signal processing effects. In recent years, the application of hypercomplex numbers is aimed at multidimensional vector signal processing problems. In color image processing, hypercomplex numbers describe the color image as a whole vector in multi-dimensional space, providing more accurate...

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Application Information

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IPC IPC(8): H04N1/46H04N9/64
Inventor 江淑红郝明非张建秋胡波
Owner 上海龙东光电子有限公司
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