CN105976341B - Image adaptive median filter method - Google Patents
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Abstract
The invention belongs to image processing fields, specially a kind of image adaptive median filter method, image pixel distribution probability is determined according to image pixel gray level distributed intelligence, distribution probability function after selecting segmentation to normalize is as quantum bit probability of state function, improve adaptability of the filtering method to interference such as illumination variations, improve filtering performance, there is good practicability.The present invention is suitable for being filtered image salt-pepper noise.
Description
Technical field
The invention belongs to image processing fields, are related to a kind of image adaptive median filter method, more particularly to a kind of base
In the image adaptive median filter method of double quantum bit states.
Background technology
In recent years, quantum theory is rapidly developed, and numerous necks such as be widely used in computer, communication, signal processing
In domain.Particularly, the research and development of quantum image procossing also rapidly, in image enhancement, image filtering and edge detection etc.
Aspect obtains preferable application effect.For the salt-pepper noise often occurred in image, medium filtering has good filtering
Energy.But, classical median filter method when smaller Filtering Template using, to the removal effect unobvious of high proportion noise, and using
Larger Filtering Template can cause the loss of image detail information again, to make image thicken, existing adaptive weighted filter
Wave method is often limited by noise conditions again.Image median filter method based on quantum theory, can be by image puppet quantum
Change and carry out Hadamard transformation, denoising, compared with conventional method, this method are carried out to image in conjunction with median filter method
More image detail informations can either be retained, and improve the noise reduction capability of filtering method.It is measured based on double quantum bit states
Quantum median filter method the detailed information of image can be protected further, and again have less operand.
But, the selection of quantum bit state probability function does not have adaptivity to handled image, when image irradiation etc. becomes
When change, it can not ensure the stability of filter effect.
Therefore, incorporating quantum signal processing Frame Theory, according to the distribution characteristics of image pixel, design one kind can be effective
It improves and the image filtering method of the adaptability of the interference such as illumination variation is worth with good promotion and application.
Invention content
The technical problem to be solved by the present invention is to for interference such as illumination variations, design a kind of adaptive double quantum ratios
The image filtering method of special state improves the adaptability that filtering method interferes illumination variation.
The technical solution adopted in the present invention is：A kind of image adaptive median filter method, it is characterised in that quantum ratio
Special probability of state function is adaptively chosen according to the pixel grey scale distributed intelligence of filtering image, to improve filtering method to illumination
The adaptability of the interference such as variation.
It is an object of the invention to be directed to quantum median filter method to lack adaptability to interference such as image irradiation variations
The shortcomings that, design a kind of adaptive double quantum median filter methods.Image slices are determined according to image pixel gray level distributed intelligence
Plain distribution probability, the distribution probability function after selecting segmentation to normalize improve filtering side as quantum bit probability of state function
Method improves filtering performance to the adaptability of the interference such as illumination variation, has good practicability.
Specific implementation mode
Invention is further described in detail With reference to embodiment.
In quantum regime, all state vectors all meet space overlapping principle, i.e., any vectorIt is represented by：
Wherein anTo correspond to the probability amplitude of ground state, | n ＞ are substrate.Quantum bit is quantum computer storage quantum information
Base unit, quantum bit state corresponds to a vector in the two dimension spaces Hilbert, is denoted as：
In formula, a0, a1Referred to as probability amplitude meets normalizing condition | a0|2+|a1|2=1, | a0|2With | a1|2Respectively represent pole
Change state | 0 ＞ and | 1 ＞ occur probability.For a composite quantum system, it is assumed that it is made of n quantum bit, is remembered i-th
The state of quantum bitFor：
Wherein ai 0, ai 1For probability amplitude.Then the system can be by the tensor product representation of n quantum bit state：
Wherein, | i ＞ indicate quantum-bit systems | i-th of the ground state of ψ ＞, aiIt indicates the probability amplitude of corresponding ground state, meets
Normalizing condition
Note input picture is I, and noisy image size is H × W, input picture is normalized, and be denoted as S.If zxyIt is
The medium filtering template size of the gray value at point (x, y) in image S, image is m × n, TxyIt represents centered on point (x, y)
The image-region covered by current filter mask, zmedRepresent TxyGrey scale pixel value intermediate value in region.Pixel in image (x,
Y) double quantum bit states are expressed as：
Wherein, any single quantum bit state meets superposition theorem, i.e.,：
According to quantum computer storage characteristics, formula (5) is equivalent to：
Wherein, aij(ij ∈ { 00,01,10,11 }) is ground state | 00 ＞, | 01 ＞, | 10 ＞, | the probability amplitude of 11 ＞ meets
Normalizing condition ∑Ij ∈ { 00,01,10,11 }|aij|2=1.Since each quantum bit state can individually consider, then quantum bit can be set
State occur probability function be：
|a1|2=f (z) (9)
|a0|2=1-f (z) (10)
|a1| and | a0| indicate single quantum | 1 ＞ states and | 0 ＞ probability of state width, | a1|2With | a0|2Both are then indicated respectively
The probability that bit state occurs.Existing method defines single quantum bit state and takes | and the probability of 1 ＞ is：
F (z)=sin2(πz) (11)
Wherein, z is the gray value z after normalizationxyOr intermediate value zmed.Why the functional form of selecting type (11), mainly
The characteristics of for salt-pepper noise and design, i.e., when the gray value of pixel is smaller or larger, normalization after gray value connect
Nearly 0 or 1, the quantum bit state at the point takes | and the probability of 1 ＞ is close to 0, can effectively filter out salt-pepper noise in this way.But it can also see
Go out, the characteristics of which does not account for image itself pixel distribution, lacks the adaptivity to handled image.
