CN110443307A - It is a kind of that the theoretical image interfusion method with HSI transformation is stretched based on phase - Google Patents
It is a kind of that the theoretical image interfusion method with HSI transformation is stretched based on phase Download PDFInfo
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Abstract
The theoretical image interfusion method with HSI transformation is stretched based on phase the invention discloses a kind of, include the following steps, construction stretches kernel function, provide PST can phenogram as detail of the high frequency theoretical foundation, HSI transformation is done to left and right focusedimage, new H, S, I component are subjected to HSI inverse transformation, obtain fusion results, the validity of verification algorithm；Inventive algorithm is mainly characterized by: utilizing the method for the present invention, the part focused image that different sensors obtain can be handled, full figure is obtained as focus is consistent, information image more abundant, the mentioned method of the present invention, it discusses the concrete thought of multi-focus image fusion and realizes result, illustrate this paper algorithm keep in fusion results information content, marginal information reserve capability and in terms of there is preferable performance, demonstrate the reasonability, superiority and validity of this paper algorithm.
Description
Technical field
It is specifically a kind of that theoretical and HSI transformation is stretched based on phase the present invention relates to handle the pictures technical field
Image interfusion method.
Background technique
Image co-registration (Image Fusion) refer to by multi-source channel the collected image data about same target
By image procossing and computer technology etc., the advantageous information in each self-channel is extracted to greatest extent, is finally integrated at high-quality
The image of amount, to improve the utilization rate of image information, improve computer interpretation precision and reliability, the space for promoting original image
Resolution ratio and spectral resolution are conducive to monitoring, and the branch that image co-registration is merged as information, is current information control fusion
In a hot spot.The data mode of image co-registration be include light and shade, color, temperature, distance and other scene features
Image.These images can be provided in the form that a width or one arrange.And image co-registration is by 2 or 2 or more figures
As being fused on 1 image for information, so that the image of fusion contains more information, can be more convenient people to observe or count
The processing of calculation machine.The target of image co-registration is to reduce to export on the basis of merging relevant information maximum under practical application target
Uncertainty and redundancy.The advantages of image co-registration it is obvious that it can time and space information contained by enlarged image, reduce not
Certainty increases reliability, improves the robust performance of system, image interfusion method is in medical imaging, security protection, remote sensing observations at present
There is critically important application in equal fields.
Currently, the deficiency of influence and camera inherently due to external environment, it tends to be difficult to obtain the complete of some scene
Focusedimage, the existing method for being generally basede on transform domain, such as Curvelet converter technique, Sheralet converter technique, there are all
Such as there is the deficiencies of blocky effect, can not obtain and be more clear image abundant.Therefore, those skilled in the art provide one kind
Theme, to solve the problems mentioned in the above background technology.
Summary of the invention
The theoretical image interfusion method with HSI transformation is stretched based on phase the purpose of the present invention is to provide a kind of, with solution
Certainly the problems mentioned above in the background art.
To achieve the above object, the invention provides the following technical scheme:
It is a kind of that the theoretical image interfusion method with HSI transformation is stretched based on phase, method includes the following steps:
1) construction stretch kernel function, provide PST can phenogram as detail of the high frequency theoretical foundation；
2) HSI transformation is done to left and right focusedimage；
3) new H, S, I component are subjected to HSI inverse transformation, obtain fusion results；
4) validity of verification algorithm.
