CN108876691A - Adaptive reversible water mark method and system - Google Patents
Adaptive reversible water mark method and system Download PDFInfo
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- CN108876691A CN108876691A CN201710326906.6A CN201710326906A CN108876691A CN 108876691 A CN108876691 A CN 108876691A CN 201710326906 A CN201710326906 A CN 201710326906A CN 108876691 A CN108876691 A CN 108876691A
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T1/00—General purpose image data processing
- G06T1/0021—Image watermarking
- G06T1/0028—Adaptive watermarking, e.g. Human Visual System [HVS]-based watermarking
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2201/00—General purpose image data processing
- G06T2201/005—Image watermarking
- G06T2201/0203—Image watermarking whereby the image with embedded watermark is reverted to the original condition before embedding, e.g. lossless, distortion-free or invertible watermarking
Abstract
The present invention provides a kind of adaptive reversible water mark method and system, method include：Carrier image is divided into multiple adjacent pixels pair not being overlapped mutually；Using gradient prediction method calculate corresponding difference to and generate two-dimentional difference value histogram；Using dynamic programming algorithm, optimal path is selected in two-dimentional difference value histogram, establishes the difference on optimal path to the first corresponding relationship of corresponding pixel pair and bit information entrained by watermark to be embedded；If pixel to corresponding difference to not on optimal path, according to preset first rules modification pixel pair；If pixel to corresponding difference on optimal path, according to the first corresponding relationship, if pixel is 1 to the value of corresponding bit information, according to preset first rules modification pixel pair；If pixel is 0 to the value of corresponding bit information, pixel pair is not modified.The Data Embedding Capacity of this programme is high, insertion distortion is low, hiding data it is highly-safe.
Description
Technical field
The present invention relates to digital watermark technology field more particularly to a kind of adaptive reversible water mark method and systems.
Background technique
As modern society enters Internet information age, the multimedia digitals carrier such as image, audio, video becomes carrying
The main media of information.The high speed development of computer science and technology and internet universal so that more and more information by
These multimedia bearers are generated, propagate and are shared by extensive.Correspondingly, the opening of Internet era makes number with sharing
There is a series of safety issue in communication process in information, such as illegally copies, illegally distorts.In addition, for propagating
Person is reluctant that hiding for disclosed confidential information also becomes an important need with protection.For problems, Information Hiding Techniques
It comes into being.
The relevant research of Information Hiding Techniques receives the extensive concern of scholar in recent decades, but for its major part
Technology such as steganography and robust watermarking technology all can damage initial carrier while being embedded in secret information, and insertion carrier is caused to mention
It cannot be losslessly recovered after taking secret information.However, obtaining patients' privacy letter in certain sensitive scene such as Medical Image Processings
While breath, it is similarly important nondestructively to restore original medical image.Therefore reversible digital watermarking technology becomes hot topic instantly
Research topic.Since there are a large amount of redundancies for natural image, even if certain pixels are modified because of embedding information, they are still
It can be restored using related pixel information, here it is the technologies to have the reason of reciprocal characteristics.Measure reversible water mark algorithm
There are two aspects for the standard of superiority and inferiority：Insertion distortion and embedding capacity.By comparing insertion carrier and initial carrier, insertion distortion is got over
The concealment of low embedded mobile GIS is better, that is, insertion carrier is more similar to initial carrier.Embedding capacity expression is embedded in carrier
Information bit.
The existing reversible water mark method based on histogram, the main pixel construction statistics histogram by carrier image
Figure, according to statistic histogram by the pixel in image be divided into insertion watermark data embeddable point set and translation can
Mobile point set executes watermark insertion processing to all pixels point in embeddable point set, to the institute in removable point set
There is pixel to execute translation processing.Since the distribution of the pixel histogram of carrier image is more uniform, so that the data of this method
Embedding capacity is limited and insertion distortion is higher, thereby reduces the safety of hiding data.
Summary of the invention
The present invention provides a kind of adaptive reversible water mark method and system, to solve the water mark method data of the prior art
Embedding capacity is low, insertion distortion is high, the low problem of the safety of hiding data.
The first aspect of the invention is to provide adaptive reversible water mark method, including：
Carrier image is divided into multiple pixels not being overlapped mutually to (x, y), two pixel phases of each pixel centering
It is adjacent, wherein x is the pixel value of previous pixel, and y is the pixel value of latter pixel；
(x, y) is calculated corresponding pre- according to the neighborhood of the pixel pair using gradient prediction method for each pixel
Measured value z, and corresponding difference is calculated to (d using the first formulax,dy), first formula is：
d1=x-z, d2=y-z；
According to multiple pixels to corresponding difference pair, two-dimentional difference value histogram is generated；
Beginning and end is selected in the two-dimentional difference value histogram, using dynamic programming algorithm, in the starting point and institute
State terminal composition grid in select optimal path, the optimal path for the starting point in the grid to the terminal institute
There is the maximum path of the sum of the frequency of the first difference pair passed through in path, and the first difference that the optimal path passes through is to institute
The embeddable capacity of the reality of corresponding pixel pair is not less than the capacity of bit information entrained by watermark to be embedded, described optimal
The adjacent difference that path is passed through is to adjacent in the horizontal direction or on vertical direction；
By first difference to be defined as expansion difference pair, by remaining difference to be defined as translation difference pair；
The expansion difference is established to corresponding pixel pair and bit information entrained by the watermark to be embedded
First corresponding relationship；
For each pixel pair, if the pixel to corresponding difference to translate difference pair, according to preset the
One rule is to the pixel to modifying；If the pixel to corresponding difference to for expand difference pair, according to
First corresponding relationship, if the pixel is 1 to the value of corresponding bit information, according to preset first rule to described
Pixel is to modifying；If the pixel is 0 to the value of corresponding bit information, not to the pixel to repairing
Change.
