CN113269715A - Isotropic image decomposition method under generalized Bedrosian criterion - Google Patents

Isotropic image decomposition method under generalized Bedrosian criterion Download PDF

Info

Publication number
CN113269715A
CN113269715A CN202110377657.XA CN202110377657A CN113269715A CN 113269715 A CN113269715 A CN 113269715A CN 202110377657 A CN202110377657 A CN 202110377657A CN 113269715 A CN113269715 A CN 113269715A
Authority
CN
China
Prior art keywords
image
bedrosian
criterion
generalized
component
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202110377657.XA
Other languages
Chinese (zh)
Other versions
CN113269715B (en
Inventor
徐冠雷
徐晓刚
王军
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Zhejiang Gongshang University
Zhejiang Lab
Original Assignee
Zhejiang Gongshang University
Zhejiang Lab
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Zhejiang Gongshang University, Zhejiang Lab filed Critical Zhejiang Gongshang University
Priority to CN202110377657.XA priority Critical patent/CN113269715B/en
Publication of CN113269715A publication Critical patent/CN113269715A/en
Application granted granted Critical
Publication of CN113269715B publication Critical patent/CN113269715B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00—Image analysis
    • G06T7/0002—Inspection of images, e.g. flaw detection

Landscapes

  • Engineering & Computer Science (AREA)
  • Quality & Reliability (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Image Analysis (AREA)
  • Image Processing (AREA)

Abstract

The invention discloses an isotropic image decomposition method under a generalized Bedrosian criterion, which belongs to an image decomposition technology in computer vision, provides the generalized Bedrosian criterion for any isotropic image, can realize pi/2 phase shift of any isotropic image, can break through double frequency limitation by utilizing the characteristics of the generalized Bedrosian criterion and auxiliary components given by experience to realize the decomposition of any isotropic image with similar frequency components, can also realize the decomposition of anisotropic images, and can realize the decomposition of isotropic images with similar but different frequencies.