Illustrate as detailed technology of the invention: in the step 1), being stretched applied to the phase before analog-to-digital conversion ADC
PST is converted, also can be applied to digital processing field, phase stretching conversion PST is applied to digital signal or image processing
Mathematical model are as follows:
Wherein, A (m, n) indicates angular image, and " ∠ " expression takes operating angle, and B (m, n) indicates original input picture,
FFT2 and IFFT2 respectively indicates two-dimensional fast fourier transform and inverse transformation, and (u, v) indicates frequency variable,It is part
Smoothing filter,It is to rely on the nonlinear phase distortion filter of frequency,It is to rely on frequency
Low-pass filter L (u, v) in (1) is placed on space for the convenience that theory is shifted by the nonlinear phase kernel function of rate variable
Domain, and image of the B (m, n) after spatial domain is low-pass filtered is still denoted as B (m, n), this spline equation (1) just becomes shape of equal value
Formula
The derived function of nuclear phase bit function φ (u, v), i.e. group delay are the linear or sublinear functions of frequency variable, this phase
One simple case of position core letter is exactly the arctan function of " S " type, for simplicity, if this phase of further requirement
Warping operations in frequency domain plane be it is isotropic, degreeof tortuosity only with the polar diameter r under o-uv frequency plane polar coordinate system
It is related, and it is unrelated with polar angle θ, i.e. the nuclear phase position prototype of hypothesis PST is that circle is symmetrical about frequency variable, has:
Wherein, r is the polar diameter under frequency plane o-uv polar coordinate system, and θ is polar angle, with the relationship between uv frequency variable
Are as follows:If it is required that φ polar (r) is the arctan function of S type about the derivative of r,
Then have:
It is noted that uv frequency plane of the image after Fourier transformation is finite region, so can be asked according to equation (3)
It solves φ polar (r):
(normalization) is normalized to the phase stretch function in equation (4), is obtained
To the phase function in equation (5), the phase tensile strength in non-linear distortion stretching conversion is added
(strength) parameter S and distortion (warped) parameter W obtains band strength parameter S and warp parameters W in final PST transformation
Nuclear phase bit function
Wherein, tan-1() indicates that arctan function, ln () are natural logrithm, rmaxRepresent the maximum frequency of uv frequency plane
Rate polar diameter is that phase used in equation (6) stretches kernel function,
Herein with a special phase stretch function, theoretically demonstrating A (m, n) reflection image gradient, this is asked
Topic, for the convenience of problem analysis, is first reduced to one-dimensional signal for equation (1), obtains equation (7):
NoteThe group delay for considering phase filter is stringent linear function, is designed following
Group delay phase filter:
It noticesUtilize the frequency domain phase stretching conversion PST equation of equation (8) phase filter
(7) become:
To lesser frequency variable u, by exp { ju2/ 2 } Taylor series expansion is pressed, there is exp { ju2/2}≈1+ju2/ 2, generation
Enter equation (9), have:
Using the property of Fourier transformation, have:(10) are substituted into obtain:
A (x)=∠ { B (x)-jB " (x) } (11)
In view of the parenthetic plural number of (11) right end, the arctan function that angle is equal to the ratio of imaginary part and real part is answered, is had:
Recycle tan-1(x) ≈ x is obtained:
A (x, y) by phase stretching conversion PST it can be seen from (13) in image processing model is effectively equivalent to
It is originally inputted certain normalization second-order partial differential coefficient of digital picture, that is, the normalization second order gradient of image, it is clear that namely
High-frequency information in image, here it is the perfect theory analysis that PST can be used for extracting characteristics of image,
Control stretches kernel function (6), and the normalized nonlinear phase twist as derived from equation (7) institute can be obtained and stretch core letter
Number:
Us are prompted for equation (10)-(13) theory analysis and derivation, " it is modulated to reduce analog signal if relaxed
The time-bandwidth product of envelope signal afterwards " or design " analog-digital converter of superelevation rate " these constraint conditions, and be used to count from it
The visual angle of word signal or image procossing is set out, and is dedicated to " pure phase position " A (x, y) the expression image after phase stretching conversion PST
In high-frequency information (or gradient information), thus be applied to digital picture edge extracting, character representation and image co-registration etc.,
Pure " amplitude " stretching conversion such as equation (15) can also be designed:
(15) are substituted into equation (9) or (10), are had:
It finally obtains:
To the net amplitude stretching conversion of equation (15), taken under two-dimensional case:
As further scheme of the invention: in the step 2), first by left focusedimage A and right focusedimage B
HSI transformation is done, the I component of two images is subjected to PST operation, the Weighted Fusion strategy of I component is constructed according to operation result, it is right
H, S component constructs allocation strategy according to the Euclidean distance of I component after fusion and source figure I component.