The second aspect of the invention is to provide a kind of adaptive reversible water mark system, including：
Pixel is to module, for carrier image to be divided into multiple pixels not being overlapped mutually to (x, y), each pixel centering
Two pixels it is adjacent, wherein x be previous pixel pixel value, y be latter pixel pixel value；
Difference is to module, for being directed to each pixel to (x, y), according to the neighborhood of the pixel pair, using gradient prediction
Method calculates corresponding predicted value z, and calculates corresponding difference to (d using the first formulax,dy), first formula is：
d1=x-z, d2=y-z；
Histogram module, for, to corresponding difference pair, generating two-dimentional difference value histogram according to multiple pixels；
Optimal path module is calculated for selecting beginning and end in the two-dimentional difference value histogram using Dynamic Programming
Method, selects optimal path in the grid that the starting point and the terminal are constituted, and the optimal path is described in the grid
The maximum path of the sum of the frequency of the first difference pair that starting point is passed through into all paths of the terminal, and the optimal path
The first difference passed through is to the embeddable capacity of the reality of corresponding pixel pair not less than bit entrained by watermark to be embedded
The capacity of information, the adjacent difference that the optimal path passes through is to adjacent in the horizontal direction or on vertical direction；
Definition module, for by first difference to expansion difference pair is defined as, by remaining difference to being defined as translating
Difference pair；
Respective modules, for establish the expansion difference to corresponding pixel pair with entrained by the watermark to be embedded
Bit information the first corresponding relationship；
Modified module, for be directed to each pixel pair, if the pixel to corresponding difference to for translation difference pair,
According to preset first rule to the pixel to modifying；If the pixel to corresponding difference to for expand difference
It is right, then according to first corresponding relationship, if the pixel is 1 to the value of corresponding bit information, according to preset
First rule is to the pixel to modifying；If the pixel is 0 to the value of corresponding bit information, not to described
Pixel is to modifying.
Adaptive reversible water mark method provided by the invention and system multiple are not overlapped mutually by the way that carrier image to be divided into
Adjacent pixel pair；Using gradient prediction method calculate corresponding difference to and generate two-dimentional difference value histogram；Using dynamic
Planning algorithm selects optimal path in two-dimentional difference value histogram, establishes the difference on optimal path to corresponding pixel pair
With the first corresponding relationship of bit information entrained by watermark to be embedded；If pixel is to corresponding difference to not on optimal road
On diameter, then according to preset first rules modification pixel pair；If pixel to corresponding difference on optimal path, basis
First corresponding relationship, if pixel is 1 to the value of corresponding bit information, according to preset first rules modification pixel
It is right；If pixel is 0 to the value of corresponding bit information, pixel pair is not modified.The Data Embedding Capacity of this programme is high, embedding
Enter to be distorted it is low, hiding data it is highly-safe.
Detailed description of the invention
Fig. 1 is a kind of flow diagram for adaptive reversible water mark method that the embodiment of the present invention one provides；
Pixel shows the neighborhood of (x, y) in a kind of adaptive reversible water mark method that Fig. 2 provides for the embodiment of the present invention one
It is intended to；
Fig. 3 is a kind of flow diagram of adaptive reversible water mark method provided by Embodiment 2 of the present invention；
Fig. 4 is a kind of flow diagram for adaptive reversible water mark method that the embodiment of the present invention three provides；
Fig. 5 is a kind of structural schematic diagram for adaptive reversible water mark system that the embodiment of the present invention four provides；
Fig. 6 is a kind of structural schematic diagram for adaptive reversible water mark system that the embodiment of the present invention five provides；
Fig. 7 is a kind of structural schematic diagram for adaptive reversible water mark system that the embodiment of the present invention six provides.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation description, it is clear that described embodiment is only a part of the embodiments of the present invention, rather than whole embodiments.It is based on
Embodiment in the present invention, the every other reality that those of ordinary skill in the art obtain without creative efforts
Example is applied, shall fall within the protection scope of the present invention.
Fig. 1 is a kind of flow diagram for adaptive reversible water mark method that the embodiment of the present invention one provides, such as Fig. 1 institute
Show, described method includes following steps：
11, carrier image is divided into multiple pixels not being overlapped mutually to (x, y), two pixels of each pixel centering
It is adjacent, wherein x is the pixel value of previous pixel, and y is the pixel value of latter pixel.
Specifically, carrier image can be divided into multiple pixels pair not being overlapped mutually using various ways, for example,
Carrier image is divided into and multiple is not overlapped mutually as one group of pixel pair by two pixels adjacent using carrier image horizontal direction
Pixel pair.
12, (x, y) is calculated corresponding according to the neighborhood of the pixel pair using gradient prediction method for each pixel
Predicted value z, and calculate corresponding difference to (d using the first formulax,dy), first formula is：
d1=x-z, d2=y-z.
Specifically, pixel is to the neighborhood of (x, y) as shown in Fig. 2, for each pixel to (x, y), according to the pixel pair
Neighborhood, the calculation method for calculating corresponding predicted value z using gradient prediction method is as follows：
Wherein, v1~v8It is pixel to the pixel value of corresponding pixel in (x, y) neighborhood, dv、dhRespectively indicate the neighbour
Gradient of the domain on vertically and horizontally, wherein：
dv=| v1-v5|+|v3-v7|+|v4-v8|；
dh=| v1-v2|+|v3-v4|+|v4-v5@；
13, two-dimentional difference value histogram is generated to corresponding difference pair according to multiple pixels.
Further, selected pixels to corresponding difference to generate two-dimentional difference value histogram method can there are many, lift
For example, in order to improve the safety of secret information insertion, for the pixel of carrier image texture complex region, without number
According to insertion, i.e., the pixel of carrier image texture complex region is not chosen to corresponding difference to generating two-dimentional difference value histogram,
Namely the pixel in image smoothing region is chosen to corresponding difference to generating two-dimentional difference value histogram.Embodiment party shown in Fig. 1
On the basis of formula, 13 be can specifically include：The level of noise for calculating each pixel pair is less than noise threshold according to the level of noise
Multiple pixels of value generate two-dimentional difference value histogram to corresponding difference pair.
Further, the pixel for being 255 or 0 for pixel value in carrier image, can not carry out+1 or -1 modification, this
Kind situation is pixel spilling.Choose difference to generate two-dimensional histogram when, can not choose there are pixel overflow pixel pair
Corresponding difference pair.As an alternative embodiment, 13 specifically can wrap on the basis of any of the above-described embodiment
It includes：Count information of the pixel overflowed there are pixel to corresponding difference pair, record to position mapping table L；Selection is not present
The pixel that pixel is overflowed is to corresponding difference to the two-dimentional difference value histogram of generation.
