CN108898146A - Picture breakdown method based on BLMD- fractal interpolation algorithm - Google Patents
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- G—PHYSICS
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- G06V—IMAGE OR VIDEO RECOGNITION OR UNDERSTANDING
- G06V10/00—Arrangements for image or video recognition or understanding
- G06V10/40—Extraction of image or video features
- G06V10/44—Local feature extraction by analysis of parts of the pattern, e.g. by detecting edges, contours, loops, corners, strokes or intersections; Connectivity analysis, e.g. of connected components
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- G—PHYSICS
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- G06V—IMAGE OR VIDEO RECOGNITION OR UNDERSTANDING
- G06V10/00—Arrangements for image or video recognition or understanding
- G06V10/40—Extraction of image or video features
- G06V10/46—Descriptors for shape, contour or point-related descriptors, e.g. scale invariant feature transform [SIFT] or bags of words [BoW]; Salient regional features
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Abstract
Picture breakdown method disclosed by the invention based on BLMD- fractal interpolation algorithm, by setting r0(m, n)=a (m, n), h1(m, n)=r0(m, n), wherein a (m, n) is the two-dimensional matrix of image to be decomposed, and M and N are respectively the line number and columns of the two-dimensional matrix of image to be decomposed, extracts h using neighborhood window methodkThe extreme value of (m, n) is composed, and according to fractal interpolation algorithm, is carried out interpolation calculation to extreme point, is obtained hkThe upper and lower envelope song maxh of (m, n)k(m, n) and minhk(m, n), according to formulaThe mean value envelope surface of image to be decomposed is obtained, according to formula hk(m, n)=hk‑1(m,n)‑meanhk(m, n), to h1(m, n) is decomposed, several two-dimentional production function BPF are obtained1(m,n)、BPF2(m,n)…BPFk(m, n) completes to treat the decomposition for decomposing image, realizes effective decomposition to image.
Description
Technical field
The present invention relates to technical field of image processing, and in particular to a kind of image based on BLMD- fractal interpolation algorithm point
Solution method.
Background technique
Things is perceived and is recognized substantially square as the rapid development of sociaty and economy, image has become people
Formula is gradually deep into people's daily life.But people contact or obtain all kinds of images generally all contain it is complex
Information, directly acquiring these information, there are still certain difficulties.Digital image processing techniques are handled using computer
Picture signal is converted into digital signal processes, and is analyzed and processed to image, meets a kind of technology of vision and other requirements.
Although digital image processing techniques have been widely used every field, the institute that image contains still can not be adaptively obtained
There is information, this also becomes the study frontier and hot issue of current academia's field of image processing.
Image processing method mainly has at present：One kind is the processing method based on Fourier's theory, and another kind of is based on small
The processing method of wave.Wavelet transformation is built upon on the basis of linear system, can carry out accurate physical interpretation to linear signal,
But wavelet basis function needs to be manually set in advance, causes the processing method not have adaptive characteristic, due to wavelet basis function
Fixed characteristic, also resulting in the processing method cannot decompose to obtain the multiple dimensioned characteristic of signal itself.So mathematics and engineering are answered
A kind of better time frequency analyzing tool is always searched for field.American scholar Huang et al. was put forward for the first time warp in 1998
It tests Mode Decomposition (Empirical Mode Decomposition, EMD), this method is based on data characteristics, adaptive non-
Steady Nonlinear harmonic oscillator method.J.C.Nune et al. of France in 2003 and 2005 by Empirical Mode Decomposition Algorithm from
One-Dimensional Extended proposes Bidimensional Empirical Mode Decomposition algorithm (Bi-dimensional Empirical Mode to two dimension
Decomposition, BEMD) and its modification method, certain effect is achieved in image domains, this method is obtained using decomposition
Two-dimentional intrinsic mode function (Bi-dimensional Intrinsic Mode Function, BIMF) and residual error or trend
Item retains the detailed information and all kinds of useful feature information of source images, but it still can not decompose to have obtained according to image adaptive
Whole BIMF, while this method the problems such as there is also stopping criterion, mode mixing, end effect, interpolation methods.For this purpose, related
Scholar is seeking always the picture breakdown algorithm with more preferable adaptive characteristic, and in this context, Smith is in EMD within 2005
Local mean value is proposed on the basis of algorithm and decomposes (Local Mean Decomposition, LMD) algorithm, is asked to solve this
Topic provides a technological approaches for exploration.LMD algorithm not only remain EMD algorithm it is adaptive the advantages that, Er Qie
The deficiency of EMD algorithm is overcome to a certain extent, and two-dimentional local mean value decomposes (Bidimensional Local Mean
Decomposition, BLMD) algorithm generated on the basis of LMD.