Description

Isotropic image decomposition method under generalized Bedrosian criterion
Technical Field
The present invention relates to image decomposition in the field of information processing, and more particularly to decomposition of isotropic images having close frequencies.
Background
Image decomposition is one of the bases of machine vision and image processing applications, and image decomposition algorithms have been mainly divided into three types so far: time domain decomposition algorithm, frequency domain decomposition algorithm and time-frequency domain decomposition algorithm.
The time domain decomposition is mainly based on a two-dimensional empirical mode decomposition (BEMD) method and an edge preserving decomposition (edge preserving decomposition) method. The BEMD method obtains an upper envelope surface and a lower envelope surface by interpolating a local maximum value point and a local minimum value point of a current image, the average value of the upper envelope surface and the lower envelope surface is used as a low-frequency image decomposition component, the difference between an original image and the low-frequency image component is the decomposition component of a high-frequency image, and the decomposition of the multi-scale and multi-resolution image can be obtained by successive recursion iteration. The BEMD method has the advantages that the effective decomposition of the nonlinear time-varying image can be realized, and the defects that the method is invalid when corresponding effective extreme points are lacked in the image, the effective decomposition cannot be carried out on components within the frequency doubling, and the mixing phenomenon can be generated. The edge preserving decomposition method mainly considers the edge characteristics of the image and obtains a high-frequency detail image and a low-frequency contour image through a smooth non-edge area, and has the advantages of preserving the edge characteristics of the image as much as possible and having the defect that the image with unobvious edges or insufficient edge information cannot be effectively decomposed.
The frequency domain decomposition method mainly uses the traditional Fourier transform (including sine-cosine transform and the like), divides the regions occupied by different frequencies of the image in the frequency domain, and performs Fourier inverse transform on the reserved frequency part to obtain the image components of corresponding frequencies, so that the decomposition of the images with different frequency components can be realized by controlling the reservation or suppression method of different frequency regions.
The time-frequency domain decomposition method mainly depends on wavelet decomposition (including traditional wavelet decomposition and recently applied third generation wavelets: novel wavelet transformation methods such as curvelet, band-limited wavelet, ridge wave and linear frequency modulation wavelets) to obtain decomposition coefficients of image components with different scales, and different decomposition coefficients are separated, so that multi-resolution decomposition of the time-frequency domain image components can be realized.
In addition to the three types of algorithms described above, there is an algorithm based on the Hilbert transform and the bedrisian theorem, that is, decomposition of image components is performed using the directional Hilbert transform and their multiple nesting in the auxiliary image component and the two-dimensional Hilbert transform. The method has the advantage of effectively solving the decomposition of some anisotropic images, but cannot be used for decomposing various isotropic images in most cases. As we know, the image not only contains direction information and frequency information, but also contains information of internal dimension, relative magnitude of frequency between components, frequency ratio of different components, amplitude ratio, frequency direction and the like.
However, none of the presently disclosed reports and corresponding patents effectively decompose isotropic image components whose time-varying frequencies are close together (mainly the local time-varying frequencies differ by less than a factor of 2). The invention can solve the problem by utilizing the generalized Bedrosian rule based on the Riesz transformation structure.
Disclosure of Invention
In order to solve the defects of the prior art and realize the purpose of effectively decomposing isotropic image components, the invention adopts the following technical scheme:
the isotropic image decomposition method under the generalized Bedrosian criterion comprises the following steps:
s1, derivation of a transformation operator under the generalized Bedrosian criterion;