Aforementioned two kinds of embodiments can be combined with implementing, with actual scene as an example it is assumed that pixel is to (xi,yi)=
(125,125), corresponding predicted value are z=124, and calculating and obtaining its level of noise is NL (xi,yi)=10, corresponding difference
To for (d1,d2)=(1,1), if noise threshold is T=25, the level of noise of difference pair is less than threshold value, and the pixel is not to
There are pixel spillings, therefore can be used to generate two-dimentional difference value histogram.Correspondingly, 13 can specifically include：Calculate each picture
The level of noise of element pair；Count information of the pixel overflowed there are pixel to corresponding difference pair, record to position mapping table
L；It chooses level of noise and is less than threshold value, and it is straight to generate two-dimentional difference to corresponding difference pair for the pixel that pixel spilling is not present
Fang Tu.
14, select beginning and end in the two-dimentional difference value histogram, using dynamic programming algorithm, in the starting point and
Optimal path is selected in the grid that the terminal is constituted, the optimal path is the starting point in the grid to the terminal
The maximum path of the sum of the frequency for the first difference pair passed through in all paths, and the first difference pair that the optimal path passes through
The embeddable capacity of the reality of corresponding pixel pair not less than bit information entrained by watermark to be embedded capacity, it is described most
The adjacent difference that shortest path passes through is to adjacent in the horizontal direction or on vertical direction.
Specifically, using dynamic programming algorithm, the optimal path that is selected in the grid that the beginning and end is constituted
Shown in the following formula of formal definitions：
D (x, y)=max { D (x-1, y), D (x, y-1) }+h (x, y)
Wherein, D (x, y) indicates the sum of the frequency of difference pair that the optimal embedding path that terminal is (x, y) is passed through, h (x, y)
It indicates in carrier image with difference to the number of (x, y) corresponding pixel pair, i.e. frequency of the difference to (x, y).The formula can
To use dynamic programming algorithm to be solved with linear time complexity.
15, by first difference to be defined as expansion difference pair, by remaining difference to be defined as translation difference pair.
16, the expansion difference is established to corresponding pixel pair and bit information entrained by the watermark to be embedded
The first corresponding relationship.
17, be directed to each pixel pair, if the pixel to corresponding difference to for translation difference pair, according to preset
First rule is to the pixel to modifying；If the pixel to corresponding difference to for expand difference pair, according to institute
The first corresponding relationship is stated, if the pixel is 1 to the value of corresponding bit information, according to preset first rule to institute
Pixel is stated to modifying；If the pixel is 0 to the value of corresponding bit information, not to the pixel to repairing
Change.
As an alternative embodiment, on the basis of any of the above-described embodiment, according to preset described in 17
First rule can specifically include the pixel to modifying：
According to first rule, by pixel described in the two-dimentional difference value histogram to corresponding difference opposite direction far from institute
The direction for stating optimal path is mobile, and the difference after moving, to not being overlapped mutually, the moving distance of the difference pair is preset threshold
Value；
According to the pixel after movement to the coordinate and first formula of corresponding difference pair, calculate presently described
The pixel value of each pixel of pixel centering, and the pixel value of each pixel of pixel centering is revised as currently being calculated
Pixel value.
By aforementioned schemes, it can be completed and be embedded in watermark in carrier image.Specifically, in order to reduce the embedding of carrier image
Enter distortion, can define the preset threshold value is 1, i.e., difference is to (d1,d2) modification direction can be (d1-1,d2), or
(d1+1,d2), or (d1,d2, or (d -1)1,d2+ 1) it, can be calculated according to first formula, difference is to corresponding
The modification direction of pixel pair be (x-1, y), or (x+1, y), or (x, y-1), or (x, y+1), i.e. pixel are to repairing
The amount of changing is 1.
Further, for bit information entrained by the subsequent watermark that can extract insertion and recovery carrier image, institute
The method of stating, which can also be included in the carrier image, is embedded in additional information, and the additional information includes：The optimal path warp
It is the location information for the first difference pair crossed, right with last bit information of bit information entrained by watermark to be embedded institute
The location information for the pixel pair answered, noise threshold, the length of position mapping table L and position mapping table L.
Adaptive reversible water mark method provided in this embodiment, by the way that carrier image is divided into multiple phases not being overlapped mutually
Adjacent pixel pair；Using gradient prediction method calculate corresponding difference to and generate two-dimentional difference value histogram；Using Dynamic Programming
Algorithm selects optimal path in two-dimentional difference value histogram, establish difference on optimal path to corresponding pixel pair with to
First corresponding relationship of bit information entrained by the watermark of insertion；If pixel is to corresponding difference to not in optimal path
On, then according to preset first rules modification pixel pair；If pixel to corresponding difference on optimal path, according to
One corresponding relationship, if pixel is 1 to the value of corresponding bit information, according to preset first rules modification pixel pair；
If pixel is 0 to the value of corresponding bit information, pixel pair is not modified.The Data Embedding Capacity of this programme is high, is embedded in
Be distorted it is low, hiding data it is highly-safe.
For example with practical application scene, beginning and end is selected in the two-dimentional difference value histogram, using dynamic
Planning algorithm, selected in the grid that the starting point and the terminal are constituted optimal path method can there are many, citing comes
Say, can the origin (0,0) of two-dimentional difference value histogram be grid that center click and sweep takes predetermined side length, on the grid diagonal line
Two differences to as beginning and end；Alternatively, two differences can also arbitrarily be chosen to as beginning and end.Specifically such as
Shown in Fig. 3, Fig. 3 is a kind of flow diagram of adaptive reversible water mark method provided by Embodiment 2 of the present invention, shown in Fig. 1
On the basis of embodiment, 14 be can specifically include：
341, any two difference is chosen to as current beginning and end；
342, according to current beginning and end, using the dynamic programming algorithm, according to preset first rule in institute
It states in the grid of starting point and terminal composition and selects current optimal path；
343, the first difference of current optimal path process is calculated to the embeddable capacity of the reality of corresponding pixel pair
Actual capacity；
If 344, the first difference that current optimal path passes through is to the embeddable capacity of the reality of corresponding pixel pair
Actual capacity is less than the capacity of bit information entrained by current watermark to be embedded, then chooses beginning and end again and be used as and work as
Preceding beginning and end；And return described in execution 342 according to current beginning and end, using the dynamic programming algorithm,
The step of selecting current optimal path in the grid that the starting point and the terminal are constituted according to preset first rule,
Until the first difference for passing through of current optimal path to the actual capacity of the embeddable capacity of the reality of corresponding pixel pair not
Less than the capacity of bit information entrained by current watermark to be embedded.
