CN101216557A - Residual hypercomplex number dual decomposition multi-light spectrum and full-color image fusion method - Google Patents

Abstract

The invention belongs to the field of image fusion technology, in particular to a multi-spectral image and panchromatic image fusion method based on residual hypercomplex symplectic decomposition. The method comprises the following steps of : respectively constructing models of residual images of a multi-spectral image and a panchromatic image by using hypercomplex, and respectively subjecting the hypercomplex residual models of the multi-spectral image to hypercomplex symplectic decomposition along the grayscale axis direction to obtain a simplex portion containing brightness information and a perplex portion including chromaticity information. The analysis shows that the residual of the multi-spectral image with high resolution can be recovered by substituting the simplex portion obtained by decomposing the low-resolution multi-spectral image with hypercomplex residual image of a high-resolution panchromatic image, and the fusion of the multi-spectral image and the panchromatic image can be achieved by synthesizing symplectic decomposition. The simulation result shows that the invention is free of visible spectral distortion. The evaluation result of various prior image fusion methods shows that the invention is superior to HIS, PCA and wavelet transformation fusion method.

Description

Multispectral and the panchromatic image fusion method that residual error supercomplex antithesis decomposes

Technical field

The invention belongs to the image fusion technology field, be specifically related to the multispectral and panchromatic image fusion method that a kind of residual error supercomplex Symplectic (antithesis) decomposes.

Background technology

At present, earth observation satellite provides the many spaces of increasing covering the same area, multiresolution, multidate and multispectral image, for carry out topographic mapping and map renewal, land use classes, crops and forest classified, ice and snow/flood monitoring etc. provides rich data.In order to utilize these data, people need be merged multispectral and full-colour image.

Based on intensity-colourity-saturation degree (Intensity-Hue-Saturate, IHS) the multispectral and panchromatic image fusion method of conversion ^[1]Become a standard procedure of earth observation graphical analysis, the color that it can be used for the view data of height correlation strengthens and improves fusion treatment such as spatial resolution.The situation that the IHS transform method of standard is suitable for is, full-colour image and be height correlation from the luminance component of multispectral acquisition.; when the spectral range of full-colour image does not cover all wave bands of multispectral image and/or full-colour image and multispectral image is not when obtaining simultaneously; obtain widely different between the luminance component of multispectral image and the full-colour image by the IHS conversion; if this moment carries out full-colour image with the IHS transform method and multispectral image merges, serious spectrum distortion will appear ^[1]Equally, pivot analysis (Principle Component Analysis, PCA) fusion method, utilize the high resolving power full-colour image to replace the first principal component of low resolution multispectral image simply, can cause the loss of some spectral characteristics in the low resolution multispectral image, therefore make the result images that merges that serious spectrum distortion takes place ^[2]Though the high-pass filtering fusion method has kept the information of multispectral image, to high-definition picture filtering the time, many texture informations have been filtered ^[3]The wavelet transformation fusion method can keep the spectral information in the multispectral image preferably, but its syncretizing effect is subjected to the influence of wavelet decomposition progression.In addition, the fusion of wavelet coefficient can destroy the orthogonality of its positive inverse transformation and cause spectrum leakage, thereby makes the result images of its fusion produce blocking artifact ^[4]

Can find that said method all is to replace certain composition by certain conversion, not consider the complete spectral information of full-colour image fully.Exist when mentioning real vector signal in the document [5] and be and decision, ignore and change arbitrary component by each component, all can not the original vector signal of reconstruct.

Multispectral image is exactly a kind of vector signal, and its each pixel is all represented with red (R), green (G) and blue (B) three primary colors vector signal.If by certain conversion, transform methods such as foregoing IHS and PCA etc., they are that the R of each vector pixel, G and B component are put into its represented matrix as an element respectively, this matrix is being carried out the needed matrixings of fusion method such as IHS and PCA so, decomposition, replacement and inverse transformation are when (for example pivot is decomposed and replaced), RGB three primary colors certain location relation, for example, if establish r ₁, g ₁And b ₁And r ₂And b ₂Be respectively two vector pixels that initial multispectral coloured image is represented with the RGB three primary colors, the conversion of matrix so, decomposition, replacement and inverse transformation, the component of a certain vector pixel is mixed with the component of other vector pixel, thereby generation is different from various combination that may be different of initial multispectral coloured image RGB three primary colors position relation (as making r ₁, g ₁And b ₁Become r ₁, g ₂And b ₁And r ₂, g ₂And b ₂Become r ₂, g ₁And b ₂).This means that such conversion has destroyed the particular kind of relationship of original image on RGB three primary colors vector space positions, its fusion results image will cause distortion so.Here it is, and why the unknown so far and inexplicable IHS and PCA fusion method can produce the reason of color distortion ^[6]