for any given real number continuous micro image signal form
Figure BDA00030118670400000216
When the frequency satisfies the relation
Figure BDA0003011867040000022
And
Figure BDA00030118670400000217
q { f (x, y) } is a transform operator under the generalized Bedrosian criterion performed on the function f (x, y), and can be obtained:
Figure BDA0003011867040000023
x represents an abscissa value, y represents an ordinate value,
Figure BDA0003011867040000024
Which represents two functions of the phase position,
Figure BDA0003011867040000025
to represent
Figure BDA0003011867040000026
The transverse angular frequency of (a) of (b),
Figure BDA0003011867040000027
to represent
Figure BDA0003011867040000028
The transverse angular frequency of (a) of (b),
Figure BDA0003011867040000029
to represent
Figure BDA00030118670400000210
The longitudinal angular frequency of (a) of (b),
Figure BDA00030118670400000211
to represent
Figure BDA00030118670400000212
The longitudinal angular frequency of (1) can break through the frequency doubling limitation for any frequency satisfying the relational expression, realize the decomposition of isotropic images of any close frequency components and realize the decomposition of anisotropic images, of course, theoretically, for more than two components, the analogy can be made, as long as the relations are satisfied, the decomposition can be carried out regardless of multiple frequency;
s2, decomposing the image, including the following steps:
s21, calculating the product of different component combinations by applying a generalized Bedrosian criterion;
for a given two-component
Figure BDA00030118670400000213
Giving a third component signal by a least squares optimization algorithm
Figure BDA00030118670400000214
And its sinusoidal form
Figure BDA00030118670400000215
Computing Q { f (x, y) g by using transformation operator under generalized Bedrosian criterion1(x,y)}；
Computing Q { f (x, y) g by using transformation operator under generalized Bedrosian criterion2(x,y)}；
S22, obtaining a first component by operation according to the result of the step S21:
f1(x,y)＝g2(x,y)·Q{f(x,y)g1(x,y)}-g1(x,y)·Q{f(x,y)g2(x,y)}
s23, obtaining a second component according to the total component and the first component:
f2(x,y)＝f(x,y)-f1(x,y)。
further, in step S2, when there are a plurality of components, decomposition is performed a plurality of times based on the two-component decomposition method.
Further, the step S21 is
Figure BDA0003011867040000031
And
Figure BDA0003011867040000032
is achieved by a least squares optimization method.
Further, the least squares method analyzes the main extrema of a given signal to be processed by constructing a single, and then
Figure BDA0003011867040000033
Simulation function of phase, determining phase by least square method
Figure BDA0003011867040000034
Basic determination
Figure BDA0003011867040000035
And
Figure BDA0003011867040000036
further, the brief analysis is to obtain the approximate phase of the signal to be processed through extreme point analysis.
Further, the phase acquisition comprises the following steps:
s211, determining a central point of an isotropic image f (x, y) structure, wherein the image center is the central point of the isotropic image structure, and if not, the image center can be realized through simple image translation;
s212, respectively taking four lines in different directions in the image f (x, y), wherein the directions are respectively 0 degrees, 45 degrees, 90 degrees and 135 degrees, and each line passes through a central point;
s213, estimating the phase by the least square optimization method
Figure BDA0003011867040000037
The phase is obtained as follows:
f (x, y) for the image f (x, y) to be decomposed1(x,y)+f2(x, y), the four selection lines are:
direction 0 °: s (t) ═ f (x, N/2) ═ f1(x,N/2)+f2(x,N/2)；
The direction is 90 degrees: s (t) ═ f (N/2, y) ═ f1(N/2,y)+f2(N/2,y)；
The direction is 45 degrees: s (t) ═ f (x, N-x) ═ f1(x,N-x)+f2(x,N-x)；
Direction 135 °: s (t) ═ f (x, x) ═ f1(x,x)+f2(x,x)；
N is the maximum value of the vertical and horizontal coordinate range of the image, for each s (t) in four directions, the maximum value is a one-dimensional signal, and for a multi-component signal s (t), the maximum value is set
Figure BDA0003011867040000038
a represents the coefficient of the component, first, all extreme points of s (t) are searched, the extreme points are set as tex＝{tex,1,tex,2,…,tex,mInstruction of
Figure BDA0003011867040000039
And
Figure BDA00030118670400000310
b represents the coefficient of the phase for tex＝{tex,1,tex,2,…,tex,mIs given p (t)ex,n) 1 and p (t)ex,n+1) Is-1, wherein s (t)ex,n) Is a maximum value, and s (t)ex,n+1) For minimum values, the equation phi (t) is usedex,n) By minimizing (n +1) pi