Specifically, choosing beginning and end again can have as the method for current beginning and end in above-mentioned 344
It is a variety of, for example, can arbitrarily to choose beginning and end again as current beginning and end, or with current starting point
The side length of the grid is expanded 2 times, chooses the diagonal of the grid after expanding by point centered on the net center of a lattice constituted with terminal
Two differences on line are to as current beginning and end.
Further, in above-mentioned 344, if the first difference that current optimal path passes through is to corresponding pixel pair
The actual capacity of practical embeddable capacity can be used much larger than the capacity of bit information entrained by current watermark to be embedded
Dichotomy chooses beginning and end as current beginning and end again, and returns to execute and be risen described in 342 according to current
Point and terminal, using the dynamic programming algorithm, the net constituted according to preset first rule in the starting point and the terminal
The step of current optimal path is selected in lattice, until the first difference that current optimal path passes through is to corresponding pixel
Pair the actual capacity of the embeddable capacity of reality be not less than and close to the appearance of bit information entrained by current watermark to be embedded
Amount.
Adaptive reversible water mark method provided in this embodiment, by choosing any two difference to as current starting point
And terminal, and dynamic programming algorithm is used, it is selected in the grid that current beginning and end is constituted according to preset first rule
Select out current optimal path；If the first difference that current optimal path passes through is embeddable to the reality of corresponding pixel pair
The actual capacity of capacity is less than the capacity of bit information entrained by current watermark to be embedded, then chooses beginning and end again
As current beginning and end；And execution is returned according to current beginning and end, using dynamic programming algorithm at described
The step of selecting current optimal path in the grid that point and the terminal are constituted, until current optimal path pass through the
One difference is to the actual capacity of the embeddable capacity of the reality of corresponding pixel pair not less than entrained by current watermark to be embedded
Bit information capacity.This programme can quickly select the pixel pair that can carry out data insertion, and data Embedding efficiency is high.
Fig. 4 is a kind of flow diagram for adaptive reversible water mark method that the embodiment of the present invention three provides, such as Fig. 4 institute
Show, on the basis of embodiment shown in Fig. 1,14 be can specifically include：
441, the two-dimentional difference value histogram is divided into mutually disjoint four subset A according to preset Second Rulen,
Wherein n=1,2,3,4；The Second Rule is：
442, according to preset third rule, the capacity of bit information entrained by the watermark to be embedded is divided into
The corresponding capacity of each subset；
Specifically, the capacity of bit information entrained by the watermark to be embedded is drawn according to preset third rule
Be divided into the corresponding capacity of each subset method can there are many, for example, can will be entrained by the watermark to be embedded
Bit information capacity it is impartial be divided into the corresponding capacity of each subset.
443, it is directed to each subset, the nearest difference of selected distance (0,0) is to for the subset in the subset
Corresponding starting point, and select the corresponding terminal of the subset；Using dynamic programming algorithm, in the corresponding starting point of the subset and institute
State the corresponding optimal path of the selection subset in the grid that the corresponding terminal of subset is constituted, the corresponding optimal path of the subset
The difference pair passed through into all paths of the corresponding terminal of the subset for the corresponding starting point of subset described in the grid
The maximum path of the sum of frequency, and the difference that the corresponding optimal path of the subset passes through can to the reality of corresponding pixel pair
Embedding capacity is not less than the corresponding capacity of the subset, and the adjacent difference that the corresponding optimal path of the subset passes through is in level
It is adjacent on direction or vertical direction；
444, the corresponding optimal path of each subset is added, obtains the optimal path.
As an alternative embodiment, selecting the subset pair on the basis of embodiment shown in Fig. 4, in 443
The terminal answered, can specifically include：
4431, any one difference is chosen in the subset to as current terminal；
4432, according to the starting point of the subset and current terminal, using the dynamic programming algorithm, according to preset
One rule selects the current optimal path of the subset in the grid that the starting point and the terminal are constituted；
4433, it is embeddable to the reality of corresponding pixel pair to calculate the difference that the current optimal path of the subset passes through
The actual capacity of capacity；
If 4434, the difference that the current optimal path of the subset passes through is to the embeddable appearance of the reality of corresponding pixel pair
The actual capacity of amount is less than the corresponding capacity of the subset, then chooses terminal again in the subset as current terminal；
And return and execute the starting point according to the subset and current terminal, using the dynamic programming algorithm in the starting point and
The step of current optimal path of the subset is selected in the grid that the terminal is constituted, until current optimal of the subset
The difference that path is passed through is corresponding not less than the subset to the actual capacity of the embeddable capacity of the reality of corresponding pixel pair
Capacity.
Specifically, in above-mentioned 4434, choosing terminal again in the subset can be with as the method for current terminal
There are many, for example, terminal can be arbitrarily chosen in the subset again as current terminal, or by the subset
Starting point and the side length of grid that constitutes of current terminal expand 2 times, choose the starting point institute of the subset on the grid after expanding
Diagonal line on another difference to as current terminal.
Further, in above-mentioned 4434, if the difference that the current optimal path of the subset passes through is to corresponding picture
The actual capacity of the embeddable capacity of reality of element pair is much larger than the corresponding capacity of the subset, can be chosen again using dichotomy
Terminal returns to starting point and the current terminal executed described in 4432 according to the subset as current terminal, using institute
Dynamic programming algorithm is stated, selects the son in the grid that the starting point and the terminal are constituted according to preset first rule
The step of collecting current optimal path, up to the difference that the current optimal path of the subset passes through is to corresponding pixel pair
The actual capacity of practical embeddable capacity is not less than and close to the corresponding capacity of the subset.
Adaptive reversible water mark method provided in this embodiment, by advising two-dimentional difference value histogram according to preset second
Mutually disjoint four subsets are then divided into, and according to preset third rule, bit entrained by watermark to be embedded is believed
The capacity of breath is divided into the corresponding capacity of each subset；For each subset, selected using dynamic programming algorithm each
The corresponding optimal path of each subset is added by the corresponding optimal path of subset, obtains the optimal of entire two-dimentional difference value histogram
Path.Therefore the sum of the frequency of the first difference pair that the optimal path that this programme obtains passes through maximum can get higher data
Embedding capacity and smaller insertion distortion.