As further scheme of the invention: in the step 4), for the validity for verifying this paper algorithm, choosing herein
Four groups of standard multiple focussing images and two groups of lytro images as test data, and by simulation result and wavelet transformation,
The simulation result of Curvelet transformation and Shearlet transformation compares, in order to more accurately comment this paper algorithm
Valence has chosen four comentropy, spatial frequency, average gradient and phase equalization indexs herein, and image co-registration result is come
It says, these refer to that target value is bigger, represent that syncretizing effect is better, and fusion results information contained amount is bigger, six groups of fusion experiments
Specific evaluation parameter such as fusion results objectively evaluate shown in index table, and objectively evaluating in index table from fusion results can see,
The contrast number of this paper algorithm and other algorithms.
Compared with prior art, the beneficial effects of the present invention are:
Inventive algorithm is mainly characterized by: utilizing the method for the present invention, the part that different sensors can be obtained focuses
Image is handled, and obtains full figure as focus is consistent, information image more abundant, the mentioned method of the present invention discusses
Concrete thought and the realization of multi-focus image fusion are as a result, illustrate this paper algorithm in the holding of fusion results information content, marginal information
Reserve capability and clarity etc. have preferable performance, demonstrate the reasonability, superiority and validity of this paper algorithm.
Detailed description of the invention
Fig. 1 is a kind of flow chart that the theoretical image interfusion method converted with HSI is stretched based on phase.
Fig. 2 is a kind of original image to be processed that the theoretical image interfusion method converted with HSI is stretched based on phase.
Fig. 3 is the treatment effect comparison diagram of various image procossing fusion method.
Fig. 4 is that fusion results objectively evaluate index table.
Specific embodiment
Technical solution of the present invention is described in more detail With reference to embodiment.
Embodiment 1: a kind of to stretch the theoretical image interfusion method with HSI transformation based on phase, this method includes following step
It is rapid:
1) construction stretch kernel function, provide PST can phenogram as detail of the high frequency theoretical foundation；
2) HSI transformation is done to left and right focusedimage；
3) new H, S, I component are subjected to HSI inverse transformation, obtain fusion results；
4) validity of verification algorithm.
In the step 1), applied to the phase stretching conversion PST before analog-to-digital conversion ADC, number also can be applied to
Field of signal processing, phase stretching conversion PST are applied to the mathematical model of digital signal or image processing are as follows:
Wherein, A (m, n) indicates angular image, and " ∠ " expression takes operating angle, and B (m, n) indicates original input picture,
FFT2 and IFFT2 respectively indicates two-dimensional fast fourier transform and inverse transformation, and (u, v) indicates frequency variable,It is part
Smoothing filter,It is to rely on the nonlinear phase distortion filter of frequency,It is to rely on frequency
Low-pass filter L (u, v) in (1) is placed on space for the convenience that theory is shifted by the nonlinear phase kernel function of rate variable
Domain, and image of the B (m, n) after spatial domain is low-pass filtered is still denoted as B (m, n), this spline equation (1) just becomes shape of equal value
Formula
The derived function of nuclear phase bit function φ (u, v), i.e. group delay are the linear or sublinear functions of frequency variable, this phase
One simple case of position core letter is exactly the arctan function of " S " type, for simplicity, if this phase of further requirement
Warping operations in frequency domain plane be it is isotropic, degreeof tortuosity only with the polar diameter r under o-uv frequency plane polar coordinate system
It is related, and it is unrelated with polar angle θ, i.e. the nuclear phase position prototype of hypothesis PST is that circle is symmetrical about frequency variable, has:
Wherein, r is the polar diameter under frequency plane o-uv polar coordinate system, and θ is polar angle, with the relationship between uv frequency variable
Are as follows:If it is required that φ polar (r) is the arctan function of S type about the derivative of r,
Then have:
It is noted that uv frequency plane of the image after Fourier transformation is finite region, so can be asked according to equation (3)