Figure BDA0003011867040000048
Obtaining the optimized coefficient b ═ ATA)-1ATΦ, wherein
Figure BDA0003011867040000041
Figure BDA0003011867040000042
And is
Figure BDA0003011867040000043
An approximate phase phi (x, y), i.e.
Figure BDA0003011867040000044
Further, the least square optimization method obtains the phase
Figure BDA0003011867040000045
Substitution into
Figure BDA0003011867040000046
And
Figure BDA0003011867040000047
determining the third component, and determining more reasonable g by testing1(x, y) and g2(x,y)。。
The invention has the advantages and beneficial effects that:
the isotropic image decomposition method under the generalized Bedrosian criterion provides a simple and effective isotropic image decomposition algorithm, is specifically implemented according to the algorithm for image decomposition, and can realize the decomposition of isotropic image components with approximate arbitrary frequencies but different frequencies.
Drawings
FIG. 1a is a schematic diagram of a first component.
FIG. 1b is a second component schematic.
Fig. 1c is a schematic diagram of an isotropic image composition formed from the two components of fig. 1a, b.
Fig. 2a is a schematic diagram (first component) of the decomposition effect of the method proposed by the present invention.
Fig. 2b is a schematic diagram (second component) of the decomposition effect of the method proposed by the present invention.
Fig. 3a is a schematic diagram of the decomposition effect (first component) of the prior art method.
Fig. 3b is a diagram of the decomposition effect of the prior art method (second component).
Fig. 4 is a schematic diagram of four line (white line) selection for a two-component composite image.
Fig. 5a is a texture image Brodatz D102.
FIG. 5b is a-pi/6 phase shifted image of the texture image Brodatz D102 achieved by this patent.
Detailed Description
The following detailed description of embodiments of the invention refers to the accompanying drawings. It should be understood that the detailed description and specific examples, while indicating the present invention, are given by way of illustration and explanation only, not limitation.
By means of a generalized Bedrosian criterion which is newly deduced and proved, isotropic images with approximate arbitrary frequencies are effectively decomposed, and a novel isotropic image decomposition method under the generalized Bedrosian criterion is provided, and the method comprises the following steps:
in the first step, the derivation of the generalized Bedrosian criterion proves.
For any given real number continuous micro image signal form
Figure BDA0003011867040000051
x represents an abscissa value, y represents an ordinate value,
Figure BDA0003011867040000052
Representing two phase functions if the frequencies satisfy the relation
Figure BDA0003011867040000053
And
Figure BDA0003011867040000054
is provided with
Figure BDA00030118670400000520
For the transformation operator under the generalized Bedrosian criterion on the function f (x, y), we then have:
Figure BDA0003011867040000055
Figure BDA0003011867040000056
to represent
Figure BDA0003011867040000057
The transverse angular frequency of (a) of (b),
Figure BDA0003011867040000058
to represent
Figure BDA0003011867040000059
The transverse angular frequency of (a) of (b),
Figure BDA00030118670400000510
to represent
Figure BDA00030118670400000511
The longitudinal angular frequency of (a) of (b),
Figure BDA00030118670400000512
to represent
Figure BDA00030118670400000513
Longitudinal angle ofThe frequency can break through the double frequency limitation for any frequency satisfying the relation, realize the decomposition of isotropic images of any nearby frequency components, and realize the decomposition of anisotropic images, of course, in theory, for more than two components, the analogy can be made, as long as the relations are satisfied, the decomposition can be performed regardless of several multiples.
And (3) proving that: for real continuous micro-image signals
Figure BDA00030118670400000514
If the frequency satisfies the relation
Figure BDA00030118670400000515
And
Figure BDA00030118670400000516
then the definition according to the Riesz transform is available
Figure BDA00030118670400000517
Figure BDA00030118670400000518
Therefore, we have the following relationship:
Figure BDA00030118670400000519
after the syndrome is confirmed.
And secondly, implementing image decomposition, comprising the following steps of:
(1) calculating the product of different component combinations by using a generalized Bedrosian criterion;
for a given two-component (two components are taken as an example in the embodiment, and other more components are completely consistent in reason and can be popularized)