Fig. 5 is a kind of structural schematic diagram for adaptive reversible water mark system that the embodiment of the present invention four provides, such as Fig. 5 institute
Show, the system comprises：
Pixel to module 51, for carrier image to be divided into multiple mutually pixels for not being overlapped to (x, y), each pixel pair
In two pixels it is adjacent, wherein x be previous pixel pixel value, y be latter pixel pixel value.
Specifically, carrier image can be divided into multiple pixels pair not being overlapped mutually using various ways, for example,
Carrier image is divided into and multiple is not overlapped mutually as one group of pixel pair by two pixels adjacent using carrier image horizontal direction
Pixel pair.
Difference to module 52, for for each pixel to (x, y), it is pre- using gradient according to the neighborhood of the pixel pair
Survey method calculates corresponding predicted value z, and calculates corresponding difference to (d using the first formulax,dy), first formula
For：
d1=x-z, d2=y-z.
Histogram module 53, for corresponding difference pair, generating two-dimentional difference value histogram according to multiple pixels.
Further, selected pixels to corresponding difference to generate two-dimentional difference value histogram method can there are many, lift
For example, in order to improve the safety of secret information insertion, for the pixel of carrier image texture complex region, without number
According to insertion, i.e., the pixel of carrier image texture complex region is not chosen to corresponding difference to generating two-dimentional difference value histogram,
Namely the pixel in image smoothing region is chosen to corresponding difference to generating two-dimentional difference value histogram.Embodiment party shown in Fig. 5
On the basis of formula, Histogram module 53 may include：Element of noise, for calculating the level of noise of each pixel pair, according to institute
Multiple pixels of the level of noise less than noise threshold are stated to corresponding difference pair, generate two-dimentional difference value histogram.
Further, the pixel for being 255 or 0 for pixel value in carrier image, can not carry out+1 or -1 modification, this
Kind situation is pixel spilling.Choose difference to generate two-dimensional histogram when, can not choose there are pixel overflow pixel pair
Corresponding difference pair.As an alternative embodiment, on the basis of any of the above-described embodiment, Histogram module 53
May include：Unit is overflowed, for counting the pixel overflowed there are pixel to the information of corresponding difference pair, record to position
Mapping table L；The pixel overflowed there is no pixel is chosen to corresponding difference to the two-dimentional difference value histogram of generation.
Aforementioned two kinds of embodiments can be combined with implementing, correspondingly, in element of noise and overflowing what unit was handled
On the basis of, Histogram module 53 be specifically used for choose level of noise be less than threshold value, and there is no pixel overflow pixel to pair
The difference pair answered generates two-dimentional difference value histogram.
Optimal path module 54 is used to select beginning and end in the two-dimentional difference value histogram, using Dynamic Programming
Algorithm selects optimal path in the grid that the starting point and the terminal are constituted, and the optimal path is institute in the grid
State the maximum path of the sum of the frequency of the first difference pair that starting point is passed through into all paths of the terminal, and the optimal road
The first difference that diameter passes through is to the embeddable capacity of the reality of corresponding pixel pair not less than ratio entrained by watermark to be embedded
The capacity of special information, the adjacent difference that the optimal path passes through is to adjacent in the horizontal direction or on vertical direction.
Specifically, using dynamic programming algorithm, the optimal path that is selected in the grid that the beginning and end is constituted
Shown in the following formula of formal definitions：
D (x, y)=max { D (x-1, y), D (x, y-1) }+h (x, y)
Wherein, D (x, y) indicates the sum of the frequency of difference pair that the optimal embedding path that terminal is (x, y) is passed through, h (x, y)
It indicates in carrier image with difference to the number of (x, y) corresponding pixel pair, i.e. frequency of the difference to (x, y).The formula can
To use dynamic programming algorithm to be solved with linear time complexity.
Definition module 55, for by first difference to expansion difference pair is defined as, by remaining difference to being defined as putting down
Move difference pair.
Respective modules 56 take corresponding pixel pair and the watermark to be embedded for establishing the expansion difference
First corresponding relationship of the bit information of band.
Modified module 57, for be directed to each pixel pair, if the pixel to corresponding difference to for translation difference pair,
Then according to preset first rule to the pixel to modifying；If the pixel to corresponding difference to for expand difference
It is right, then according to first corresponding relationship, if the pixel is 1 to the value of corresponding bit information, according to preset
First rule is to the pixel to modifying；If the pixel is 0 to the value of corresponding bit information, not to described
Pixel is to modifying.
As an alternative embodiment, on the basis of any of the above-described embodiment, modified module 57 may include：
Mobile unit, for regular according to described first, by pixel described in the two-dimentional difference value histogram to corresponding
Direction of the difference opposite direction far from the optimal path is mobile, and the difference after moving is to being overlapped mutually, the movement of the difference pair
Distance is preset threshold value；
Unit is modified, for the coordinate and first formula according to the pixel after movement to corresponding difference pair,
The pixel value of presently described each pixel of pixel centering is calculated, and the pixel value of each pixel of pixel centering is revised as
The pixel value being currently calculated.
By aforementioned schemes, it can be completed and be embedded in watermark in carrier image.Specifically, in order to reduce the embedding of carrier image
Enter distortion, can define the preset threshold value is 1, i.e., difference is to (d1,d2) modification direction can be (d1-1,d2), or
(d1+1,d2), or (d1,d2, or (d -1)1, d2+ 1) it, can be calculated according to first formula, difference is to corresponding
The modification direction of pixel pair be (x-1, y), or (x+1, y), or (x, y-1), or (x, y+1), i.e. pixel are to repairing
The amount of changing is 1.
Further, for bit information entrained by the subsequent watermark that can extract insertion and recovery carrier image, institute
The system of stating can also include add-on module, and for being embedded in additional information in the carrier image, the additional information includes：Institute
The location information of stating the first difference pair of optimal path process, last position with bit information entrained by watermark to be embedded
The location information of pixel pair corresponding to bit information, noise threshold, the length of position mapping table L and position mapping table L.
Adaptive reversible water mark system provided in this embodiment, by the way that carrier image is divided into multiple phases not being overlapped mutually
Adjacent pixel pair；Using gradient prediction method calculate corresponding difference to and generate two-dimentional difference value histogram；Using Dynamic Programming
Algorithm selects optimal path in two-dimentional difference value histogram, establish difference on optimal path to corresponding pixel pair with to
First corresponding relationship of bit information entrained by the watermark of insertion；If pixel is to corresponding difference to not in optimal path
On, then according to preset first rules modification pixel pair；If pixel to corresponding difference on optimal path, according to
One corresponding relationship, if pixel is 1 to the value of corresponding bit information, according to preset first rules modification pixel pair；
If pixel is 0 to the value of corresponding bit information, pixel pair is not modified.The Data Embedding Capacity of this programme is high, is embedded in
Be distorted it is low, hiding data it is highly-safe.