Summary of the invention

In order to overcome this shortcoming that existing Multispectral Image Fusion Methods exists, the vector pixel that the present invention will represent multispectral image is carried out integral body with super-complex vector and is described and handle, purpose is that it is maintained in follow-up conversion with in handling at the particular kind of relationship on the RGB three primary colors vector space positions, to avoid handling the distortion of back image.

The present invention is at first by obtaining the residual image of multispectral image and full-colour image respectively, adopt the super-complex vector pixel directly to carry out integral body to the residual image of the multispectral image represented with RGB and describe, with the particular kind of relationship of maintenance RGB three primary colors vector pixel on vector space positions.And for the residual image of full-colour image, because its pixel is a scalar, for the expression that makes it so that subsequent treatment and fusion consistent with colored residual image, we are the vector pixel of three-dimensional with its each scalar pixel-expansion ^[7]Simultaneously, for the energy that guaranteed the vector pixel consistance when representing with the scalar pixel, we multiply by each scalar pixel value

The residual image of full-colour image behind the vector quantization is described and has been handled with regard to also carrying out integral body with super-complex vector like this.Secondly, the residual image of the multispectral image represented with supercomplex is carried out supercomplex symplectic along the direction of gray scale axle decompose, obtain comprising simplex (list) part and perplex (answering) part that comprises chrominance information of monochrome information.We know because full-colour image has comprised the luminance detail information abundanter than its corresponding multispectral image, this means if the simplex part that its residual image monochrome information of full-colour image is replaced the multispectral image residual image, so just can recover that high-resolution multispectral image does not have and the luminance detail information that is present in full-colour image.Analyze and simulation result shows: the fusion method of the multispectral and full-colour image that decomposes by this residual error supercomplex and available high-resolution multi-spectral fused images, owing to adopt supercomplex that the vector pixel is described and handles, can when having kept the details spectral information of full-colour image, can not produce color distortion.

The concrete steps of the inventive method are as follows:

(1) for multispectral image MS, by interpolation algorithm Z, the multispectral image of low resolution is amplified to the size same with full-colour image, obtain interpolation image I;

(2) interpolation image I is carried out low-pass filtering and down-sampled, the low-resolution image that obtains former multispectral image is estimated MS _LEstimate MS with multispectral image MS and image then _LSubtract each other the residual image e that obtains multispectral image _gFull-colour image MP through same low-pass filtering, is obtained the estimation MP of former full-colour image _L, subtract each other with it with former full-colour image again, can obtain the residual image e of full-colour image _p

(3) with residual image e _gBe amplified to residual image e with full-colour image _pSame size obtains e _f';

(4) to e _fWith e behind the vector quantization _pWith carrying out the supercomplex modeling, obtain Qe respectively _f(x, y) and Qe _p(x, y);

(5) to Qe _f(x, y) it carries out supercomplex symplectic and decomposes along the direction of gray scale axle, obtains the simplex part f of packet content monochrome information ₁(x is y) with the perplex part f that comprises chrominance information ₂(x, y);

(6) use Qe _p(x y) replaces f ₁(x, y), the residual error after being restored: e _f' (x, y)=Qe _p(x, y)+f ₂(x, y) μ ₂

(7) obtain fusion results: MS '=I+e at last _f'.