It solves φ polar (r):
(normalization) is normalized to the phase stretch function in equation (4), is obtained
To the phase function in equation (5), the phase tensile strength in non-linear distortion stretching conversion is added
(strength) parameter S and distortion (warped) parameter W obtains band strength parameter S and warp parameters W in final PST transformation
Nuclear phase bit function
Wherein, tan-1() indicates that arctan function, ln () are natural logrithm, rmaxRepresent the maximum frequency of uv frequency plane
Rate polar diameter is that phase used in equation (6) stretches kernel function,
Herein with a special phase stretch function, theoretically demonstrating A (m, n) reflection image gradient, this is asked
Topic, for the convenience of problem analysis, is first reduced to one-dimensional signal for equation (1), obtains equation (7):
NoteThe group delay for considering phase filter is stringent linear function, is designed following
Group delay phase filter:
It noticesUtilize the frequency domain phase stretching conversion PST equation of equation (8) phase filter
(7) become:
To lesser frequency variable u, by exp { ju2/ 2 } Taylor series expansion is pressed, there is exp { ju2/2}≈1+ju2/ 2, generation
Enter equation (9), have:
Using the property of Fourier transformation, have:(10) are substituted into obtain:
A (x)=∠ { B (x)-jB " (x) } (11)
In view of the parenthetic plural number of (11) right end, the arctan function that angle is equal to the ratio of imaginary part and real part is answered, is had:
Recycle tan-1(x) ≈ x is obtained:
A (x, y) by phase stretching conversion PST it can be seen from (13) in image processing model is effectively equivalent to
It is originally inputted certain normalization second-order partial differential coefficient of digital picture, that is, the normalization second order gradient of image, it is clear that namely
High-frequency information in image, here it is the perfect theory analysis that PST can be used for extracting characteristics of image,
Control stretches kernel function (6), and the normalized nonlinear phase twist as derived from equation (7) institute can be obtained and stretch core letter
Number:
Us are prompted for equation (10)-(13) theory analysis and derivation, " it is modulated to reduce analog signal if relaxed
The time-bandwidth product of envelope signal afterwards " or design " analog-digital converter of superelevation rate " these constraint conditions, and be used to count from it
The visual angle of word signal or image procossing is set out, and is dedicated to " pure phase position " A (x, y) the expression image after phase stretching conversion PST
In high-frequency information (or gradient information), thus be applied to digital picture edge extracting, character representation and image co-registration etc.,
Pure " amplitude " stretching conversion such as equation (15) can also be designed:
(15) are substituted into equation (9) or (10), are had:
It finally obtains:
To the net amplitude stretching conversion of equation (15), taken under two-dimensional case:
In the step 2), left focusedimage A and right focusedimage B are done into HSI transformation first, by the I of two images points
Amount carries out PST operation, and the Weighted Fusion strategy of I component is constructed according to operation result, to H, S component, according to I component after fusion with
The Euclidean distance of source figure I component constructs allocation strategy, takes out its I component (I respectivelyA, IB), then using proposed in this paper
Linear phase stretches kernel functionCalculate separately IAAnd IBPhase information, be as a result denoted as PSTAAnd PSTB, connect down
To reconstruct the I component of blending image, concrete measure are as follows: to the phase value (PST at source images (i, j) pointAAnd PSTB) for, it
Reflect the detail of the high frequency of image, by comparing the phase value (PST at source images (i, j) pointAAnd PSTB), draw I points
The reconfiguration rule of amount is shown in formula (19), and wherein k is weighting coefficient, and the empirical value range that experiment obtains k is [1.2,1.4],
H, the reconstructing method of S component: on the basis of I component fusion, I is calculatedfusionWith the Europe of source images I component it is several in
Distance, if being closer, correspond to be located at source figure focal zone a possibility that it is bigger, specific reconfiguration rule is shown in formula
(20), (21):
In formula (20), (21), HAAnd HBThe respectively H component of source images A, B, SAAnd SBThe respectively S of source images A, B
Component, HfusionAnd SfusionH component, S component as fusion results image.
In the step 4), for the validity for verifying this paper algorithm, four groups of standard multiple focussing images and two groups are chosen herein
Lytro image is as test data, and the emulation that simulation result and wavelet transformation, Curvelet transformation and Shearlet are converted
As a result it compares, the emulation experiment environment of this paper is Intel i5-6500,3.2GHz CPU, 8GB RAM, MATLAB
The simulation result of 2014a, source images and four kinds of algorithms is as shown in figure 3, Fig. 2 Coca-Cola source images, wherein figure a is right focusing source
Image, figure b are left focusing source images, Fig. 3 Coca-Cola fusion results, wherein figure a is Wavelet Transform Fusion as a result, figure b is
Curvelet converts fusion results, and figure c is that Shearlet converts fusion results, and figure d is this paper algorithm fusion as a result, comparison diagram 2
The fusion results of source images and four kinds of blending algorithms, four kinds of algorithms largely improve the information content of fusion results,
As a result clarity has relative to source images significantly to be promoted, and the fusion results color of this paper algorithm is closer and source
Image has chosen comentropy, spatial frequency, average gradient and phase to more accurately evaluate this paper algorithm herein
Four indexs of bit integrity, for image co-registration result, these refer to that target value is bigger, and it is better to represent syncretizing effect, melt
Conjunction result information contained amount is bigger, and the specific evaluation parameter such as fusion results of six groups of fusion experiments objectively evaluate shown in index table,
Objectively evaluating in index table from Fig. 4, that is, fusion results can see, and this paper algorithm is compared with other algorithms, in addition to phase equalization
In parameter, Lytro-02 is slightly below wavelet transformation, Lytro-18 is slightly below wavelet transformation and Shearlet transformation is outer, remaining refers to
Mark parameter this paper algorithm is superior to comparison algorithm, illustrates this paper algorithm in information content holding, fusion results clarity, marginal information
Holding capacity etc. achieves good effect, with subjective assessment result having the same.
The working principle of the invention is:
For Color Multi-Focus Image Fusion, one kind is proposed based on phase and stretches what theory (PST) was combined with HSI transformation
Fusion method, firstly, construction stretch kernel function, provide PST can phenogram as detail of the high frequency theoretical foundation, secondly,
HSI transformation is done to left and right focusedimage, the I component of two images is subjected to PST operation, I component is constructed according to operation result
Weighted Fusion strategy；To H, S component, allocation strategy is constructed according to the Euclidean distance of I component after fusion and source figure I component,
Finally, new H, S, I component are carried out HSI inverse transformation, fusion results are obtained, are the validity of verification algorithm, utilize six groups of coloured silks
Color multiple focussing image has carried out emulation experiment, is analyzed by Objective and subjective evaluations to fusion results, and with other 3 kinds of algorithms
It is compared, this paper algorithm achieves good effect.
Better embodiment of the invention is explained in detail above, but the present invention is not limited to above-mentioned embodiment party
Formula within the knowledge of one of ordinary skill in the art can also be without departing from the purpose of the present invention
Various changes can be made.
Claims (4)
1. a kind of stretch the theoretical image interfusion method with HSI transformation based on phase, comprising the following steps:
1) construction stretch kernel function, provide PST can phenogram as detail of the high frequency theoretical foundation；
2) HSI transformation is done to left and right focusedimage；
3) new H, S, I component are subjected to HSI inverse transformation, obtain fusion results；
4) validity of verification algorithm.
2. a kind of image interfusion method for being stretched theoretical and HSI transformation based on phase according to claim 1, feature are existed
In applied to the phase stretching conversion PST before analog-to-digital conversion ADC, also can be applied at digital signal in the step 1)
Reason field, phase stretching conversion PST are applied to the mathematical model of digital signal or image processing are as follows:
Wherein, A (m, n) indicates angular image, and " ∠ " expression takes operating angle, and B (m, n) indicates original input picture, FFT2 with
IFFT2 respectively indicates two-dimensional fast fourier transform and inverse transformation, and (u, v) indicates frequency variable,It is local smoothing method filter
Wave device,It is to rely on the nonlinear phase distortion filter of frequency,It is to rely on frequency variable
Low-pass filter L (u, v) in (1) is placed on spatial domain for the convenience shifted onto of theory by nonlinear phase kernel function, and by B
The image of (m, n) after spatial domain is low-pass filtered is still denoted as B (m, n), this spline equation (1) just becomes equivalent form
The derived function of nuclear phase bit function φ (u, v), i.e. group delay are the linear or sublinear functions of frequency variable, this phase core