For this purpose, the present invention redefines quantum bit state according to the pixel distribution information of handled image | what 1 ＞ occurred
Probability function.Assuming that the grey scale pixel value z of image meets normal distribution, mean value μ, variance σ2, i.e. grey scale pixel value point
Cloth meets normal distribution N (μ, σ2), it is denoted as：
It can then acquire：
In this way, f (z) can be defined as to segmentation normalized function：
F (z) be substantially by acquired results after g (z) segmentation normalization, due to f (0)=f (1)=0, f (z)
Meet the requirement for filtering out salt-pepper noise.Simultaneously as f (z) can also reflect therefore the information of image pixel gray level distribution carries
The high adaptability to interference such as illumination variations.
Definition | a1|2 med、|a0|2 medWith | a1|2 xy、|a0|2 xyIt is that quantum exists respectively in double quantum bit state systems | 1 ＞ states
With | the probability at 0 ＞ states, i.e.,：
In the double quantum bit state systems of image, | 11 ＞ states can indicate double quantum of some point of image while be in | 1 ＞
State, | 10 ＞ states indicate that first single quantum is in | 1 ＞ states, and second single quantum is in | and 0 ＞ states, | 01 ＞ states indicate first
A quantum is in | 0 ＞ states and second quantum is in | 1 ＞ states, | 00 ＞ states indicate that double quantum are all | 0 ＞ states.In the present invention
Double quantum bit states describe the middle value information and half-tone information of image respectively, therefore have：
|a11|2=f (zmed)·f(zxy) (18)
|a10|2=f (zmed)·(1-f(zxy)) (19)
|a01|2=(1-f (zmed))·f(zxy) (20)
|a00|2=(1-f (zmed))·(1-f(zxy)) (21)
Wherein, | a11|2、|a10|2、|a01|2、|a00|2Respectively represent in bipartite quantum system and occur | 11 ＞ states, | 10 ＞ states, |
01 ＞ states and | 00 ＞ probability of states.
When being measured to the particle in quantized system, it is empty that state can be projected onto state corresponding with measured value
Between.By measurement consistency it is found that carrying out result and the first time progress of repeated measurement with the image that quantized system indicates to a width
Result after measurement is identical.Assuming that double quantum bit states of input picture are stored in matrix H, it is double to each in matrix H
Quantum bit state enables it generate random number r, and r ∈ [0,1], uses the measurement result of double quantum bits | hij＞ is expressed as：
Definition output image is W, its label matrix is F, and pixel value ws (x, y) of the W at (x, y) point is by measurement result |
hij＞ decisions, specially：
(1) W=0, F=0 are initialized, size is H × W, and the size of medium filtering template is m × n；
(2) whether there is 0 element in traversal search label matrix F, if so, assuming that its position coordinates in matrix F is
(i, j), i.e. f (i, j)=0 then find the element in H corresponding with its position, and carry out quantum measurement to it, if measured
As a result it is | 11 ＞ then enable w (i, j)=zij, zijFor the gray value at the point (i, j) in image, f (i, j)=1；If measured
As a result it is | 10 ＞ then enable w (i, j)=zmed, f (i, j)=1；If measurement result is | 01 ＞ or | 00 ＞, w (i, j) and f
The value of (i, j) remains unchanged；
(3) whether there is 0 element in judge mark matrix F, if so, increasing medium filtering template size；
(4) step (2), (3) are repeated, until all elements in F are all that 1 or Filtering Template size reach maximum
Value.When Filtering Template size reaches maximum value, if it is 0 still to have element in F, the corresponding w (i, j) in the position of 0 element in F is enabled
=zmed, and f (i, j)=1.
Use the Lena images that size is 256 × 256 as initial pictures, by the Lena images work after addition salt-pepper noise
For input picture, and using classical median filter method, adaptive median filter method, double quantum bit state filtering methods and this
Inventive method is respectively filtered in the case of three kinds of normal illumination, low intensity light photograph and high-intensity illumination plus image of making an uproar respectively
Analysis, and the filtering performance of more various methods.