Figure BDA0003011867040000061
We pass the least squares bestThe quantization algorithm gives a third component signal
Figure BDA0003011867040000062
And its sinusoidal form
Figure BDA0003011867040000063
Figure BDA0003011867040000064
And
Figure BDA0003011867040000065
the given of (b) can be achieved by the following method.
F (x, y) for a given band-decomposed image1(x,y)+f2(x, y) (more components are completely consistent),
Figure BDA0003011867040000066
phase position
Figure BDA0003011867040000067
The estimation process of (2) is as follows:
(1) determining the central point of the structure of the isotropic image f (x, y) (in general, it is not assumed that the image center is the central point of the structure of the isotropic image, and if not, the center point can be realized by simple image translation);
(2) taking four lines in the image f (x, y) respectively, wherein the directions of the four lines are 0 degrees, 45 degrees, 90 degrees and 135 degrees respectively, and each line passes through the central point;
(3) phase estimation using the least squares method in appendix 1
Figure BDA0003011867040000068
Thus we can get the image
Figure BDA0003011867040000069
And
Figure BDA00030118670400000610
computing Q { f (x, y) g by using transformation operator under generalized Bedrosian criterion1(x,y)}；
Computing Q { f (x, y) g by using transformation operator under generalized Bedrosian criterion2(x,y)}；
(2) Obtaining a first component through operation according to the result of the step (1):
f1(x,y)＝g2(x,y)·Q{f(x,y)g1(x,y)}-g1(x,y)·Q{f(x,y)g2(x,y)}
(3) obtaining a second component from the total component and the first component:
f2(x,y)＝f(x,y)-f1(x,y)
in this way isotropic images of different components can be obtained.
An example of the algorithm for two-component decomposition of an isotropic image is as follows:
as shown in fig. 1a, b, the first component f1(x,y)＝cos(0.0005π((x-200)2+(y-200)2) A second component f)2(x,y)＝cos(0.0007π((x-200)2+(y-200)2) Fig. 1c is a synthesized component (400 × 400 pixels), fig. 2a and b are schematic diagrams of decomposition effects of the present embodiment on an example image, respectively, where fig. 2a is a first component, fig. 2b is a second component, and fig. 3a and b are schematic diagrams of decomposition effects of a method in the prior art on an example image, and compared with the present embodiment, it can be found that the effect of the present embodiment is significantly better than the effect of the prior art, and the experimental effectiveness of formula values is reflected, so that pi/2 phase shift of any isotropic image is realized. FIG. 5a shows the natural image texture Brodatz D102, and FIG. 5b shows a-pi/6 (or any other angle) phase shift component, which other methods currently cannot achieve any phase shift application based on pi/2. The method for realizing the arbitrary phase shift comprises the following steps: f. ofρ(x,y)＝IMAG{fM(x,y)·eiρ(x,y)Therein of
Figure BDA0003011867040000071
Here "IMAG { }" is the imaginary operator. ρ (x, y) is a specified arbitrary phase, such as- π/6 as described above.
Appendix 1: obtaining a third component by a least squares optimization algorithm
F (x, y) for the image f (x, y) to be decomposed1(x,y)+f2(x, y) (here we take the two-component image as an example, and assume that the maximum value of the vertical and horizontal coordinate ranges of the image is N), the four selection lines are shown in fig. 4, and they are respectively:
direction 0 °: s (t) ═ f (x, N/2) ═ f1(x,N/2)+f2(x,N/2)；
The direction is 90 degrees: s (t) ═ f (N/2, y) ═ f1(N/2,y)+f2(N/2,y)；
The direction is 45 degrees: s (t) ═ f (x, N-x) ═ f1(x,N-x)+f2(x,N-x)；
Direction 135 °: s (t) ═ f (x, x) ═ f1(x,x)+f2(x,x)。
For each s (t) in the four directions, which are now one-dimensional signals, we analyze the calculations in the following manner in turn.
For a multi-component signal s (t) (
Figure BDA0003011867040000072
). First, all extreme points (including maximum and minimum) of s (t) are searched, and the extreme points are set as tex＝{tex,1,tex,2,…,tex,m}。
Order to
Figure BDA0003011867040000073
And
Figure BDA0003011867040000074
for tex＝{tex,1,tex,2,…,tex,mIs given p (t)ex,n) 1 and p (t)ex,n+1) Is-1, wherein s (t)ex,n) Is a maximum value, and s (t)ex,n+1) Is a minimum value.
Next we have the equation φ (t)ex,n)＝(n+1)π。
At the moment through minimization
Figure BDA0003011867040000075
Obtaining an optimization coefficient
b＝(ATA)-1AT·Φ，
Wherein
Figure BDA0003011867040000076
And is
Figure BDA0003011867040000077
So that we can get the approximate phase phi (x, y), i.e.
Figure BDA0003011867040000081
At this time, substitution
Figure BDA0003011867040000082
A third component is obtained.
The above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.