One simple case of letter is exactly the arctan function of " S " type, for simplicity, if this phase twist of further requirement
It is isotropic for operating in frequency domain plane, and degreeof tortuosity is only related with the polar diameter r under o-uv frequency plane polar coordinate system,
And it is unrelated with polar angle θ, i.e. the nuclear phase position prototype of hypothesis PST is that circle is symmetrical about frequency variable, has:
Wherein, r is the polar diameter under frequency plane o-uv polar coordinate system, and θ is polar angle, with the relationship between uv frequency variable are as follows:If it is required that φ polar (r) is the arctan function of S type about the derivative of r,
Have:
It is noted that uv frequency plane of the image after Fourier transformation is finite region, so φ can be solved according to equation (3)
Polar (r):
(normalization) is normalized to the phase stretch function in equation (4), is obtained
To the phase function in equation (5), phase tensile strength (strength) ginseng in non-linear distortion stretching conversion is added
Number S and distortion (warped) parameter W obtains the nuclear phase bit function of band strength parameter S and warp parameters W in final PST transformation
Wherein, tan-1() indicates that arctan function, ln () are natural logrithm, rmaxRepresent uv frequency plane maximum frequency pole
Diameter is that phase used in equation (6) stretches kernel function,
Herein with a special phase stretch function, A (m, n) reflection this problem of image gradient is theoretically demonstrated, is
The convenience of problem analysis, is first reduced to one-dimensional signal for equation (1), obtains equation (7):
NoteThe group delay for considering phase filter is stringent linear function, designs following group delay
Phase filter:
It noticesFrequency domain phase stretching conversion PST equation (7) using equation (8) phase filter becomes:
To lesser frequency variable u, by exp { ju2/ 2 } Taylor series expansion is pressed, there is exp { ju2/2}≈1+ju2/ 2, substitution side
Journey (9), has:
Using the property of Fourier transformation, have:(10) are substituted into obtain:
A (x)=∠ { B (x)-jB " (x) } (11)
In view of the parenthetic plural number of (11) right end, the arctan function that angle is equal to the ratio of imaginary part and real part is answered, is had:
Recycle tan-1(x) ≈ x is obtained:
The A (x, y) being used in image processing model by phase stretching conversion PST it can be seen from (13) is effectively equivalent to original
Certain normalization second-order partial differential coefficient of input digital image, that is, the normalization second order gradient of image, it is clear that namely image
In high-frequency information, here it is the perfect theory analysis that PST can be used for extracting characteristics of image,
Control stretches kernel function (6), and the normalized nonlinear phase twist as derived from equation (7) institute can be obtained and stretch kernel function:
Us are prompted for equation (10)-(13) theory analysis and derivation, " reduces the modulated rear packet of analog signal if relaxed
The time-bandwidth product of network signal " or design " analog-digital converter of superelevation rate " these constraint conditions, and digital letter is used for from it
Number or the visual angle of image procossing set out, be dedicated to in " pure phase position " A (x, y) the expression image after phase stretching conversion PST
High-frequency information (or gradient information) may be used also to be applied to edge extracting, character representation and the image co-registration etc. of digital picture
Pure " amplitude " stretching conversion of design such as equation (15):
(15) are substituted into equation (9) or (10), are had:
It finally obtains:
To the net amplitude stretching conversion of equation (15), taken under two-dimensional case:
3. a kind of image interfusion method for being stretched theoretical and HSI transformation based on phase according to claim 1, feature are existed
In in the step 2), left focusedimage A and right focusedimage B are done HSI transformation first, the I components of two images is carried out
PST operation constructs the Weighted Fusion strategy of I component according to operation result, to H, S component, according to I component after fusion and source figure I
The Euclidean distance of component constructs allocation strategy.
4. a kind of image interfusion method for being stretched theoretical and HSI transformation based on phase according to claim 1, feature are existed
In for the validity for verifying this paper algorithm, choosing four groups of standard multiple focussing images and two groups of lytro herein in the step 4)
Image is as test data, and the simulation result that simulation result and wavelet transformation, Curvelet transformation and Shearlet are converted
It compares, in order to more accurately evaluate this paper algorithm, has chosen comentropy, spatial frequency, average gradient herein
And four indexs [13-15] of phase equalization, for image co-registration result, these refer to that target value is bigger, represent fusion
Effect is better, and fusion results information contained amount is bigger, and the specific evaluation parameter such as fusion results of six groups of fusion experiments objectively evaluate
Shown in index table, objectively evaluating in index table from fusion results be can see, the contrast number of this paper algorithm and other algorithms.
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