So design it is a kind of can effectively picture breakdown method be at present there is an urgent need to.
Summary of the invention
To solve the above-mentioned problems, the embodiment of the invention provides a kind of images based on BLMD- fractal interpolation algorithm point
Solution method, enables the characteristic information for reflecting image to the component that picture breakdown obtains, and ensure that the multi-resolution decomposition of image, real
Effective decomposition to image is showed, this method includes：
Step1, treat decompose image initialized, specifically include：
Set r0(m, n)=a (m, n), h1(m, n)=r0(m, n), wherein a (m, n) is the Two-Dimensional Moment of image to be decomposed
Battle array, r0(m, n) is the trend term of image to be decomposed, h1(m, n) is the two dimension production letter that image to be decomposed needs to decompose for the first time
Number, 0≤m≤M-1,0≤n≤N-1, M and N are respectively the line number and columns of the two-dimensional matrix of image to be decomposed；
Step2, h is extracted using neighborhood window methodkThe extreme value of (m, n) is composed, wherein k=1,2,3 ...；
Step3, h is obtained to extreme point progress interpolation calculation according to fractal interpolation algorithmkThe upper and lower envelope of (m, n) is bent
Face maxhk(m, n) and minhk(m,n)；
Step4, according to formulaObtain the mean value packet of image to be decomposed
Network curved surface；
Step5, according to formula hk(m, n)=hk-1(m,n)-meanhk(m, n), to h1(m, n) is decomposed, and is obtained several
A two dimension production function BPF1(m,n)、BPF2(m,n)…BPFk(m, n), wherein BPFk(m, n)=hk(m,n)；
Step6, according to formula rk(m, n)=rk-1(m,n)-BPFk(m, n) obtains r1(m,n)、 r2(m,n)...rk(m,
n)；
Step7, repeating said steps Step2-Step6, and according to the stop condition of setting, obtain two-dimentional production function
BPFkWhole components of (m, n) are completed to treat the decomposition for decomposing image.
Preferably, according to fractal interpolation algorithm, carrying out interpolation calculation to extreme point includes extracting the feature of image to be decomposed,
It specifically includes：
According to formula E | L (t+ Δ t)-L (t) |2, calculate the expectation for the pixel grey scale value difference that space length in image is Δ t
Value, according to desired value, obtains limit of size parameter | Δ t |minAnd | Δ t |max, wherein L (t) is one dimensional fractal Blang function, t
For RnThe point in space, Δ t are offset a little；
According to formula
And σ2=E | L (t+1)-L (t) |2, obtain H and pixel grey scale normal distribution mark
The value of quasi- difference δ, completes image characteristics extraction, wherein and H is straight slope, | | △ t | | the distance between sample.
Preferably, according to fractal interpolation algorithm, carrying out interpolation calculation to extreme point includes：
Work as i, when j is even number, according to formula
Calculate the gray value of the pixel (i, j) of image to be decomposed；
Work as i, when j only has one for even number, according to formula
Calculate the gray value of the pixel (i, j) of image to be decomposed；
Wherein, G is the Gauss stochastic variable for obeying N (0,1) distribution.
Stop condition is：
Wherein,△k+1=Tk+1-Tk, k >=2, n >=3, b is constant, TkFor hk(m, n) is every
Total extreme point number after once decomposing.
The beneficial effect that picture breakdown method provided in an embodiment of the present invention based on BLMD- fractal interpolation algorithm generates is such as
Under：
Image is decomposed by using BLMD and fractal interpolation algorithm, two-dimentional production function can more reflect figure to be decomposed
The characteristic information and marginal information of picture can obtain whole components of the two-dimentional production function BPFk (m, n) of image to be decomposed, real
Effective decomposition to the image to be decomposed is showed, solving the prior art cannot effectively decomposing to the image to be decomposed
Defect.
Detailed description of the invention
Fig. 1 is that the process of the picture breakdown method provided in an embodiment of the present invention based on BLMD- fractal interpolation algorithm is illustrated
Figure；
Fig. 2 a is the one of the image of the picture breakdown method provided in an embodiment of the present invention based on BLMD- fractal interpolation algorithm
A matrix indicates schematic diagram；
Fig. 2 b is the one of the image of the picture breakdown method provided in an embodiment of the present invention based on BLMD- fractal interpolation algorithm
The maximum spectral representation schematic diagram of a matrix；
Fig. 2 c is the one of the image of the picture breakdown method provided in an embodiment of the present invention based on BLMD- fractal interpolation algorithm
The minimum spectral representation schematic diagram of a matrix.
Specific embodiment
Present invention is further described in detail with reference to the accompanying drawing.
The picture breakdown method based on BLMD- fractal interpolation algorithm that the embodiment of the present invention proposes, as shown in Figure 1, the party
Method includes the following steps：
101, it treats decomposition image and is initialized, specifically included：
Set r0(m, n)=a (m, n), h1(m, n)=r0(m, n), wherein a (m, n) is the two dimension of the image to be decomposed
Matrix, r0(m, n) is the trend term of the image to be decomposed, h1(m, n) is that the image to be decomposed needs to decompose for the first time
Two-dimentional production function, 0≤m≤M-1,0≤n≤N-1, M and N be respectively the two-dimensional matrix of the image to be decomposed line number and
Columns.
102, h is extracted using neighborhood window methodkThe extreme value of (m, n) is composed, k=1,2,3 ....
Wherein, extracting extreme value spectrum is to find all extreme points from a given two dimensional image, which includes pole
Value point position and extreme point size.The array that all maximum points are constituted, referred to as maximum are composed；The battle array that all minimum points are constituted
Column, referred to as minimum are composed.
In an example it is assumed that b × c pixel two dimensional image f (x, y) can be indicated with following formula matrix：
In formula (1), abcB row, c column data in representing matrix.First assume that neighborhood window window size is wn×wn, then pole
Value point can be described by following formula：
In formula：
For picture signal, it is a more satisfactory method that extreme value is generally found using 3 × 3 windows.It is special
In the case of bigger sliding window can be used to find extreme value, but will lead to extreme point quantity and sharply decline.As shown in Figure 2 a
8 × 8 matrixes, illustrated using neighborhood window method its find step.Extreme point is found using 3 × 3 windows, the black in figure is thick
The window that line is surrounded is sliding window, can be scanned one by one respectively to ranks, obtained maximum spectrum and minimum spectrum point
Not as shown in Fig. 2 b and Fig. 2 c.Window is respectively with a32、a75And a26Centered on found, by formula (2) it is recognised that a32、
a75It is very big and minimum respectively, but a26It is non-extreme point.
103, according to fractal interpolation algorithm, interpolation calculation is carried out to the extreme point, obtains hkThe upper and lower envelope of (m, n)
Curved surface maxhk(m, n) and minhk(m,n)。
Wherein, fractal interpolation algorithm includes image to be decomposed and the image characteristics extraction to be decomposed described in feature extraction point
Amount carries out interpolation calculation.
104, according to formulaObtain the mean value of the image to be decomposed
Envelope surface.
105, according to formula hk(m, n)=hk-1(m,n)-meanhk(m, n), to h1(m, n) is decomposed, several are obtained
Two-dimentional production function BPF1(m,n)、BPF2(m,n)…BPFk(m, n), wherein BPFk(m, n)=hk(m, n), k=1,2,3 ....
106, according to formula rk(m, n)=rk-1(m,n)-BPFk(m, n) obtains r1(m,n)、r2(m, n)...rk(m,n)。
107, repeat the above steps 102-106, and according to the stop condition of setting, obtains the two-dimentional production function BPFk
Whole components of (m, n) complete the decomposition to the image to be decomposed.
Wherein,
Optionally, according to fractal interpolation algorithm, carrying out interpolation calculation to the extreme point includes extracting the figure to be decomposed
The feature of picture, specifically includes：
According to formula E | L (t+ Δ t)-L (t) |2, calculate the expectation for the pixel grey scale value difference that space length in image is Δ t
Value, according to the desired value, obtains limit of size parameter | Δ t |minAnd | Δ t |max, wherein L (t) is one dimensional fractal Blang letter
Number, t RnThe point in space, Δ t are the offset of the point；
According to formulaAnd σ2=E | L (t+1)-L (t) |2, obtaining H and pixel grey scale just
The value of state distribution standard deviation δ completes image characteristics extraction, wherein and H is straight slope, | | △ t | | the distance between sample.