For example with practical application scene, beginning and end is selected in the two-dimentional difference value histogram, using dynamic
Planning algorithm, selected in the grid that the starting point and the terminal are constituted optimal path method can there are many, citing comes
Say, can the origin (0,0) of two-dimentional difference value histogram be grid that center click and sweep takes predetermined side length, on the grid diagonal line
Two differences to as beginning and end；Alternatively, two differences can also arbitrarily be chosen to as beginning and end.Specifically such as
Shown in Fig. 6, Fig. 6 is a kind of structural schematic diagram for adaptive reversible water mark system that the embodiment of the present invention five provides, shown in Fig. 5
On the basis of embodiment, optimal path module 54 may include：
First selection unit 641, for choosing any two difference to as current beginning and end；
Optimal path unit 642, for according to current beginning and end, using the dynamic programming algorithm, according to pre-
If the first rule select current optimal path in the grid that the starting point and the terminal are constituted；
Computing unit 643, reality of first difference to corresponding pixel pair for calculating current optimal path process
The actual capacity of the embeddable capacity in border；
If the second selection unit 644, the first difference passed through for current optimal path are to corresponding pixel pair
The actual capacity of practical embeddable capacity is less than the capacity of bit information entrained by current watermark to be embedded, then chooses again
Beginning and end is as current beginning and end；And it returns described in execution 342 according to current beginning and end, using institute
Dynamic programming algorithm is stated, is selected in the grid that the starting point and the terminal are constituted according to preset first rule current
The step of optimal path, until the first difference that current optimal path passes through is to the embeddable appearance of the reality of corresponding pixel pair
Capacity of the actual capacity of amount not less than bit information entrained by current watermark to be embedded.
Specifically, the second selection unit 644 choose beginning and end again can as the method for current beginning and end
There are many, for example, can arbitrarily choose beginning and end again as current beginning and end, or with current
The side length of the grid is expanded 2 times, chooses the grid after expanding by point centered on the net center of a lattice that beginning and end is constituted
Two differences on diagonal line are to as current beginning and end.
Further, if the second selection unit 644 can be also used for the first difference of current optimal path process to institute
The actual capacity of the embeddable capacity of the reality of corresponding pixel pair is much larger than bit information entrained by current watermark to be embedded
Capacity, choose beginning and end again using dichotomy as current beginning and end, and indicate the optimal path list
Member 642 executes the current beginning and end of the basis again, using the dynamic programming algorithm, according to preset first rule
The step of selecting current optimal path in the grid that the starting point and the terminal are constituted, until current optimal path
The first difference passed through is not less than the actual capacity of the embeddable capacity of the reality of corresponding pixel pair and close to currently to embedding
The capacity of bit information entrained by the watermark entered.
Adaptive reversible water mark system provided in this embodiment, by choosing any two difference to as current starting point
And terminal, and dynamic programming algorithm is used, it is selected in the grid that current beginning and end is constituted according to preset first rule
Select out current optimal path；If the first difference that current optimal path passes through is embeddable to the reality of corresponding pixel pair
The actual capacity of capacity is less than the capacity of bit information entrained by current watermark to be embedded, then chooses beginning and end again
As current beginning and end；And execution is returned according to current beginning and end, using dynamic programming algorithm at described
The step of selecting current optimal path in the grid that point and the terminal are constituted, until current optimal path pass through the
One difference is to the actual capacity of the embeddable capacity of the reality of corresponding pixel pair not less than entrained by current watermark to be embedded
Bit information capacity.This programme can quickly select the pixel pair that can carry out data insertion, and data Embedding efficiency is high.
Fig. 7 is a kind of structural schematic diagram for adaptive reversible water mark system that the embodiment of the present invention six provides, such as Fig. 7 institute
Show, on the basis of embodiment shown in Fig. 5, optimal path module 54 may include：
First division unit 741, for the two-dimentional difference value histogram to be divided into mutually not according to preset Second Rule
Four subset A of intersectionn, wherein n=1,2,3,4；The Second Rule is：
Second division unit 742 is used for according to preset third rule, by bit entrained by the watermark to be embedded
The capacity of information is divided into the corresponding capacity of each subset；
Specifically, the capacity of bit information entrained by the watermark to be embedded is drawn according to preset third rule
Be divided into the corresponding capacity of each subset method can there are many, for example, can will be entrained by the watermark to be embedded
Bit information capacity it is impartial be divided into the corresponding capacity of each subset.
Subset unit 743 is used to be directed to each subset, in the subset the nearest difference of selected distance (0,0)
To for the corresponding starting point of the subset, and select the corresponding terminal of the subset；Using dynamic programming algorithm, in the subset pair
The corresponding optimal path of the selection subset, the subset pair in the grid that the corresponding terminal of the starting point and the subset answered is constituted
The optimal path answered passes through for the corresponding starting point of subset described in the grid into all paths of the corresponding terminal of the subset
The maximum path of the sum of frequency of difference pair crossed, and the difference that the corresponding optimal path of the subset passes through is to corresponding picture
The embeddable capacity of reality of element pair is not less than the corresponding capacity of the subset, and the corresponding optimal path of the subset passes through adjacent
Difference is to adjacent in the horizontal direction or on vertical direction；
Assembled unit 744 is used to for the corresponding optimal path of each subset being added, and obtains the optimal path.
As an alternative embodiment, on the basis of embodiment shown in Fig. 7, subset unit 743 may include：
First selection subelement, for choosing in the subset any one difference to as current terminal；
Optimal path subelement, for according to the subset starting point and current terminal, using the Dynamic Programming calculate
Method selects current optimal of the subset according to preset first rule in the grid that the starting point and the terminal are constituted
Path；
Computation subunit, the difference for calculating the current optimal path process of the subset are to corresponding pixel pair
The actual capacity of practical embeddable capacity；
If the difference that second chooses subelement, the optimal path current for the subset passes through is to corresponding pixel pair
The embeddable capacity of reality actual capacity be less than the corresponding capacity of the subset, then in the subset again choose terminal make
For current terminal；And return and execute the starting point according to the subset and current terminal, it is calculated using the Dynamic Programming
Method selects the step of subset current optimal path in the grid that the starting point and the terminal are constituted, until described
The difference that the current optimal path of subset passes through is not less than the actual capacity of the embeddable capacity of the reality of corresponding pixel pair
The corresponding capacity of the subset.