Claims (8)

1. The isotropic image decomposition method under the generalized Bedrosian criterion is characterized by comprising the following steps of:
s1, derivation of a transformation operator under the generalized Bedrosian criterion;
for any given real number continuous micro image signal form
Figure FDA0003011867030000011
When the frequency satisfies the relation
Figure FDA0003011867030000012
And
Figure FDA0003011867030000013
q { f (x, y) } is a transform operator under the generalized Bedrosian criterion performed on the function f (x, y), and can be obtained:
Figure FDA0003011867030000014
x represents an abscissa value, y represents an ordinate value,
Figure FDA0003011867030000015
Which represents two functions of the phase position,
Figure FDA0003011867030000016
to represent
Figure FDA0003011867030000017
The transverse angular frequency of (a) of (b),
Figure FDA0003011867030000018
to represent
Figure FDA0003011867030000019
The transverse angular frequency of (a) of (b),
Figure FDA00030118670300000110
to represent
Figure FDA00030118670300000111
The longitudinal angular frequency of (a) of (b),
Figure FDA00030118670300000112
to represent
Figure FDA00030118670300000113
Longitudinal angular frequency of (d);
s2, decomposing the image, including the following steps:
s21, calculating the product of different component combinations by applying a generalized Bedrosian criterion;
for a given two-component
Figure FDA00030118670300000114
By a given third component signal
Figure FDA00030118670300000115
And its sinusoidal form
Figure FDA00030118670300000116
(x,y∈R)；
Computing Q { f (x, y) g by using transformation operator under generalized Bedrosian criterion1(x,y)}；
Computing Q { f (x, y) g by using transformation operator under generalized Bedrosian criterion2(x,y)}；
S22, obtaining a first component by operation according to the result of the step S21:
f1(x,y)＝g2(x,y)·Q{f(x,y)g1(x,y)}-g1(x,y)·Q{f(x,y)g2(x,y)}
s23, obtaining a second component according to the total component and the first component:
f2(x,y)＝f(x,y)-f1(x,y)。
2. the method for isotropic image decomposition under the generalized Bedrosian rule as claimed in claim 1, wherein said step S2 is performed for a plurality of decompositions based on a two-component decomposition method when there are a plurality of components.
3. The method for isotropic image decomposition under the generalized Bedrosian criterion as recited in claim 1, wherein said step S21 is performed
Figure FDA0003011867030000021
And
Figure FDA0003011867030000022
is achieved by a least squares optimization method.
4. The method as claimed in claim 3, wherein the least squares optimization method is to perform a brief analysis on the main frequency components of the given signal to be processed, and the brief analysis is to obtain the phase of the signal to be processed through extreme points.
5. The method of isotropic image decomposition under the generalized Bedrosian criterion as claimed in claim 4, wherein said phase acquisition comprises the steps of:
s211, determining the central point of the structure of the isotropic image f (x, y);
s212, respectively taking a group of lines in different directions in the image f (x, y), wherein each line passes through a central point;
s213, estimating the phase by the least square optimization method
Figure FDA0003011867030000023
6. The method of isotropic image decomposition under the generalized Bedrosian criterion as claimed in claim 5, wherein said lines have four directions of 0 °, 45 °, 90 ° and 135 °, respectively, and the phases are obtained as follows:
f (x, y) for the image f (x, y) to be decomposed1(x,y)+f2(x, y), the four selection lines are:
direction 0 °: s (t) ═ f (x, N/2) ═ f1(x,N/2)+f2(x,N/2)；
The direction is 90 degrees: s (t) ═ f (N/2, y) ═ f1(N/2,y)+f2(N/2,y)；
The direction is 45 degrees: s (t) ═ f (x, N-x) ═ f1(x,N-x)+f2(x,N-x)；
Direction 135 °: s (t) ═ f (x, x) ═ f1(x,x)+f2(x,x)；
N is the maximum value of the vertical and horizontal coordinate range of the image, and for each s (t) in four directions,in this case, the signals are all one-dimensional signals, and for the multi-component signal s (t), let
Figure FDA0003011867030000024
a represents the coefficient of the component, first, all extreme points of s (t) are searched, the extreme points are set as tex＝{tex,1,tex,2,…,tex,mInstruction of
Figure FDA0003011867030000025
And
Figure FDA0003011867030000026
b represents the coefficient of the phase for tex＝{tex,1,tex,2,…,tex,mIs given p (t)ex,n) 1 and p (t)ex,n+1) Is-1, wherein s (t)ex,n) Is a maximum value, and s (t)ex,n+1) For minimum values, the equation phi (t) is usedex,n) By minimizing (n +1) pi
Figure FDA0003011867030000027
Obtaining the optimized coefficient b ═ ATA)-1ATΦ, wherein
Figure FDA0003011867030000031
And is
Figure FDA0003011867030000032
An approximate phase phi (x, y), i.e.
Figure FDA0003011867030000033
7. The method of isotropic image decomposition under the generalized Bedrosian criterion as claimed in claim 5, wherein the center of the image is taken as the center point of the isotropic image structure.
8. Under the generalized Bedrosian criterion as claimed in claim 3Isotropic image decomposition method, characterized in that the least square optimization method obtains phase
Figure FDA0003011867030000034
Substitution into
Figure FDA0003011867030000035
And
Figure FDA0003011867030000036
a third component is determined.
CN202110377657.XA 2021-04-08 2021-04-08 Isotropic image decomposition method under generalized Bedrosian criterion Active CN113269715B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202110377657.XA CN113269715B (en) 2021-04-08 2021-04-08 Isotropic image decomposition method under generalized Bedrosian criterion