Optionally, according to fractal interpolation algorithm, carrying out interpolation calculation to the extreme point includes：
Work as i, when j is even number, according to formula
Calculate the gray value of the pixel (i, j) of the image to be decomposed；
Work as i, when j only has one for even number, according to formula
Calculate the gray value of the pixel (i, j) of the image to be decomposed, wherein G is to obey N (0,1) to be distributed
Gauss stochastic variable, | | △ t | | the distance between sample.
Further, it is substantially Method of Random Mid-point Displacement Recursive Implementation that two-dimentional local mean value, which decomposes fractal interpolation algorithm,
Process needs constantly to repeat the above steps before not up to setting spatial resolution.Wherein each time in iterative process, need
The midpoint to be inserted into is Gaussian random variable, and desired value is the mean value of four consecutive points.The offset of point can be by can
The H and σ for describing picture characteristics information are codetermined.As H=0, this offset for putting four mean values relatively adjacent thereto is needed
It is determined by σ；Work as H=1, when variance is 0, obtained adjacent four mean values are equivalent to linear interpolation.If σ value is certain
In the case of, H is smaller, then interpolation point randomness will be bigger.
Wherein, the thinking of two-dimensional random Diamond-Square algorithm is：First to existing endpoint attribute line segment midpoint as two-end-point
Mean value and any random file amount and, then two line segments after being displaced repeat the above steps, until reaching given stopping
Condition.
Further, by above-mentioned decomposable process it is found that the decomposable process can smooth irregular amplitude and weakening picture number
According to singularity, but will affect the physical significance of image data, so cannot unlimitedly handle down.And due to actual
Usually there is crossing for mean value curved surface in calculating process to decompose and owe to decompose.And mean value and decomposition will be will affect by crossing to decompose and owe to decompose
The result of process.Therefore, it is necessary to terminate decomposable process according to picture signal feature itself.
Optionally, the stop condition is：
Wherein,△k+1=Tk+1-Tk, k >=2, n >=3, b is constant, TkFor hk(m, n) is every
Total extreme point number after once decomposing.
Further, according to multiple correlation test interpretation of result, available, b value compares between 0.09-0.32
Rationally.
Relative to the two-dimentional production function that other conditions obtain, the two-dimentional production function obtained by above-mentioned stop condition is more
It can reflect characteristic information and marginal information of image to be decomposed etc..
Picture breakdown method provided in an embodiment of the present invention based on BLMD- fractal interpolation algorithm, including：Set r0(m,
N)=a (m, n), h1(m, n)=r0(m, n), wherein a (m, n) is the two-dimensional matrix of image to be decomposed, r0(m, n) is to be decomposed
The trend term of image, h1The two-dimentional production function that (m, n) needs first time to decompose for image to be decomposed, 0≤m≤M-1,0≤n≤
N-1, M and N are respectively the line number and columns of the two-dimensional matrix of image to be decomposed, extract h using neighborhood window methodkThe extreme value of (m, n)
Spectrum, k=1,2,3 ... carry out interpolation calculation to extreme point, obtain h according to fractal interpolation algorithmkThe upper and lower envelope of (m, n) is bent
Face maxhk(m, n) and minhk(m, n), according to formulaObtain figure to be decomposed
The mean value envelope surface of picture, according to formula hk(m, n)=hk-1(m,n)-meanhk(m, n), to h1(m, n) is decomposed, and is obtained
Several two-dimentional production function BPF1(m,n)、BPF2(m,n)…BPFk(m, n), wherein BPFk(m, n)=hk(m, n), according to
Formula rk(m, n)=rk-1(m,n)-BPFk(m, n) obtains r1(m, n)、r2(m,n)...rk(m, n) repeats the above steps, and
According to the stop condition of setting, two-dimentional production function BPF is obtained1Whole components of (m, n) are completed to treat point for decomposing image
Solution, realizes effective decomposition to image.
In the above-described embodiments, it all emphasizes particularly on different fields to the description of each embodiment, there is no the portion being described in detail in some embodiment
Point, reference can be made to the related descriptions of other embodiments.