Specifically, second choose subelement choose terminal again in the subset can be with as the method for current terminal
There are many, for example, terminal can be arbitrarily chosen in the subset again as current terminal, or by the subset
Starting point and the side length of grid that constitutes of current terminal expand 2 times, choose the starting point institute of the subset on the grid after expanding
Diagonal line on another difference to as current terminal.
Further, if the second selection subelement can be also used for the difference pair that the current optimal path of the subset passes through
The actual capacity of the embeddable capacity of the reality of corresponding pixel pair is much larger than the corresponding capacity of the subset, can use two points
Method chooses terminal as current terminal again, and it is described according to the subset to indicate that the optimal path subelement executes again
Starting point and current terminal, using the dynamic programming algorithm, according to preset first rule in the starting point and the end
The step of current optimal path of the subset is selected in the grid that point is constituted, until the optimal path warp that the subset is current
The difference crossed is not less than the actual capacity of the embeddable capacity of the reality of corresponding pixel pair and corresponding close to the subset
Capacity.
Adaptive reversible water mark system provided in this embodiment, by advising two-dimentional difference value histogram according to preset second
Mutually disjoint four subsets are then divided into, and according to preset third rule, bit entrained by watermark to be embedded is believed
The capacity of breath is divided into the corresponding capacity of each subset；For each subset, selected using dynamic programming algorithm each
The corresponding optimal path of each subset is added by the corresponding optimal path of subset, obtains the optimal of entire two-dimentional difference value histogram
Path.Therefore the sum of the frequency of the first difference pair that the optimal path that this programme obtains passes through maximum can get higher data
Embedding capacity and smaller insertion distortion.
It is apparent to those skilled in the art that for convenience and simplicity of description, the system of foregoing description
Specific work process, can refer to corresponding processes in the foregoing method embodiment, details are not described herein.
Finally it should be noted that：The above embodiments are only used to illustrate the technical solution of the present invention., rather than its limitations；To the greatest extent
Present invention has been described in detail with reference to the aforementioned embodiments for pipe, those skilled in the art should understand that：Its according to
So be possible to modify the technical solutions described in the foregoing embodiments, or to some or all of the technical features into
Row equivalent replacement；And these are modified or replaceed, various embodiments of the present invention technology that it does not separate the essence of the corresponding technical solution
The range of scheme.
Claims (10)
1. a kind of adaptive reversible water mark method, which is characterized in that including：
Carrier image is divided into multiple pixels not being overlapped mutually to (x, y), two pixels of each pixel centering are adjacent,
In, x is the pixel value of previous pixel, and y is the pixel value of latter pixel；
For each pixel to (x, y), according to the neighborhood of the pixel pair, corresponding predicted value is calculated using gradient prediction method
Z, and corresponding difference is calculated to (d using the first formulax,dy), first formula is：
d1=x-z, d2=y-z；
According to multiple pixels to corresponding difference pair, two-dimentional difference value histogram is generated；
Beginning and end is selected in the two-dimentional difference value histogram, using dynamic programming algorithm, in the starting point and the end
Optimal path is selected in the grid that point is constituted, the optimal path is the starting point in the grid to all roads of the terminal
The maximum path of the sum of the frequency for the first difference pair passed through in diameter, and the first difference that the optimal path passes through is to corresponding
Pixel pair capacity of the embeddable capacity of reality not less than bit information entrained by watermark to be embedded, the optimal path
The adjacent difference passed through is to adjacent in the horizontal direction or on vertical direction；
By first difference to be defined as expansion difference pair, by remaining difference to be defined as translation difference pair；
Establish first of the expansion difference to corresponding pixel pair with bit information entrained by the watermark to be embedded
Corresponding relationship；
For each pixel pair, if the pixel to corresponding difference to translate difference pair, according to preset first rule
Then to the pixel to modifying；If the pixel to corresponding difference to for expand difference pair, according to described first
Corresponding relationship, if the pixel is 1 to the value of corresponding bit information, according to preset first rule to the pixel
To modifying；If the pixel is 0 to the value of corresponding bit information, not to the pixel to modifying.
2. the method according to claim 1, wherein it is described according to multiple pixels to corresponding difference
It is right, two-dimentional difference value histogram is generated, including：
The level of noise for calculating each pixel pair is less than multiple pixels of noise threshold to corresponding according to the level of noise
Difference pair generates two-dimentional difference value histogram.
3. the method according to claim 1, wherein it is described according to it is preset first rule to the pixel into
Row is modified：
According to first rule, by pixel described in the two-dimentional difference value histogram to corresponding difference opposite direction far from it is described most
The direction of shortest path is mobile, and the difference after moving, to not being overlapped mutually, the moving distance of the difference pair is preset threshold value；
According to the pixel after movement to the coordinate and first formula of corresponding difference pair, presently described pixel is calculated
The pixel value of each pixel of centering, and the pixel value of each pixel of pixel centering is revised as the pixel being currently calculated
Value.
4. the method according to claim 1, wherein it is described selected in the two-dimentional difference value histogram starting point and
Terminal selects optimal path in the grid that the starting point and the terminal are constituted using dynamic programming algorithm, including：
Any two difference is chosen to as current beginning and end；
According to current beginning and end, using the dynamic programming algorithm, according to preset first rule in the starting point and
Current optimal path is selected in the grid that the terminal is constituted；
Calculate practical appearance of first difference to the embeddable capacity of the reality of corresponding pixel pair of current optimal path process
Amount；
If the first difference that current optimal path passes through is to the actual capacity of the embeddable capacity of the reality of corresponding pixel pair
Less than the capacity of bit information entrained by current watermark to be embedded, then beginning and end is chosen again as current starting point
And terminal；And return and execute the current beginning and end of the basis, using the dynamic programming algorithm, according to preset first
The step of rule selects current optimal path in the grid that the starting point and the terminal are constituted, until current is optimal
The first difference that path is passed through is to be embedded not less than current to the actual capacity of the embeddable capacity of the reality of corresponding pixel pair
Watermark entrained by bit information capacity.
5. the method according to claim 1, wherein it is described selected in the two-dimentional difference value histogram starting point and
Terminal selects optimal path in the grid that the starting point and the terminal are constituted using dynamic programming algorithm, including：
The two-dimentional difference value histogram is divided into mutually disjoint four subset A according to preset Second Rulen, wherein n=1,
2,3,4；The Second Rule is：
According to preset third rule, the capacity of bit information entrained by the watermark to be embedded is divided into each subset
Corresponding capacity；
For each subset, the nearest difference of selected distance (0,0) is to being the subset corresponding in the subset
Point, and select the corresponding terminal of the subset；Using dynamic programming algorithm, in the corresponding starting point of the subset and the subset pair
The corresponding optimal path of the selection subset in the grid that the terminal answered is constituted, the corresponding optimal path of the subset is the net
The sum of the frequency of difference pair that the corresponding starting point of the subset is passed through into all paths of the corresponding terminal of the subset in lattice
Maximum path, and the difference that the corresponding optimal path of the subset passes through is to the embeddable capacity of the reality of corresponding pixel pair
Capacity corresponding not less than the subset, the adjacent difference that the corresponding optimal path of the subset passes through in the horizontal direction or
It is adjacent on vertical direction；
The corresponding optimal path of each subset is added, the optimal path is obtained.
6. a kind of adaptive reversible water mark system, which is characterized in that including：
Pixel is to module, for carrier image to be divided into multiple pixels not being overlapped mutually to (x, y), the two of each pixel centering
A pixel is adjacent, wherein x is the pixel value of previous pixel, and y is the pixel value of latter pixel；
Difference is to module, for being directed to each pixel to (x, y), according to the neighborhood of the pixel pair, using gradient prediction method
Corresponding predicted value z is calculated, and calculates corresponding difference to (d using the first formulax,dy), first formula is：
d1=x-z, d2=y-z；
Histogram module, for, to corresponding difference pair, generating two-dimentional difference value histogram according to multiple pixels；
Optimal path module, for selecting beginning and end in the two-dimentional difference value histogram, using dynamic programming algorithm,
Select optimal path in the grid that the starting point and the terminal are constituted, the optimal path is that the starting point is extremely in the grid
The maximum path of the sum of the frequency of the first difference pair passed through in all paths of the terminal, and optimal path process
First difference is to the embeddable capacity of the reality of corresponding pixel pair not less than bit information entrained by watermark to be embedded
Capacity, the adjacent difference that the optimal path passes through is to adjacent in the horizontal direction or on vertical direction；
Definition module, for by first difference to be defined as expansion difference pair, by remaining difference to be defined as translation difference
It is right；
Respective modules, for establishing the expansion difference to corresponding pixel pair and ratio entrained by the watermark to be embedded
First corresponding relationship of special information；
Modified module, for be directed to each pixel pair, if the pixel to corresponding difference to for translation difference pair, according to
Preset first rule is to the pixel to modifying；If the pixel to corresponding difference to for expand difference pair,
According to first corresponding relationship, if the pixel is 1 to the value of corresponding bit information, according to preset first rule
Then to the pixel to modifying；If the pixel is 0 to the value of corresponding bit information, not to the pixel pair
It modifies.
7. system according to claim 6, which is characterized in that the Histogram module includes：
Element of noise is less than the multiple of noise threshold according to the level of noise for calculating the level of noise of each pixel pair
Pixel generates two-dimentional difference value histogram to corresponding difference pair.
8. system according to claim 6, which is characterized in that the modified module includes：
Mobile unit, for regular according to described first, by pixel described in the two-dimentional difference value histogram to corresponding difference
The opposite direction far from the optimal path is mobile, and the difference after moving is to being overlapped mutually, the moving distance of the difference pair
For preset threshold value；
Unit is modified, for the coordinate and first formula according to the pixel after movement to corresponding difference pair, is calculated
The pixel value of presently described each pixel of pixel centering out, and the pixel value of each pixel of pixel centering is revised as currently
The pixel value being calculated.
9. system according to claim 6, which is characterized in that the optimal path module includes：
First selection unit, for choosing any two difference to as current beginning and end；
Optimal path unit, for according to current beginning and end, using the dynamic programming algorithm in the starting point and institute
It states in the grid of terminal composition and selects current optimal path；
Computing unit, it is embeddable to the reality of corresponding pixel pair for calculating the first difference that current optimal path passes through
The actual capacity of capacity；
Second selection unit, if the first difference for current optimal path to pass through can be embedding to the reality of corresponding pixel pair
The actual capacity for entering capacity is less than the capacity of bit information entrained by current watermark to be embedded, then chooses starting point and end again
Point is as current beginning and end；And indicate that the optimal path unit executes the current starting point of the basis and end again
Point is selected in the grid that the starting point and the terminal are constituted using the dynamic programming algorithm according to preset first rule
The step of selecting out current optimal path, until the first difference that the current optimal path passes through is to corresponding pixel pair
The embeddable capacity of reality actual capacity not less than bit information entrained by current watermark to be embedded capacity.
10. system according to claim 6, which is characterized in that the optimal path module includes：
First division unit, for the two-dimentional difference value histogram to be divided into mutually disjoint four according to preset Second Rule
A subset An, wherein n=1,2,3,4；The Second Rule is：
Second division unit, for regular according to preset third, by bit information entrained by the watermark to be embedded
Capacity is divided into the corresponding capacity of each subset；
Subset unit, for be directed to each subset, in the subset the nearest difference of selected distance (0,0) to be described in
The corresponding starting point of subset, and select the corresponding terminal of the subset；Using dynamic programming algorithm, in the corresponding starting point of the subset
The corresponding optimal path of the subset is selected in the grid that terminal corresponding with the subset is constituted, the subset is corresponding optimal
The difference that path is passed through for the corresponding starting point of subset described in the grid into all paths of the corresponding terminal of the subset
Pair the maximum path of the sum of frequency, and the difference passed through of the corresponding optimal path of the subset is to the reality of corresponding pixel pair
The embeddable capacity in border is not less than the corresponding capacity of the subset, the adjacent difference that the corresponding optimal path of the subset passes through to
It is adjacent in horizontal direction or vertical direction；
Assembled unit obtains the optimal path for the corresponding optimal path of each subset to be added.
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