When containing 50% salt-pepper noise in image, normal illumination, illumination brightness reduce by 20%, illumination brightness and improve 20%
In the case of, the Y-PSNR of the method for the present invention can be respectively increased 2.13%, 2.71%, 3.22%, and image similarity can carry
High 1.52%, 1.82%, 2.08%, normalization mean square error can reduce by 11.85%, 15.70%, 15.65%, it can be seen that,
The method of the present invention is not only able to improve the filtering performance of image, and has stronger adaptability to interference such as illumination variations.
It is an advantage of the current invention that according to input image pixels distributed intelligence, determines quantum bit probability of state function, carry
The high adaptive ability of filtering method.The present invention is suitable for being filtered image salt-pepper noise.
Claims (1)
1. a kind of image adaptive median filter method, it is characterised in that quantum bit probability of state function is according to filtering image
Pixel grey scale distributed intelligence is adaptively chosen, to improve the adaptability that filtering method interferes illumination variation；If image S's
Grey scale pixel value z meets normal distribution, mean value μ, variance σ2, i.e., pixel grey scale Distribution value meet normal distribution N (μ,
σ2), it is denoted as：
It can then acquire：
In this way, f (z) can be defined as to segmentation normalizing
Change function：
F (z) is substantially by acquired results after g (z) segmentation normalization；Definition | a1|2 med、|a0|2 medWith | a1|2 xy、|a0|2 xyIt is
Quantum exists respectively in double quantum bit state systems | and 1>State and | 0>Probability at state, i.e.,：
Wherein, zxyIt is the gray value at the point (x, y) in image S, the medium filtering template size of image is m × n, TxyRepresent with
The image-region covered by current filter mask centered on point (x, y), zmedRepresent TxyGrey scale pixel value intermediate value in region；
In the double quantum bit state systems of image, | 11>State can indicate double quantum of some point of image while be in | 1>State, | 10>State indicates
First single quantum is in | and 1>State, and second single quantum is in | 0>State, | 01>State indicates that first quantum is in | 0>State and
Second quantum is in | and 1>State, | 00>State indicates that double quantum are all | 0>State；Double quantum bit states describe the intermediate value of image respectively
Information and half-tone information, therefore have：
|a11|2=f (zmed)·f(zxy) (7)
|a10|2=f (zmed)·(1-f(zxy)) (8)
|a01|2=(1-f (zmed))·f(zxy) (9)
|a00|2=(1-f (zmed))·(1-f(zxy)) (10)
Wherein, | a11|2、|a10|2、|a01|2、|a00|2Respectively represent in bipartite quantum system and occur | 11>State, | 10>State, | 01>State
With | 00>Probability of state；When being measured to the particle in quantized system, state can be projected onto corresponding with measured value
State space；If double quantum bit states of input picture are stored in matrix H, to each double quantum bit state in matrix H,
Enable it generate random number r, and r ∈ [0,1], the measurement result of double quantum bits used | hij>It is expressed as：
Definition output image is W, its label matrix is F, and pixel value ws (x, y) of the W at (x, y) point is by measurement result | hij>
It determines, specially：
(1) W=0, F=0 are initialized, size is H × W, and the size of medium filtering template is m × n；
(2) traversal search label matrix F in whether have 0 element, if so, assume its position coordinates in matrix F be (i,
J), i.e. f (i, j)=0 then finds the element in H corresponding with its position, and carries out quantum measurement to it, if measuring knot
Fruit is | 11>, then w (i, j)=z is enabledij, zijFor the gray value at the point (i, j) in image, f (i, j)=1；If measurement result
For | 10>, then w (i, j)=z is enabledmed, f (i, j)=1；If measurement result is | 01>Or | 00>, then w (i, j) and f (i, j)
Value remains unchanged；
(3) whether there is 0 element in judge mark matrix F, if so, increasing medium filtering template size；
(4) step (2), (3) are repeated, until all elements in F are all that 1 or Filtering Template size reach maximum value；When
When Filtering Template size reaches maximum value, if still have in F element be 0, enable the corresponding w (i, j) in the position of 0 element in F=
zmed, and f (i, j)=1.
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| CN106358029B (en) * | 2016-10-18 | 2019-05-03 | 北京字节跳动科技有限公司 | A kind of method of video image processing and device |
| CN107993211A (en) * | 2017-12-04 | 2018-05-04 | 中国科学院遥感与数字地球研究所 | A kind of image de-noising method |
| CN108507606A (en) * | 2017-12-06 | 2018-09-07 | 上海交通大学 | Adaptive weak measurement method and system for the statistical estimation of parametric mixer |
| CN114782281B (en) * | 2022-05-05 | 2022-12-09 | 连云港问鼎环保科技有限公司 | Image self-adaptive quantum median filtering method |
| CN116758854B (en) * | 2023-08-18 | 2023-10-31 | 山东晶大光电科技有限公司 | LED display screen control system and method based on Internet of things |
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