It is understood that the correlated characteristic in the above method and device can be referred to mutually.In addition, in above-described embodiment
" first ", " second " etc. be and not represent the superiority and inferiority of each embodiment for distinguishing each embodiment.
It is apparent to those skilled in the art that for convenience and simplicity of description, the system of foregoing description,
The specific work process of device and unit, can refer to corresponding processes in the foregoing method embodiment, and details are not described herein.
Algorithm and display are not inherently related to any particular computer, virtual system, or other device provided herein.
Various general-purpose systems can also be used together with teachings based herein.As described above, it constructs required by this kind of system
Structure be obvious.In addition, the present invention is also not directed to any particular programming language.It should be understood that can use various
Programming language realizes summary of the invention described herein, and the description done above to language-specific is to disclose this hair
Bright preferred forms.
In addition, memory may include the non-volatile memory in computer-readable medium, random access memory
(RAM) and/or the forms such as Nonvolatile memory, such as read-only memory (ROM) or flash memory (flash RAM), memory includes extremely
A few storage chip.
It should be understood by those skilled in the art that, embodiments herein can provide as method, system or computer program
Product.Therefore, complete hardware embodiment, complete software embodiment or reality combining software and hardware aspects can be used in the application
Apply the form of example.Moreover, it wherein includes the computer of computer usable program code that the application, which can be used in one or more,
The computer program implemented in usable storage medium (including but not limited to magnetic disk storage, CD-ROM, optical memory etc.) produces
The form of product.
The application is referring to method, the process of equipment (system) and computer program product according to the embodiment of the present application
Figure and/or block diagram describe.It should be understood that every one stream in flowchart and/or the block diagram can be realized by computer program instructions
The combination of process and/or box in journey and/or box and flowchart and/or the block diagram.It can provide these computer programs
Instruct the processor of general purpose computer, special purpose computer, Embedded Processor or other programmable data processing devices to produce
A raw machine, so that being generated by the instruction that computer or the processor of other programmable data processing devices execute for real
The device for the function of being specified in present one or more flows of the flowchart and/or one or more blocks of the block diagram.
These computer program instructions, which may also be stored in, is able to guide computer or other programmable data processing devices with spy
Determine in the computer-readable memory that mode works, so that it includes referring to that instruction stored in the computer readable memory, which generates,
Enable the manufacture of device, the command device realize in one box of one or more flows of the flowchart and/or block diagram or
The function of being specified in multiple boxes.
These computer program instructions also can be loaded onto a computer or other programmable data processing device, so that counting
Series of operation steps are executed on calculation machine or other programmable devices to generate computer implemented processing, thus in computer or
The instruction executed on other programmable devices is provided for realizing in one or more flows of the flowchart and/or block diagram one
The step of function of being specified in a box or multiple boxes.
In a typical configuration, calculating equipment includes one or more processors (CPU), input/output interface, net
Network interface and memory.
Memory may include the non-volatile memory in computer-readable medium, random access memory (RAM) and/
Or the forms such as Nonvolatile memory, such as read-only memory (ROM) or flash memory (flash RAM).Memory is computer-readable Jie
The example of matter.
Computer-readable medium includes permanent and non-permanent, removable and non-removable media can be by any method
Or technology come realize information store.Information can be computer readable instructions, data structure, the module of program or other data.
The example of the storage medium of computer includes, but are not limited to phase change memory (PRAM), static random access memory (SRAM), moves
State random access memory (DRAM), other kinds of random access memory (RAM), read-only memory (ROM), electric erasable
Programmable read only memory (EEPROM), flash memory or other memory techniques, read-only disc read only memory (CD-ROM) (CD-ROM),
Digital versatile disc (DVD) or other optical storage, magnetic cassettes, tape magnetic disk storage or other magnetic storage devices
Or any other non-transmission medium, can be used for storage can be accessed by a computing device information.As defined in this article, it calculates
Machine readable medium does not include temporary computer readable media (transitory media), such as the data-signal and carrier wave of modulation.
It should also be noted that, the terms "include", "comprise" or its any other variant are intended to nonexcludability
It include so that the process, method, commodity or the equipment that include a series of elements not only include those elements, but also to wrap
Include other elements that are not explicitly listed, or further include for this process, method, commodity or equipment intrinsic want
Element.In the absence of more restrictions, the element limited by sentence "including a ...", it is not excluded that including element
There is also other identical elements in process, method, commodity or equipment.
It will be understood by those skilled in the art that embodiments herein can provide as method, system or computer program product.
Therefore, complete hardware embodiment, complete software embodiment or embodiment combining software and hardware aspects can be used in the application
Form.It is deposited moreover, the application can be used to can be used in the computer that one or more wherein includes computer usable program code
The shape for the computer program product implemented on storage media (including but not limited to magnetic disk storage, CD-ROM, optical memory etc.)
Formula.
The above is only embodiments herein, are not intended to limit this application.To those skilled in the art,
Various changes and changes are possible in this application.It is all within the spirit and principles of the present application made by any modification, equivalent replacement,
Improve etc., it should be included within the scope of the claims of this application.
Claims (4)
1. a kind of picture breakdown method based on BLMD- fractal interpolation algorithm, which is characterized in that including：
Step1, treat decompose image initialized, specifically include：
Set r0(m, n)=a (m, n), h1(m, n)=r0(m, n), wherein a (m, n) is the Two-Dimensional Moment of the image to be decomposed
Battle array, r0(m, n) is the trend term of the image to be decomposed, h1(m, n) is the two dimension that the image to be decomposed needs to decompose for the first time
Production function, 0≤m≤M-1,0≤n≤N-1, M and N are respectively the line number and columns of the two-dimensional matrix of the image to be decomposed；
Step2, h is extracted using neighborhood window methodkThe extreme value of (m, n) is composed, wherein k=1,2,3 ...；
Step3, h is obtained to extreme point progress interpolation calculation according to fractal interpolation algorithmkThe upper and lower envelope surface of (m, n)
maxhk(m, n) and minhk(m,n)；
Step4, according to formulaObtain the mean value envelope of the image to be decomposed
Curved surface；
Step5, according to formula hk(m, n)=hk-1(m,n)-meanhk(m, n), to h1(m, n) is decomposed, obtain several two
Tie up production function BPF1(m,n)、BPF2(m,n)…BPFk(m, n), wherein BPFk(m, n)=hk(m,n)；
Step6, according to formula rk(m, n)=rk-1(m,n)-BPFk(m, n) obtains r1(m,n)、r2(m,n)...rk(m,n)；
Step7, repeating said steps Step2-Step6, and according to the stop condition of setting, obtain the two-dimentional production function
BPFkWhole components of (m, n) complete the decomposition to the image to be decomposed.
2. the method according to claim 1, wherein being carried out to the extreme point slotting according to fractal interpolation algorithm
It includes the feature for extracting the image to be decomposed that value, which calculates, is specifically included：
According to formula E | L (t+ Δ t)-L (t) |2, calculate the desired value for the pixel grey scale value difference that space length in image is Δ t, root
According to the desired value, limit of size parameter is obtained | Δ t |minAnd | Δ t |max, wherein L (t) is one dimensional fractal Blang function, and t is
RnThe point in space, Δ t are the offset of the point；
According to formula
And σ2=E | L (t+1)-L (t) |2, obtain H and pixel grey scale normal distribution standard difference δ
Value, complete image characteristics extraction, wherein H is straight slope, | | Δ t | | the distance between sample.
3. the method according to claim 1, wherein being carried out to the extreme point slotting according to fractal interpolation algorithm
Value calculates：
Work as i, when j is even number, according to formula
Calculate the gray value of the pixel (i, j) of the image to be decomposed；
Work as i, when j only has one for even number, according to formula
Calculate the gray value of the pixel (i, j) of the image to be decomposed；
Wherein, G is the Gauss stochastic variable for obeying N (0,1) distribution.
4. the method according to claim 1, wherein the stop condition is：
Wherein,Δk+1=Tk+1-Tk, k >=2, n >=3, b is constant, TkFor hk(m, n) is every to pass through one
Total extreme point number after secondary decomposition.
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| CN113298890A (en) * | 2021-05-14 | 2021-08-24 | 之江实验室 | Non-scale aliasing and edge preserving image multi-scale decomposition method and color matching method |
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| CN113298890B (en) * | 2021-05-14 | 2022-07-15 | 之江实验室 | Non-scale aliasing and edge preserving image multi-scale decomposition method and color matching method |
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