Generally speaking, multispectral image and full-colour image have different resolution.In order to merge their information, at first need the low resolution multispectral image is transformed into image with the same resolution of full-colour image resolution.This conversion is normally finished with interpolation.For multispectral image MS, if represent the interpolation algorithm of a certain image, the multispectral image of low resolution is amplified to the size same with full-colour image with Z, promptly the estimated statement that obtains the high-definition picture I of its interpolation by interpolation algorithm Z is shown:

I＝Z(MS) (1)

The estimation to high-resolution multi-spectral image MS ' of I with regard to representing to obtain so with interpolation algorithm Z.I with the residual error of true high-definition picture MS ' is:

e _f＝MS’-I＝MS’-Z(MS) (2)

E in the following formula _fBe called high-resolution residual image and refer to detail of the high frequency in the multispectral image ^[10]

The analysis showed that of document [8]: if low-pass filtering and down-sampled H are acted on e _f, just be equivalent to I is carried out low-pass filtering and down-sampled, obtain estimation MS than the lower image of resolution of former multispectral image _L, with MS and MS _LDifference can obtain the residual image e of multispectral image _g:

e _g＝He _f＝H[MS′-Z(MS)]＝HMS′-HI≈MS-MS _L (3)

e _gAnd e _fBetween have certain linear mapping relation, so can use e _gEstimate e _fThis conclusion of document [8] means, for full-colour image, if after allowing it by above-mentioned same low-pass filtering, uses former full-colour image and it image subtraction by low-pass filtering again, obtains the residual image e of full-colour image _pTo comprise the detail of the high frequency that multispectral image MS does not comprise, this is because the resolution of multispectral image MS is lower than the resolution of full-colour image.These are analyzed and have illustrated that also multispectral image is carried out residual error to be extracted, and can separate image space information and obtain its detailed information, the image detail information that the multispectral image that promptly obtains mainly comprises with spectral information.Equally, the residual image of full-colour image has also comprised its detail of the high frequency, and these details are the detailed information that lacked of multispectral image residual error just.Therefore, if can strengthen the spatial information of multispectral image by go to strengthen the residual error of multispectral image someway with the residual image of full-colour image, the spectral information of the multispectral image that the while also keeps.

Utilize the residual image modeling of supercomplex to the multispectral image represented by RGB three colouring components ^[9]:

f(x，y)＝r(x，y)i+g(x，y)j+b(x，y)k， (4)

Wherein ((x, y), (x, y), (x y) represents the RGB component of multispectral image respectively to b to g to r to f for x, y) the supercomplex model for being represented by R, G, B three colouring components.Above-mentioned expression is expressed as the integral body of a vector to RGB three colouring components of describing multispectral image by supercomplex, and so no matter by which kind of conversion, this vector globality can both keep, and the relative position between the RGB composition of vector pixel just can not change.

For the spectral information of the multispectral image of the spatial information that better merges high-resolution full-colour image and low resolution, we carry out the supercomplex modeling respectively to the residual error of full-colour image and multispectral image.Yet for the residual image of full-colour image,, need be three-dimensional vector pixel therefore,, each pixel value be multiply by for the amplitude that has guaranteed the vector pixel is consistent with the scalar pixel with each scalar pixel-expansion because its pixel is a scalar

So, just obtain the supercomplex model of residual image of the full-colour image of the multispectral image represented by RGB and vector quantization:

$Q{e}_p(x,y)=\frac{1}{\sqrt{3}}{e}_p(x,q)i+\frac{1}{\sqrt{3}}{e}_p(x,y)j+\frac{1}{\sqrt{3}}{e}_p(x,y)k---\left(5\right)$

Qe _f(x，y)＝r(x，y)i+g(x，y)j+b(x，y)k

Wherein, e _p(x y) is the pixel value of the residual image of full-colour image, r (x, y), g (x, y), (x y) is respectively e to b _f(x, RGB component y).

It is the plural form that a hypercomplex number is defined as broad sense that the Cayley-Dickson of hypercomplex number decomposes, and promptly this real and imaginary part are plural number.The Cayley-Dickson that is q=a+bi+cj+dk can be write as ^[10]:

q＝A+Bj (6)

A=a+bi wherein, B=c+di.

Cayley-Dickson decomposes also the Fundamentals of Mathematics of symplectic decomposition just.Use the complex operator μ of broad sense, if select two pure quaternion μ of unit arbitrarily ₁, μ ₂And μ ₁⊥ μ ₂, hypercomplex number arbitrarily can be expressed as the plural form of broad sense, we are referred to as the symplectic form of hypercomplex number:

q＝A′+B′μ ₂

A=a '+b ' μ wherein ₁, B=c ' d ' μ ₁Just:

q＝(a′+b′μ ₁)+(c′+d′μ ₁)μ ₂ ((7)

Wherein A is called the simplex part, and B is called the perplex part.Since hypercomplex number symplectic form is present in the complex number space of broad sense, so these two parts all homomorphism in plural number.Top expression formula is taken advantage of out, can be write:

q＝a′+b′μ ₁+c′μ ₂+d′’μ ₃ (8)

μ wherein ₃=μ ₁μ ₂, and μ ₃⊥ μ ₁, μ ₃⊥ μ ₂Like this, we have just had the other cover operator μ of homomorphism in standard quaternion operator i, j, k ₁, μ ₂, μ ₃(a ', b ', c ', d ') can obtain by following formula:

a′＝S[q]

$b^{\′}=-\frac{1}{2}\left(V\right[q]{\mathrm{\μ}}_1+{\mathrm{\μ}}_{1}V[q\left]\right)$

$c^{\′}=-\frac{1}{2}\left(V\right[q]{\mathrm{\μ}}_2+{\mathrm{\μ}}_{2}V[q\left]\right)---((\left(9\right)$

$d^{\′}=-\frac{1}{2}\left(V\right[q]{\mathrm{\μ}}_1{\mathrm{\μ}}_2+{\mathrm{\μ}}_1{\mathrm{\μ}}_{2}V[q\left]\right)$

S[q wherein] be the real part of hypercomplex number q, i.e. S[q]=a; V[q] be the pure imaginary number part of hypercomplex number q, i.e. V[q]=bi+cj+dk.

For the supercomplex model f of coloured image (x, y)=r (x, y) i+g (x, y)+b (x, y) k, thereby obtain:

f(x，y)＝f ₁(x，y)+f ₂(x，y)μ ₂( ((10)

Wherein claim f ₁(x, y), f ₂(x y) is respectively simplex part and perplex part.If μ ₁Be gray scale axle, f so ₁(x, what y) provide is exactly monochrome information (still the image three-colo(u)r of a RGB is not a simple gray image), and f ₂(x, a chrominance information that y) provides (same also is a RGB coloured image).

According to the characteristic of the vector pixel of residual image, to by Qe _f(x, y) carrying out supercomplex Symplectic along the direction of gray scale axle decomposes, supercomplex residual error model with full-colour image is replaced the simplex part, so just can realize the recovery of the residual image of low resolution, thereby realizes the fusion of multispectral image and full-colour image.

Embodiment

We use the multispectral image in the area, Shanghai that Landsat 7 ETM+ sensors take on June 14th, 2000 and full-colour image (north latitude 314460.0000N, east longitude 1215360.0000E) and the full-colour image of the SPOT satellite in the Hanoi area taken in October 26 nineteen ninety-five and the multispectral image of TM describe performance of the present invention.Wherein, full-colour image has the spatial resolution of 15m, and multispectral image has the spatial resolution of 30m.

Because Landsat 7 ETM+ and SPOT do not provide the true as a comparison multispectral of 15m resolution, for the true multispectral image with 30m resolution comes comparison, we degenerate to 30m and 60m respectively with full-colour image and multispectral image.Full-colour image and 60m multispectral image to 30m merge, and the multispectral image of result that will merge and 30m resolution compares.

Below by simulating, verifying performance of the present invention.In order to weigh the enhancing of space information in the remote sensing image fusion process, this paper adopts the SDD parameter ^[11]Its fusion results is estimated, and the SDD parameter is the standard deviation that merges full-colour image and low resolution multispectral image difference, and it is defined as follows:

$\mathrm{SDD}=\sqrt{\frac{1}{\mathrm{MN}}\underset{x}{\mathrm{\Σ}}\underset{y}{\mathrm{\Σ}}{((F(x,y)-M{S}_i(x,y))-(\stackrel{\‾}{F}-{\stackrel{\‾}{\mathrm{MS}}}_i))}^2}$

In the formula, the image that F obtains for fusion,

Average for image pixel.In general, the SDD parameter of fused images is good with the SDD parameter that approaches high-resolution multispectral image, will be in the spatial information that comprises in this moment fused images and also comprised spatial information in the high-resolution multispectral image.If the SDD parameter that merges is bigger than the SDD parameter of high-resolution multispectral image, the too much panchromatic spatial information of possibility is dissolved in the multispectral image and is gone so, causes the change of the spectral characteristic of fused images.

In order to weigh the reservation situation of spectral signature in the remote sensing image fusion process, we adopt following statistical parameter:

1) Y-PSNR (PSNR)

If think fused images F (x, y) with canonical reference image R (x, difference y) is noise, and canonical reference image R (x y) is exactly information.The Y-PSNR PSNR of fused images is defined as ^[12]

$\mathrm{PSNR}=10\×{\log }_{10}\frac{\mathrm{MN}[\max \left(F(x,y)\right)-\min \left(F(x,y)\right)]}{\underset{x}{\mathrm{\Σ}}\underset{y}{\mathrm{\Σ}}{[R(x,y\left)\right)-F(x,y\left)\right)]}^2}$

The unit of Y-PSNR is a decibel (dB).In general, the Y-PSNR that calculates is just big more, illustrates that the spectral signature of fused images and canonical reference image is approaching more, and the effect of fusion is good more.

2) related coefficient (CC)

The related coefficient of fused images F and canonical reference image R can reflect the similarity degree of the spectral signature of two width of cloth images, and it is defined as follows:

$\mathrm{cc}=\frac{\underset{x}{\mathrm{\Σ}}\underset{y}{\mathrm{\Σ}}(F(x,y)-\stackrel{\‾}{F})(R(x,y)-\stackrel{\‾}{R})}{\sqrt{\left(\underset{x}{\mathrm{\Σ}}\underset{y}{\mathrm{\Σ}}{(F(x,y)-\stackrel{\‾}{F})}^2\right)(\underset{x}{\mathrm{\Σ}}\underset{y}{\mathrm{\Σ}}R(x,y)-{\stackrel{\‾}{R}}^2)}}$

The related coefficient of calculating is big more, illustrates that the similarity degree of spectral signature of fused images and canonical reference image is high more, and the effect of fusion is good more.Y-PSNR and related coefficient are to calculate respectively on each wave band of fused images and high-resolution multi-spectral image.

3) relative global error (ERGAS)

Global error can reflect that the spectrum of fused images on each wave band changes situation relatively, and it is defined as follows ^[15]:

$\mathrm{ERGAS}=100\frac{h}{l}\sqrt{\frac{1}{K}\underset{i=1}{\overset{K}{\mathrm{\Σ}}}\frac{\underset{x}{\mathrm{\Σ}}\underset{y}{\mathrm{\Σ}}{(F_i(x,y)-R_i(x,y))}^2}{\underset{x}{\mathrm{\Σ}}\underset{y}{\mathrm{\Σ}}{R}_i(x,y)}}$

Wherein, l is the resolution of low resolution multispectral image, and h is the resolution of high-resolution multi-spectral image, and K is the wave band that participates in fusion.The relative global error of calculating is more little, and fused images and canonical reference image are approaching more, and the effect of fusion is just good more.

In the remote sensing image fusion of reality is estimated, take all factors into consideration the SDD parameter of reflection spatial information enhancing and Y-PSNR PSNR, related coefficient CC, the relative global error ERGAS that the reflection spectral information keeps.The remote sensing image fusion method of an optimum not only should improve the spatial resolution of fused images, and requires to keep as much as possible the spectral signature of original image, therefore need average out between above-mentioned two class parameters.

Table 1 has provided the SDD parameter of various fused images.Wherein, the SDD parameter of 30m resolution multi-spectral image is used for doing standard.The SDD parameter of HIS conversion and PCA transform method correspondence is far longer than the SDD parameter of true picture as can be seen from the table, the information that the full-colour image in the multispectral image is dissolved in this explanation surpassed high-resolution multispectral image the spatial information that should comprise.In small wave converting method, the SDD parameter of each wave band is all very approaching, illustrates that the spatial information of being dissolved into the full-colour image on each wave band is similarly, however with the SDD parameter of true picture be differentiated.The present invention proposes the SDD parameter that the pairing SDD parameter of method approaches true picture most, and the SDD parameter distributions rule on each wave band is also similar to the SDD parameter distributions rule on each wave band of true picture, this has illustrated that the present invention can treat with a certain discrimination each wave band of multispectral image when incorporating the spatial information of full-colour image, with realistic situation.

Table 2 has provided various fusion methods at the statistical parameter that keeps on the spectral signature.The fusion method that residual error supercomplex antithesis decomposes all has bigger Y-PSNR PSNR and related coefficient CC on each wave band, illustrate that its spectral signature of fused images and the spectral signature of the multispectral image of 30m resolution are very approaching, the relative global error ERGAS of this method on all wave bands is minimum simultaneously, and this has illustrated the validity of method on the maintenance spectral signature that the present invention proposes.

The statistical parameter of the enhancing spatial information of table 1 fusion results

Parameter	Wave band	True picture	IHS	PCA	Wavelet transformation	Residual error symplectic
							SDD	R	0.061	0.245	0.195	0.076	0.071
G	0.060	0.253	0.268	0.075	0.069
						B		0.051	0.253	0.325	0.075	0.056

The statistical parameter of the maintenance spectral signature of table 2 fusion results

Parameter	Wave band	IHS	PCA	Wavelet transformation	Residual error symplectic
						PSNR	R	12.17	14.13	22.62	23.2896
G	11.93	11.46	22.64	24.2447
					B		11.95	9.83	23.02.	25.2401
CC	R	0.45	0.61	0.92							0.96
					G	0.19	0.19	0.93	0.97
	B	0.26	0.11	0.95						0.99
					ERGAS		22.22	23.15	6.47		2.77

Table 3 and table 4 have provided the analysis result that the multispectral image to the image of SPOT satellite and TM merges respectively.The result shows that also the result that this paper proposes is better than IHS, PCA method and method of wavelet.

The statistical parameter of the enhancing spatial information of table 3 fusion results

Parameter	Wave band	True picture	IHS	PCA	Wavelet transformation	Residual error symplectic
							SDD	R	0.063	0.092	0.179	0.066	0.065
G	0.062	0.117	0.281	0.065	0.063
						B		0.057	0.117	0.279	0.064	0.056

The statistical parameter of the maintenance spectral signature of table 4 fusion results

Parameter	Wave band	IHS	PCA	Wavelet transformation	Residual error symplectic
						PSNR	R	20.87	13.49	24.69	27.28
G	18.75	11.37	24.43	26.85
					B		18.72	11.42	24.66	26.24
CC	R	0.92	0.25	0.95							0.97
					G	0.88	0.33	0.96	0.97
	B	0.88	0.27	0.95						0.98
					ERGAS		11.36	26.6	6.36		4.04

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Claims (1)

1. the multispectral and panchromatic image fusion method that decomposes of a residual error supercomplex antithesis is characterized in that concrete steps are as follows:

(1) for multispectral image MS, by interpolation algorithm Z, the multispectral image of low resolution is amplified to the size same with full-colour image, obtain interpolation image I;

(2) interpolation image I is carried out low-pass filtering and down-sampled, the low-resolution image that obtains former multispectral image is estimated MS _LEstimate MS with multispectral image MS and image then _LSubtract each other the residual image e that obtains multispectral image _gFull-colour image MP through same low-pass filtering, is obtained the estimation MP of former full-colour image _L, subtract each other with it with former full-colour image again, can obtain the residual image e of full-colour image _p

(3) with residual image e _gBe amplified to residual image e with full-colour image _pSame size obtains e _f

(4) to e _fWith e behind the vector quantization _pWith carrying out the supercomplex modeling, obtain Qe respectively _f(x, y) and Qe _p(x, y);

(5) to Qe _f(x, y) it carries out supercomplex symplectic and decomposes along the direction of gray scale axle, obtains the simplex part f of packet content monochrome information ₁(x is y) with the perplex part f that comprises chrominance information ₂(x, y);

(6) use Qe _p(x y) replaces f ₁(x, y), the residual error after being restored: e _f' (x, y)=Qe _p(x, y)+f ₂(x, y) μ ₂

(7) obtain fusion results: MS '=I+e at last _f'.