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202110377657.XA CN113269715B (en) 2021-04-08 2021-04-08 Isotropic image decomposition method under generalized Bedrosian criterion

Publications (2)

Publication Number Publication Date
CN113269715A true CN113269715A (en) 2021-08-17
CN113269715B CN113269715B (en) 2022-09-09

Family

ID=77228565

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202110377657.XA Active CN113269715B (en) 2021-04-08 2021-04-08 Isotropic image decomposition method under generalized Bedrosian criterion

Country Status (1)

Country Link
CN (1) CN113269715B (en)

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20100092028A1 (en) * 2008-10-10 2010-04-15 National Central University Data Decomposition Method and Computer System Therefrom
CN106373149A (en) * 2015-07-23 2017-02-01 中国人民解放军海军大连舰艇学院 Image decomposition method based on auxiliary image component and Hilbert transformation
CN110163830A (en) * 2019-04-19 2019-08-23 三峡大学 Image interfusion method based on Riesz-Lap transformation and PCNN

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20100092028A1 (en) * 2008-10-10 2010-04-15 National Central University Data Decomposition Method and Computer System Therefrom
CN106373149A (en) * 2015-07-23 2017-02-01 中国人民解放军海军大连舰艇学院 Image decomposition method based on auxiliary image component and Hilbert transformation
CN110163830A (en) * 2019-04-19 2019-08-23 三峡大学 Image interfusion method based on Riesz-Lap transformation and PCNN

Non-Patent Citations (5)

* Cited by examiner, † Cited by third party
Title
GUANLEI XU ET AL.: "The Bi-Dimensional Bedrosian’s Principle for Image Decomposition", 《APPLIED MECHANICS AND MATERIALS》 *
J. L. STARCK ET AL.: "Image decomposition via the combination of sparse representations and a variational approach", 《IEEE TRANSACTIONS ON IMAGE PROCESSING》 *
崇元 等: "基于局部梯度极值点的经验模式分解图像增强", 《兵工自动化》 *
徐冠雷 等: "二维Bedrosian定理理论及其应用研究", 《应用数学进展》 *
李洋 等: "多角度极化SAR图像散射特征分解及SVM分类", 《电波科学学报》 *

Also Published As

Publication number Publication date
CN113269715B (en) 2022-09-09

Similar Documents

Publication Publication Date Title
Martens Local orientation analysis in images by means of the Hermite transform
CN102646269B (en) A kind of image processing method of laplacian pyramid and device thereof
Shi et al. Translation invariant directional framelet transform combined with Gabor filters for image denoising
CN104715461A (en) Image noise reduction method
Xu et al. A denoising algorithm via wiener filtering in the shearlet domain
CN110322404B (en) Image enhancement method and system
Hamdi Modified Algorithm marker-controlled watershed transform for Image segmentation Based on Curvelet Threshold
CN114779343A (en) Seismic data denoising method based on curvelet transform-joint bilateral filtering
CN113269715B (en) Isotropic image decomposition method under generalized Bedrosian criterion
CN104182944A (en) Optical image denoising method based on serial connection of curvelet transform and wavelet transform
CN104978720A (en) Video image raindrop removal method and apparatus
Sadaghiani et al. Image interpolation based on 2D-DWT with novel regularity-preserving algorithm using RLS adaptive filters
CN108171741B (en) Image texture decomposition method based on self-adaptive multi-directional empirical mode decomposition
Muramatsu SURE-LET image denoising with multiple directional LOTs
Muhammad et al. Image noise reduction based on block matching in wavelet frame domain
CN102289793A (en) Cyber foraging-oriented multi-scale image processing method
CN101882301B (en) Shearing wave image denoising method based on cutoff window
Chen et al. Low-contrast microscopic image enhancement based on multi-technology fusion
CN104574308A (en) SAR image denoising method based on sampling matrix direction optimization
CN112465719A (en) Transform domain image denoising method and system
CN106373149B (en) The picture breakdown method converted based on assistant images component and Hilbert
CN103839235B (en) Method for denoising global Bandelet transformation domain based on non-local directional correction
Wang et al. Image zoom method based on bandelet transform modified bilinear interpolation
Arfia et al. Choosing interpolation RBF function in image filtering with the bidimentional empirical modal decomposition
Chen et al. Image reconstruction based on combination of wavelet decomposition, inpainting and texture synthesis

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant