CN105447808A - Reversible data hiding method and recovering method - Google Patents

Abstract

The invention relates to a reversible data hiding method and a recovering method. The reversible data hiding method comprises a preprocessing step in which an original pixel-domain image is divided into blocks and the blocks are sorted according to the gray values, a marking step in which the sequence after sorting is detected and identified and feature-class blocks are marked, a watermark information embedding step in which watermark information is embedded into the feature-class blocks through a second embedding method, and an auxiliary information embedding step in which corresponding auxiliary information is embedded. According to the invention, on-demand watermark information embedding is realized, equal-maximum pixel redundancy in the image is fully exploited, 'one-position multi-bit embedding' is realized, and the information capacity is improved effectively. Meanwhile, seamless integration of a first embedding method and the second embedding method is achieved effectively.

Description

Reversible data concealing method and restoration methods

Technical field

The present invention relates to data hiding technique field, be specifically related to a kind of reversible data concealing method and restoration methods, the Sensitive Domains such as medical science, law and military affairs can be used in.

Background technology

Image watermarking became the research field of reinforcement in recent years.In data hiding process, therefore most of multi-medium data concealing technology amendment overwrite media also makes overwrite media distortion.Even if the usually very little and human visual system (HVS) of distortion can not perceive, but usually can not recover original cover media completely.In other words, these data hiding techniques are most of irreversible, to some sensitive application, as law and medical image, are unacceptable.For law, medical science and other sensitive application, need hiding reversible data to extract the data of embedding and to recover original host signal, so the shortcoming that prior art is brought, real to be improved.

In the face of shortcoming above, have Mr. Bruce Lee etc. to propose a kind of new embedding grammar, the present invention is called the first embedding grammar, and this first embedding grammar mainly achieves at the maximal value of each piecemeal and minimum value place embedding data, can embed at most two bits.Original image is divided into the identical but block n of non-overlapping copies of size ₁× n ₂, and by gray-scale value, ascending sort is carried out to pixel in block, please refer to Fig. 1.

As shown in Figure 1, original pixels sequence is (p ₁, p ₂..., p _n-1, p _n)=(162,161,159,157,163,158), after ascending sort, become (p ^s ₁, p ^s ₂..., p ^s _n-1, p ^s _n)=(157,158,159,161,162,163), wherein n=n ₁× n ₂.

By secondary maximal value prediction maximal value, by time minimum value prediction minimum value, perform data and embed.Maximal value predicated error e _max=p ^s _n-p ^s _n-1, minimum value predicated error e _min=p ^s ₁-p ^s ₂, embedding formula is

${\tilde{p}}_n^s=\left\{\begin{array}{ccc}{p^s}_n& if& e_{max}=0\\ {p^s}_n+b& if& e_{max}=1\\ {p^s}_n+1& if& e_{\max }>1\end{array}\right.---\left(1\right)$

${\tilde{p}}_1^s=\left\{\begin{array}{ccc}{p^s}_1& if& e_{\min }=0\\ {p^s}_1-b& if& e_{\min }=-1\\ {p^s}_1-1& if& e_{\min }<-1\end{array}\right.---\left(2\right)$

Can find out, the first embedding grammar mainly make use of one pole value piecemeal, achieves the reversible of information and hides, please refer to Fig. 2.There is following features:

1, the two ends that the pixel embedded is positioned at the rear gray value sequence of sequence are performed

2, each piecemeal has influence at most 2 pixels, and the maximum change 1 of pixel value, therefore have and can ensure very high fidelity

Although 3 each piecemeals can embed 2 Bit datas at most, only utilize the two ends of gray value sequence, do not make full use of multipole value piecemeal, therefore embedding capacity is less, needs to excavate pixel redundancy further, remains to be further improved in fact.

Summary of the invention

The object of this invention is to provide a kind of reversible data concealing method and restoration methods.

To achieve these goals, the technical solution used in the present invention is:

A kind of reversible data concealing method, comprising:

Pre-treatment step, carries out piecemeal by original, pixel domain image and sorts by gray-scale value in block;

Identification of steps, is undertaken the sequence after sequence detecting, identifying and identification characteristics class block;

Embed watermark information step, to feature class block by the second embedding grammar embed watermark information, this second embedding grammar comprises:

Determine secondary maximum value: the secondary maximum value location of pixels in identification characteristics class block is 1, form secondary maximum value location of pixels figure;

Computational prediction difference: the difference calculating maximum value and secondary maximum value in feature class block;

Embed watermark information: when difference equals 1, be then added on multipole value sequence by the binary code of watermark data;

Embed supplementary step, embed corresponding supplementary.

Further, this pre-treatment step comprises:

Block: original image is divided into the identical but block of non-overlapping copies of size;

Sequence: pixel in block is sorted by gray-scale value.

Further, in this block, pixel is ascending order or descending by gray-scale value sortord.

On above-mentioned any embodiment basis, further, the feature class block in this identification of steps comprises: k ₁class block, k ₂class block and mixing k class block.

On above-mentioned any embodiment basis, further, this k ₁class block is minimum gray-value pixel quantity is 1, equivalent greatly number of gray values 1<n _p-max≤ n-1, wherein k ₁=n _p-maxand 1<k1≤n-1.

On above-mentioned any embodiment basis, further, this k ₂class block is very big gray-value pixel quantity is 1, equivalent minimum number of gray values 1<n _p-min≤ n-1, wherein k ₂=n _p-minand 1<k2≤n-1.

On above-mentioned any embodiment basis, further, this mixing k class block is equivalent greatly gray-value pixel quantity 1<n _p-max≤ n-1, equivalent minimum number of gray values 1<n _p-min≤ n-1, wherein k ₁=n _p-max, k ₂=n _p-minand k ₁+ k ₂≤ n-1.

On above-mentioned any embodiment basis, further, the gray-scale value order sequence by size of this block pixel, secondary maximum value is called secondary maximum base p ^s _b-max, respective pixel is called secondary maximum base pixel p _b-max; Secondary minimum value is called secondary minimum base p ^s _b-min, respective pixel is called secondary minimum base pixel p _b-min.

On above-mentioned any embodiment basis, further, this embedding supplementary step comprises:

Replace least significant bit (LSB): calculate supplementary length, extract the least significant bit (LSB) of the front and supplementary equal length number pixel of image, and replace by supplementary;

Embed least significant bit (LSB): the least significant bit (LSB) sequence extracted be embedded in the later pixel of the last embedded block of data.

On above-mentioned any embodiment basis, further, the supplementary in this embedding supplementary step comprises: the location drawing and supplementary mark.

Further, the location drawing in this embedding supplementary step comprises spilling location of pixels figure, the full smooth block location drawing and base location of pixels figure.

On above-mentioned any embodiment basis, further, the supplementary in this embedding supplementary step identifies the location drawing size after comprising payload size, block size, compression, last embedded block index and finally embeds pixel index.

A restoration methods for hiding reversible data, comprising:

Read supplementary step, after receiving the image of embed watermark information, read and obtain complete supplementary, this supplementary comprises the location drawing and supplementary mark;

Pre-treatment step, carries out piecemeal by the image of embed watermark information and sorts by gray-scale value in block;

Identification of steps, is undertaken the sequence after sequence detecting, identifying and identification characteristics class block;

Treatment step, the secondary maximum that decompresses out from location drawing value location of pixels figure, determines each piece of location drawing, identification block type; Determine secondary maximum value pixel: according to the secondary maximum value location of pixels figure decompressed, determine the secondary maximum value pixel of each piece, be called secondary maximum base pixel; Calculate the difference of the large pixel of secondary maximum base grey scale pixel value and secondary maximum base pixel, difference is 1 extraction watermark information 0, and grey scale pixel value is constant; Difference is 2 extraction watermark informations 1, and grey scale pixel value subtracts 1; Difference is greater than 2 marks without embedding information, and grey scale pixel value is constant; From the pixel that the last embedded block of data is later, extract the least significant bit (LSB) sequence of embedding, and be substituted in the pixel that supplementary takies;

Extract watermark information and Recovery image step, duplicate marking step and treatment step, process each block successively and extract watermark information and each maximum pixel gray-scale value in recovery block, obtaining original image.

Further, this supplementary identifies the location drawing size after comprising payload size, block size, compression, last embedded block index and finally embeds pixel index.

On above-mentioned any embodiment basis, further, this location drawing comprises spilling location of pixels figure, the full smooth block location drawing and base location of pixels figure.

On above-mentioned any embodiment basis, further, this feature class block comprises: k ₁class block, k ₂class block and mixing k class block.

Further, this k ₁class block is minimum gray-value pixel quantity is 1, equivalent greatly number of gray values 1<n _p-max≤ n-1, wherein k ₁=n _p-maxand 1<k ₁≤ n-1.

Further, when identifying k ₁during class block, in the case, the information bit extracted is:

$b={\tilde{p}}_i^s-({p^s}_{n-k_1}+1),$

Image recovery scheme is:

${p^s}_i=\left\{\begin{array}{ccc}{\tilde{p}}_i^s& if& 1\&le;i\&le;n-k_1\\ {\tilde{p}}_i^s-b& if& n-k_1+1\&le;i\&le;nand{\tilde{e}}_{\max }^k\&Element;\left\{1,2\right\}\\ {\tilde{p}}_i^s-1& if& n-k_1+1\&le;i\&le;nand{\tilde{e}}_{\max }^k>2\end{array}\right.$

The image intensity value recovered is:

${p^s}_i={\tilde{p}}_i^s-b={\tilde{p}}_i^s-({\tilde{p}}_i^s-({p^s}_{n-k_1}+1\left)\right)={p^s}_{n-k_1}+1.$

On above-mentioned any embodiment basis, further, this k ₂class block is very big gray-value pixel quantity is 1, equivalent minimum number of gray values 1<n _p-min≤ n-1, wherein k ₂=n _p-minand 1<k ₂≤ n-1.。

Further, when identifying k ₂during class block, in the case, $i\&Element;\{1,2,...,n\},{\tilde{e}}_{min}^k={\tilde{p}}_{k_2}^s-{p^s}_{k_2+1},$ The information bit extracted is:

$b=({p^s}_{k_2}-1)-{\tilde{p}}_i^s$

Image recovery scheme is:

${p^s}_i=\left\{\begin{array}{ccc}{\tilde{p}}_i^s& if& k_2+1\&le;i\&le;n\\ {\tilde{p}}_i^s+b& if& 1\&le;i\&le;k_{2}and{\tilde{e}}_{\min }^k\&Element;\left\{-1,-2\right\}\\ {\tilde{p}}_i^s+1& if& 1\&le;i\&le;k_{2}and{\tilde{e}}_{\min }^k<-2\end{array}\right.$

The image intensity value recovered is:

${p^s}_i={\tilde{p}}_i^s+b={\tilde{p}}_i^s+\left(\right({p^s}_{k_2}-1)-{\tilde{p}}_i^s)={p^s}_{k2}+1.$

On above-mentioned any embodiment basis, further, this mixing k class block is equivalent greatly gray-value pixel quantity 1<n _p-max≤ n-1, equivalent minimum number of gray values 1<n _p-min≤ n-1, wherein k ₁=n _p-max, k ₂=n _p-min, and k ₁+ k ₂≤ n-1.

Further, when identifying mixing k class block, in the case, the information bit that equivalent maximum value place extracts is:

$b_1={\tilde{p}}_i^s-({p^s}_{n-k_1}+1)$

The information bit that equivalent minimal value place extracts is:

$b_2=({p^s}_{k_2}-1)-{\tilde{p}}_i^s$

Image recovery scheme is:

${p^s}_i=\left\{\begin{array}{ccc}{\tilde{p}}_i^s& if& k_2+1\&le;i\&le;n-k_1\\ {\tilde{p}}_i^s-b_1& if& n-k_1+1\&le;i\&le;nand{\tilde{e}}_{\max }^k\&Element;\left\{1,2\right\}\\ {\tilde{p}}_i^s-1& if& n-k_1+1\&le;i\&le;nand{\tilde{e}}_{\max }^k>2\\ {\tilde{p}}_i^s+b_2& if& 1\&le;i\&le;k_{2}and{\tilde{e}}_{\min }^k\&Element;\left\{-1,-2\right\}\\ {\tilde{p}}_i^s+1& if& 1\&le;i\&le;k_{2}and{\tilde{e}}_{\min }^k<-2\end{array}\right.$

The image intensity value recovered is:

${p^s}_i={\tilde{p}}_i^s-b={\tilde{p}}_i^s-({\tilde{p}}_i^s-({p^s}_{n-k_1}+1\left)\right)={p^s}_{n-k_1}+1.$

On above-mentioned any embodiment basis, further, this pre-treatment step comprises:

Block: original image is divided into the identical but block of non-overlapping copies of size;

Sequence: pixel in block is sorted by gray-scale value.

Further, in this block, pixel is ascending order or descending by gray-scale value sortord.

Other features and advantages of the present invention will be set forth in the following description, and, partly become apparent from instructions, or understand by implementing the present invention.Object of the present invention and other advantages realize by structure specifically noted in write instructions, claims and accompanying drawing and obtain.

Accompanying drawing explanation

Fig. 1 is the block of pixels ordering chart of picture in prior art first embedding grammar;

Fig. 2 is the ordering chart of the embed watermark information of prior art first embedding grammar;

Fig. 3 is the outline flowchart of embed watermark information in reversible data concealing method of the present invention;

Fig. 4 is the block diagram of embed watermark information in reversible data concealing method of the present invention;

Fig. 5 a-Fig. 5 h is the comparison diagram of reversible data concealing method of the present invention and other three kinds of methods, wherein, the comparison diagram of Fig. 5 a to be Lena picture be example, the comparison diagram of 5b to be Baboon picture be example, the comparison diagram of 5c to be Airplane picture be example, the comparison diagram of 5d to be Barbara picture be example, the comparison diagram of 5e to be Elaine picture be example, the comparison diagram of 5f to be Lake picture be example, the comparison diagram of Fig. 5 g to be Boat picture be example, the comparison diagram of Fig. 5 h to be Peppers picture be example.

Embodiment

The present invention relates to data hiding technique field, be specifically related to a kind of reversible data concealing method.Reversible data hiding technique, refers in Digital Image Processing process, and to carrier image embed watermark information, authorized user can extract watermark information from the image after embed watermark, also can revert to original carrier image simultaneously.

Invention thinking of the present invention is that after image is carried out piecemeal, in each piecemeal, pixel grey scale has maximal value and minimum value, can have a lot of extreme value for whole original image, comprises maximum value and minimal value.When use first embedding grammar embeds, only make use of the one pole value pixel in piecemeal.In order to better utilize piecemeal etc. extreme value pixel carry information bit, the present invention proposes the second embedding grammar.Specifically, usage flag strengthens and utilizes secondary extreme value pixel of image, and namely secondary maximum gray-scale pixels of piecemeal and time minimal gray pixel, go to predict maximum gray-scale pixels and minimal gray pixel, the secondary extreme value location of pixels figure of formation.On this basis, secondary maximum value pixel in the figure marking image of use location, with its predict in each piecemeal etc. maximal value pixel, realize the embedding as required of watermark information, fully excavated in image etc. maximum value pixel redundancy, achieve " 1 position, Multi-bit embedding ", effectively improve information capacity.Meanwhile, the seamless fusion of the first embedding grammar and the second embedding grammar has effectively been accomplished.

As shown in Figure 3, Fig. 3 is the outline flowchart of embed watermark information in reversible data concealing method of the present invention.Pre-treatment step comprises overflow block identification and full smooth block identification.Overflow block identification is mainly set up and is overflowed location of pixels figure.

Be exactly mainly recognition feature class block below, the feature class set out carries out embed watermark information according to the second embedding grammar soon.At analytical characteristic class block, according to k ₁class block, k ₂class block and mixing k class block embed again.If be that non-feature class is fast, just carry out the first embedding grammar and carry out embed watermark information.So the first embedding grammar and the second embedding grammar are seamless fusions, flexible embed watermark information as required.

Herein, term " watermark information " is information, and it can form a part for coherent message, and scrambler it can be embedded in the picture and demoder can be extracted subsequently from image.So, the uncoded form of the watermark information before also existing watermark information embedded images.Once be embedded in image, by adopting the demoder according to the method for one or more embodiment of the present invention, watermark information is reversibly complete to be recovered.

The terminological interpretation that the present invention also uses is as follows:

Difference expansion: calculate the difference between two pixels, utilizes difference to carry out the expanded application of information insertion.

Etc. maximal value pixel: after pixel presses gray-scale value sequence in image class block, have multiple size identical, and the pixel that numerical value is maximum.

Etc. maximum value pixel: the maximal value pixel in image class block, for whole image, the maximum value pixel such as to be called.

Secondary maximal value pixel: after pixel presses gray-scale value sequence in image class block, the maximum pixel less than maximal value.

Secondary maximum value pixel: the secondary maximal value pixel in image class block, for whole image, is called secondary maximum value pixel.

Below by embodiment, above term and technical scheme of the present invention are described in further detail.

A kind of reversible data concealing method, comprises pre-treatment step, identification of steps, embed watermark information step and embedding supplementary step.

Pre-treatment step, just original, pixel domain image carries out piecemeal and sorts by gray-scale value in block.

Pre-treatment step comprises: piecemeal and sequence.Piecemeal is exactly original image is divided into the identical but block of non-overlapping copies of size.Original image is divided into the identical but block n of non-overlapping copies of size ₁× n ₂, and by gray-scale value, ascending sort is carried out to pixel in block.

Sequence is sorted by gray-scale value to pixel in block exactly.In this block, pixel is ascending order or descending by gray-scale value sortord.

Pre-treatment step also comprises overflow block identification and full smooth block identification.Wherein, overflow block identification is mainly set up and is overflowed location of pixels figure, and pixel 0 and 255 is adjusted to 1 and 254 respectively.Full smooth block identification refers to that the gray-scale value of all pixels in piecemeal is identical, sets up the full smooth block location drawing.In complete level and smooth identification, as above this type of pixel (pixel 0 and 255) in full smooth block remains unchanged, and only identifies with the smooth block location drawing.Run into this type of block to be no longer further analyzed, monoblock pixel value remains unchanged.

When base location of pixels figure refers to scanning point block type, run into certain kinds block, then identify secondary maximum base pixel and secondary minimum base pixel, set up base location of pixels figure, be convenient to the invertible operation realizing information in follow-up embedding, extraction and recovery link.

, there is this type of situation and be namely designated " 1 ", otherwise be designated " 0 " in above-mentioned three kinds of locations drawing.After each position figure sets up, Lossless Compression is just adopted to reduce its size.

This identification of steps, is undertaken the sequence after sequence detecting, identifying and identification characteristics class block.This feature class block comprises: k ₁class block, k ₂class block and mixing k class block.

This minimum gray-value pixel quantity is 1, equivalent greatly number of gray values 1<n _p-max≤ n-1, is called k ₁class block, wherein k ₁=n _p-max, be designated as

c(k ₁)＝1<k ₁≤n-1(5)

This very big gray-value pixel quantity is 1, equivalent minimum number of gray values 1<n _p-min≤ n-1, is called k ₂class block, wherein k ₂=n _p-min, be designated as

c(k ₂)＝1<k ₂≤n-1(6)

This equivalence is gray-value pixel quantity 1<n greatly _p-max≤ n-1, equivalent minimum number of gray values 1<n _p-min≤ n-1, is called mixing k class block, wherein k ₁=n _p-max, k ₂=n _p-min, and k ₁+ k ₂≤ n-1, is designated as

$c(k_1,k_2)=\left\{\begin{array}{c}1<k_1\&le;n-1\\ 1<k_2\&le;n-1\\ k_1+k_2\&le;n-1\end{array}\right.---\left(7\right)$

The gray-scale value order sequence by size of this piecemeal pixel, secondary maximum value is called secondary maximum base p ^s _b-max, respective pixel is called secondary maximum base pixel p _b-max; Secondary minimum value is called secondary minimum base p ^s _b-min, respective pixel is called secondary minimum base pixel p _b-min.

In sum, except waiting gray-scale value piecemeal, k ₁p is only had in class block _b-max, gray-scale value is k ₂p is only had in class block _b-min, gray-scale value is then existing p in mixing k class block and non-k class block _b-maxalso p is had _b-min, and likely p ^s _b-max=p ^s _b-min.

As shown in Figure 4, Fig. 4 is the block diagram of embed watermark information in reversible data concealing method of the present invention.The situation of the only maximum value embedding such as analysiss in the present embodiment.As can be seen from Figure 4, the 1st piecemeal, Label _k=0, represent that this is not a k class block, be suitable for the embedding method of conventional P VO, here, e _max=163-162=1, can embed information, herein b=0 at maximum gray scale 163 pixel place, therefore, and e _min=157-158=-1, can embed information, herein b=1 at minimal gray 157 pixel place, therefore,

2nd, 3,4 piecemeals, represent that these are all k ₁class block, is suitable for the embedding method of PVO-kAdaptive.In 2nd piecemeal, k ₁=2, p _b-maxpixel place mark position figure ${\mathrm{Label}}_{k_1}=1,$ Size remains unchanged, and ${e^k}_{max}={p^s}_{n-k_1+1}-{p^s}_{n-k_1}={p^s}_5-{p^s}_4=162-161=1,$ Therefore at eq (k ₁)={ n-k ₁+ 1, n-k ₁+ 2 ..., the pixel of the positions such as n}={5,6} embed information bit, herein b ₅=0, b ₆=1, perform ${\tilde{p}}_{eq\left(k_1\right)}^s={p^s}_{eq\left(k_1\right)}+b,$ Obtain ${\tilde{p}}_5^s={p^s}_5+b=162+0=162,{\tilde{p}}_6^s={p^s}_6+b=162+1=163.$ In 3rd piecemeal, k ₁=2, p _b-maxpixel place mark position figure size remains unchanged, and ${e^k}_{max}={p^s}_{n-k_1+1}-{p^s}_{n-k_1}={p^s}_5-{p^s}_4=162-160=2>1,$ Therefore by eq (k ₁)={ n-k ₁+ 1, n-k ₁+ 2 ..., the pixel of the positions such as n}={5,6} right shift, performs ${\tilde{p}}_{eq\left(k_1\right)}^s={p^s}_{eq\left(k_1\right)}+1,$ Obtain ${\tilde{p}}_5^s={p^s}_5+1=162+1=163,{\tilde{p}}_6^s={p^s}_6+1=162+1=163.$ In 4th piecemeal, k ₁=4, p _b-maxpixel place mark position figure size remains unchanged, and ${e^k}_{\max }={p^s}_{n-k_1+1}-{p^s}_{n-k_1}={p^s}_3-{p^s}_2=160-159=1,$ Therefore at eq (k ₁)={ n-k ₁+ 1, n-k ₁+ 2 ..., n}={3, the pixel of the positions such as 4,5,6} embed information bit, herein b ₃=0, b ₄=1, b ₅=1, b ₆=0, perform obtain ${\tilde{p}}_4^s={p^s}_4+b=160+1=161,{\tilde{p}}_5^s={p^s}_5+b=160+1=161,{\tilde{p}}_6^s={p^s}_6+b=160+0=160.$

It should be noted that the 2nd, 3, no matter its neighbor size of 157 pixels in 4 piecemeals, remain constant, this is different from the embedding condition of the first embedding grammar.Therefore the second embedding grammar and the first embedding grammar parallel running, do not interfere with each other.

Said process is with k ₁class block is illustrational, k ₂class block method is similar, and feature is identical.Be not difficult to find, the second embedding grammar of the present invention and the first embedding grammar independently carry out, and is independent of each other, enormously simplify data processing complexity.Certainly, now sacrifice the one pole value pixel in part k class block, available first embedding grammar embeds originally, but cannot carry information bit because being judged to be feature class block, have lost the capacity of being partially submerged into.In fact, because there is the pixel of k>1 bit to utilize in feature class block, and can sequentially embed, therefore population size does not reduce, and improves on the contrary.

Embed the average interference brought from information bit, the square error of k class block is

$\begin{array}{c}{\mathrm{MSE}}_k=\frac{1}{n_1\&times;n_2}\underset{i_k=1}{\overset{n_1}{\&Sigma;}}\underset{j_k=1}{\overset{n_2}{\&Sigma;}}{||I_k\left(i_k,j_k\right)-I_k^e\left(i_k,j_k\right)||}^2\\ =\frac{1}{n}\underset{i=1}{\overset{n}{\&Sigma;}}{\left(p_i-p_i^e\right)}^2\\ =\frac{1}{n}\left(\underset{i=1}{\overset{k_2}{\&Sigma;}}{\left(p_i-p_i^e\right)}^2+\underset{i=n-k_1+1}{\overset{n}{\&Sigma;}}{\left(p_i-p_i^e\right)}^2\right)\end{array}---\left(8\right)$

And

$\underset{i=1}{\overset{k_2}{\&Sigma;}}{(p_i-{p^e}_i)}^2=\left\{\begin{array}{ccc}{k}_2/2& if& {e^k}_{min}=1\\ k_2& if& {e^k}_{min}>1\end{array}\right.---\left(9\right)$

$\underset{i=n-k_1+1}{\overset{n}{\&Sigma;}}{(p_i-{p^e}_i)}^2=\left\{\begin{array}{ccc}{k}_1/2& if& {e^k}_{\max }=1\\ k_1& if& {e^k}_{\max }>1\end{array}\right.---\left(10\right)$

Thus, k ₁the embedding interference of class block

${\mathrm{MSE}}_{k_1}=\left\{\begin{array}{ccc}{k}_1/2n& if& {e^k}_{\max }=1\\ k_1/n& if& {e^k}_{\max }>1\end{array}\right.---\left(11\right)$

K ₂the embedding interference of class block

${\mathrm{MSE}}_{k2}=\left\{\begin{array}{ccc}{k}_2/2n& if& {e^k}_{min}=1\\ k_2/n& if& {e^k}_{min}>1\end{array}\right.---\left(12\right)$

The embedding interference of mixing k class block

${\mathrm{MSE}}_{k_h}=\left\{\begin{array}{ccc}(k_1+k_2)/2n& if& {e^k}_{\max }=1and{e^k}_{\min }=1\\ (k_1/2+k_2)/n& if& {e^k}_{\max }=1and{e^k}_{\min }>1\\ (k_1+k_2)/2n& if& {e^k}_{\max }>1and{e^k}_{\min }=1\\ (k_1+k_2)/n& if& {e^k}_{\max }>1and{e^k}_{\min }>1\end{array}\right.---\left(13\right)$

As mentioned above, embedding flexibility ratio and practicality has comparatively had very large lifting, makes each equivalent extreme value can carry information bit as required, embeds quality simultaneously and also obtain enhancing.

This embed watermark information step passes through the second embedding grammar embed watermark information to feature class block.In this embed watermark information step, the second embedding grammar comprises: determine secondary maximum value: the secondary maximum value location of pixels in identification characteristics class block is 1, forms secondary maximum value location of pixels figure; Computational prediction difference: the difference calculating maximum value and secondary maximum value in feature class block; Embed watermark information: when difference equals 1, then perform and be added on this multipole value sequence by the binary code of watermark data.

Specifically, recognition feature class block, carries out embedding information according to the second embedding grammar.This feature class block comprises: k ₁class block, k ₂class block and mixing k class block.After searching out feature class block, according to the piecemeal grey scale pixel value after ascending order arrangement, obtain the maximum value of sequence and minimal value size, number and position, and the size of secondary maximum value and secondary minimum value and position, carry out information bit embedding according to three kind blocks.

First kind block, is k ₁class block.Some maximum value pixels are only had likely to be modified.Mark i ∈ 1,2 ..., n}, ${e^k}_{max}={p^s}_{n-k_1+1}-{p^s}_{n-k_1},$ Then have

${\tilde{p}}_i^s=\left\{\begin{array}{ccc}{p^s}_i& if& 1\&le;i\&le;n-k_1\\ {p^s}_i+b& if& n-k_1+1\&le;i\&le;nand{e^k}_{\max }=1\\ {p^s}_i+1& if& n-k_1+1\&le;i\&le;nand{e^k}_{\max }>1\end{array}\right.---\left(14\right)$

Herein, e ^k _maxbe the predicated error of maximum value, { 0,1} is the information bit that will embed to b ∈.Clearly, just information insertion is performed when only having maximal value predicated error to be 1.

Equations of The Second Kind block, is k ₂class block.Some minimal value pixels are only had likely to be modified.Mark i ∈ 1,2 ..., n}, ${e^k}_{\min }={p^s}_{k_2}-{p^s}_{k_2+1},$ Then have

${\tilde{p}}_i^s=\left\{\begin{array}{ccc}{p^s}_i& if& k_2+1\&le;i\&le;n\\ {p^s}_i-b& if& 1\&le;i\&le;k_{2}and{e^k}_{\min }=-1\\ {p^s}_i-1& if& 1\&le;i\&le;k_{2}and{e^k}_{\min }<-1\end{array}\right.---\left(15\right)$

Herein, e ^k _minbe minimizing predicated error, { 0,1} is the information bit that will embed to b ∈.Clearly, just information insertion is performed when only having minimum value predicated error to be 1.

3rd class block, is mixing k class block.Existing some maximum value pixels are likely modified, and also have some minimal value pixels to be likely modified.Mark i ∈ 1,2 ..., n}, e ^k _maxand e ^k _minrespectively with k ₁class block and k ₂class block is identical, then have

${\tilde{p}}_i^s=\left\{\begin{array}{ccc}{p^s}_i& if& k_2+1\&le;i\&le;n-k_1\\ {p^s}_i+b& if& n-k_1+1\&le;i\&le;nand{e^k}_{\max }=1\\ {p^s}_i+1& if& n-k_1+1\&le;i\&le;nand{e^k}_{\max }>1\\ {p^s}_i-b& if& 1\&le;i\&le;k_{2}and{e^k}_{\min }=-1\\ {p^s}_i-1& if& 1\&le;i\&le;k_{2}and{e^k}_{\min }<-1\end{array}\right.---\left(16\right)$

Herein, { 0,1} is the information bit that will embed to b ∈.Clearly, only have maximum value error be 1 and minimal value predicated error for-1 time just perform information insertion.

This embedding supplementary step, embeds corresponding supplementary.This embedding supplementary step comprises: replace least significant bit (LSB): calculate supplementary length, extracts the least significant bit (LSB) of the front and supplementary equal length number pixel of image, and replaces by supplementary; Embed least significant bit (LSB): the least significant bit (LSB) sequence extracted is embedded into data and finally embeds in the later pixel of piecemeal.

Supplementary in this embedding supplementary step comprises: the location drawing and supplementary mark.The location drawing in this embedding supplementary step comprises spilling location of pixels figure, the full smooth block location drawing and base location of pixels figure.Supplementary in this embedding supplementary step identifies the location drawing size after comprising payload size, point block size, compression, finally embedding block index and finally embeds pixel index.

Specifically, supplementary mainly refers to embedding capacity, point block size, overflows location of pixels figure and finally embeds block index.The special supplementary of feature class block then comprises the full smooth block location drawing, base location of pixels figure and finally embed pixel index.

In sum, the total information of embedding can be designated watermark payload (PWP)+location drawing (LM)+supplementary mark (All), and wherein the location drawing comprises spilling location of pixels figure, the full smooth block location drawing and base location of pixels figure; For the image of picture size 512*512, supplementary mark (All) has 112bits, comprises

Payload size (18bits)

Divide block size n1*n2 (4bits)

Location drawing size 54bits after compression

Finally embed block index (18bits)

Finally embed pixel index (18bits)

The present invention and the first embedding grammar and two kinds of prior aries carry out control methods.Adopt MatlabR2013a platform, 64 Windows7 Ultimate operating systems, Intel (R) Core (TM) i7-2600CPU, dominant frequency 3.40Hz, internal memory 4.00GB environment carries out constant load and embeds experiment simulation.Consider n ₁, n ₂{ different partitioned mode in totally 16 such as 2,3,4,5} etc., is promoted to target determines that point block size is to obtain the highest PSNR value with fidelity for ∈.

For ease of comparison, the present invention selects identical test picture, mainly comprises Lena, Baboon, Airplane, Barbara, Elaine, Lake, Boat and Peppers eight comparative result of standard grayscale picture of width 512*512 resolution.Method of the present invention mainly embeds information bit by revising at most certain grey scale pixel value 1 unit, puts forth effort to promote to embed quality.Herein, contrast examination embeds 5000bits to PSNR value during maximum embedding capacity, and step size settings is 1000bits.The maximum embedding capacity of this eight width image is followed successively by 37000,13000,47000,21000,23000,26000, and 26000 and 31000bits.

As shown in Figure 5, wherein, Fig. 5 is the comparison diagram of reversible data concealing method of the present invention and other three kinds of methods, wherein, the comparison diagram of Fig. 5 a to be Lena picture be example, the comparison diagram of 5b to be Baboon picture be example, the comparison diagram of 5c to be Airplane picture be example, the comparison diagram of 5d to be Barbara picture be example, the comparison diagram of 5e to be Elaine picture be example, the comparison diagram of 5f to be Lake picture be example, the comparison diagram of Fig. 5 g to be Boat picture be example, the comparison diagram of Fig. 5 h to be Peppers picture be example.On figure, the first control methods is referred to as " Sachnevetal "..Second control methods referred to as " Lietal. ", namely the first embedding grammar.3rd control methods is referred to as Ouetal.).The present invention is referred to as " Proposed ".

As can be seen from Figure 5, compared with the 3rd control methods, the two Performance comparision is close.At the low embedding rate place of Lena and Airplane two width picture, performance is lower, but middle high embedding rate part then has obvious improvement, this is because low embedding rate place, 3rd control methods have employed thresholding preference policy, and our rule causes greatly higher interference due to location drawing accounting; In Baboon and Barbara picture, performance is slightly low, this is because this two width picture texture level is complicated, and the 3rd control methods performs embed wholly, and has coordinated thresholding preference policy.Elaine, Lake, Boat and Peppers tetra-in width picture performance then promote a lot, this illustrates that this method has more outstanding fidelity performance in middle high embedding rate application.Reference table 1 and table 2, the method for method of the present invention corresponding 10000bits embedding ratio the 3rd control methods on average improves 0.66dB, and corresponding 20000bits embeds and improves 1.13dB.

Table 1

Table 2

As can be seen from table 1 above and table 2, at given embedding load in most cases, the method that the present invention proposes can obtain higher PSNR value.

Relatively the first control methods, the method that the present invention proposes all achieves better performance in most circumstances, but when close to max cap., performance is equally matched.Reference table 1 and table 2, the method for method of the present invention corresponding 10000bits embedding ratio first control methods on average improves 2.91dB, and corresponding 20000bits embeds and improves 2.73dB.

Comparatively speaking, corresponding all test pictures, the method that the present invention proposes all obtains better performance.Reference table 1 and table 2, the method for method of the present invention corresponding 10000bits embedding ratio second control methods on average improves 1.53dB, and corresponding 20000bits embeds and improves 2.02dB.

In general, method of the present invention achieves good performance, and embedding flexibility ratio and practicality has comparatively had very large lifting, makes each equivalent extreme value can carry information bit as required, embeds quality simultaneously and also obtain enhancing.

The present invention also provides a kind of information extraction and image recovery method.Because the present invention has effectively accomplished the seamless fusion of the first embedding grammar and the second embedding grammar, when recovery, the first embedding grammar and the two or two embedding grammar independently carry out, find that there is the image section of employing first embedding grammar, then use extraction and the Postprocessing technique of the first embedding grammar, owing to being prior art, be not repeated.Find feature class block employing second embedding grammar information extraction and image recovery process.

Specifically, this feature class block comprises: k ₁class block, k ₂class block and mixing k class block, recover according to the difference of class block below.

When identifying k ₁during class block, in the case, the information bit extracted is

$b={\tilde{p}}_i^s-({p^s}_{n-k_1}+1)---\left(17\right)$

Image recovery scheme is,

${p^s}_i=\left\{\begin{array}{ccc}{\tilde{p}}_i^s& if& 1\&le;i\&le;n-k_1\\ {\tilde{p}}_i^s-b& if& n-k_1+1\&le;i\&le;nand{\tilde{e}}_{\max }^k\&Element;\left\{1,2\right\}\\ {\tilde{p}}_i^s-1& if& n-k_1+1\&le;i\&le;nand{\tilde{e}}_{\max }^k>2\end{array}\right.---\left(18\right)$

Herein, it is the predicated error of maximum value.Clearly, for the pixel embedding information bit, the information bit b utilizing formula [17] to extract is with secondary maximum base p ^s _b-maxbased on weigh, the image intensity value therefore recovered is

${p^s}_i={\tilde{p}}_i^s-b={\tilde{p}}_i^s-({\tilde{p}}_i^s-({p^s}_{n-k_1}+1\left)\right)={p^s}_{n-k_1}+1---\left(19\right)$

That is, the image intensity value of recovery is completely by secondary maximum base p ^s _b-maxdecide.And with then identify b=0 and b=1 respectively.

When setting out k ₂during class block, in the case, the information bit extracted is

$b=({p^s}_{k_2}-1)-{\tilde{p}}_i^s---\left(20\right)$

Image recovery scheme is,

${p^s}_i=\left\{\begin{array}{ccc}{\tilde{p}}_i^s& if& k_2+1\&le;i\&le;n\\ {\tilde{p}}_i^s+b& if& 1\&le;i\&le;k_{2}and{\tilde{e}}_{\min }^k\&Element;\left\{-1,-2\right\}\\ {\tilde{p}}_i^s+1& if& 1\&le;i\&le;k_{2}and{\tilde{e}}_{\min }^k<-2\end{array}\right.---\left(21\right)$

Herein, it is minimizing predicated error.Clearly, for the pixel embedding information bit, the information bit b utilizing formula [20] to extract is the following minimal basis p ^s _b-maxbased on weigh, the image intensity value therefore recovered is

${p^s}_i={\tilde{p}}_i^s+b={\tilde{p}}_i^s+\left(\right({p^s}_{k_2}-1)-{\tilde{p}}_i^s)={p^s}_{k2}-1---\left(22\right)$

That is, the image intensity value of recovery is completely by secondary minimum base p ^s _b-mindecide.And with then identify b=0 and b=1 respectively.

When identifying mixing k class block, in the case, $i\&Element;\{1,2,...,n\},{\tilde{e}}_{max}^k={\tilde{p}}_{n-k_1+1}^s-{p^s}_{n-k_1},{\tilde{e}}_{\min }^k={\tilde{p}}_{k_2}^s-{p^s}_{k_2+1},$ The information bit that equivalent maximum value place extracts is

$b_1={\tilde{p}}_i^s-({p^s}_{n-k_1}+1)---\left(23\right)$

The information bit that equivalent minimal value place extracts is

$b_2=({p^s}_{k_2}-1)-{\tilde{p}}_i^s---\left(24\right)$

Image recovery scheme is,

${p^s}_i=\left\{\begin{array}{ccc}{\tilde{p}}_i^s& if& k_2+1\&le;i\&le;n-k_1\\ {\tilde{p}}_i^s-b_1& if& n-k_1+1\&le;i\&le;nand{\tilde{e}}_{\max }^k\&Element;\left\{1,2\right\}\\ {\tilde{p}}_i^s-1& if& n-k_1+1\&le;i\&le;nand{\tilde{e}}_{\max }^k>2\\ {\tilde{p}}_i^s+b_2& if& 1\&le;i\&le;k_{2}and{\tilde{e}}_{\min }^k\&Element;\left\{-1,-2\right\}\\ {\tilde{p}}_i^s+1& if& 1\&le;i\&le;k_{2}and{\tilde{e}}_{\min }^k<-2\end{array}\right.---\left(25\right)$

Herein, with maximum value and minimizing predicated error respectively.Clearly, for the pixel embedding information bit, the information bit b that formula [23] extracts is utilized ₁with secondary maximum base p ^s _b-maxbased on weigh, the image intensity value therefore recovered is

${p^s}_i={\tilde{p}}_i^s-b={\tilde{p}}_i^s-({\tilde{p}}_i^s-({p^s}_{n-k_1}+1\left)\right)={p^s}_{n-k_1}+1---\left(26\right)$

That is, the image intensity value of recovery is completely by secondary maximum base p ^s _b-maxdecide.And with then identify b=0 and b=1 respectively.

Utilize the information bit b that formula [23] extracts ₂the following minimal basis p ^s _b-minbased on weigh, the image intensity value therefore recovered is

${p^s}_i={\tilde{p}}_i^s+b_2={\tilde{p}}_i^s+\left(\right({p^s}_{k_2}-1)-{\tilde{p}}_i^s)={p^s}_{k_2}-1---\left(27\right)$

That is, the image intensity value of recovery is completely by secondary minimum base p ^s _b-mindecide.And with then identify b=0 and b=1 respectively.

The present invention can also implement in the systems such as windows and Linux.The embodiment of the present invention describes with reference to according to the process flow diagram of the method for the embodiment of the present invention, terminal device (system) and computer program and/or block scheme.Should understand can by the combination of the flow process in each flow process in computer program instructions realization flow figure and/or block scheme and/or square frame and process flow diagram and/or block scheme and/or square frame.These computer program instructions can being provided to the processor of multi-purpose computer, special purpose computer, Embedded Processor or other programmable data processing terminal equipment to produce a machine, making the instruction performed by the processor of computing machine or other programmable data processing terminal equipment produce device for realizing the function of specifying in process flow diagram flow process or multiple flow process and/or block scheme square frame or multiple square frame.

This type of computer program instructions also can be stored in can in the computer-readable memory that works in a specific way of vectoring computer or other programmable data processing terminal equipment, the instruction making to be stored in this computer-readable memory produces the manufacture comprising command device, and this command device realizes the function of specifying in process flow diagram flow process or multiple flow process and/or block scheme square frame or multiple square frame.

This type of computer program instructions also can be loaded on computing machine or other programmable data processing terminal equipment, make to perform sequence of operations step to produce computer implemented process on computing machine or other programmable terminal equipment, thus the instruction performed on computing machine or other programmable terminal equipment is provided for the step realizing the function of specifying in process flow diagram flow process or multiple flow process and/or block scheme square frame or multiple square frame.

Although described the preferred embodiment of the embodiment of the present invention, those skilled in the art once obtain the basic creative concept of cicada, then can make other change and amendment to these embodiments.So claims are intended to be interpreted as comprising preferred embodiment and falling into all changes and the amendment of embodiment of the present invention scope.

Finally, also it should be noted that, in this article, the such as relational terms of first and second grades and so on is only used for an entity or operation to separate with another entity or operational zone, and not necessarily requires or imply the relation that there is any this reality between these entities or operation or sequentially.And, term " comprises ", " comprising " or its any other variant are intended to contain comprising of nonexcludability, thus make to comprise the process of a series of key element, method, article or terminal device and not only comprise those key elements, but also comprise other key elements clearly do not listed, or also comprise by the intrinsic key element of this process, method, article or terminal device.When not more restrictions, the key element limited by statement " comprising ... ", and be not precluded within process, method, article or the terminal device comprising described key element and also there is other identical element.

A kind of the synchronous method above embodiment of the present invention provided and synchro system, be described in detail, apply specific case herein to set forth the principle of the embodiment of the present invention and embodiment, the explanation of above embodiment is just for helping method and the core concept thereof of understanding the embodiment of the present invention; Meanwhile, for one of ordinary skill in the art, according to the thought of the embodiment of the present invention, all will change in specific embodiments and applications, in sum, this description should not be construed as the restriction to the embodiment of the present invention.

Claims (10)

1. a reversible data concealing method, is characterized in that, comprising:

Pre-treatment step, carries out piecemeal by original, pixel domain image and sorts by gray-scale value in block;

Identification of steps, is undertaken the sequence after sequence detecting, identifying and identification characteristics class block;

Embed watermark information step, to feature class block by the second embedding grammar embed watermark information, this second embedding grammar comprises:

Determine secondary maximum value: the secondary maximum value location of pixels in identification characteristics class block is 1, form secondary maximum value location of pixels figure;

Computational prediction difference: the difference calculating maximum value and secondary maximum value in feature class block;

Embed watermark information: when difference equals 1, be then added on multipole value sequence by the binary code of watermark data;

Embed supplementary step, embed corresponding supplementary.

2. reversible data concealing method according to claim 1, is characterized in that, the feature class block in this identification of steps comprises: k ₁class block, k ₂class block and mixing k class block;

This k ₁class block is minimum gray-value pixel quantity is 1, equivalent greatly number of gray values 1<n _p-max≤ n-1, wherein k ₁=n _p-maxand 1<k1≤n-1;

This k ₂class block is very big gray-value pixel quantity is 1, equivalent minimum number of gray values 1<n _p-min≤ n-1, wherein k ₂=n _p-minand 1<k2≤n-1;

This mixing k class block is equivalent greatly gray-value pixel quantity 1<n _p-max≤ n-1, equivalent minimum number of gray values 1<n _p-min≤ n-1, wherein k ₁=n _p-max, k ₂=n _p-minand k ₁+ k ₂≤ n-1.

3. reversible data concealing method according to claim 1 and 2, is characterized in that, the gray-scale value order sequence by size of this block pixel, secondary maximum value is called secondary maximum base p ^s _b-max, respective pixel is called secondary maximum base pixel p _b-max; Secondary minimum value is called secondary minimum base p ^s _b-min, respective pixel is called secondary minimum base pixel p _b-min.

4. reversible data concealing method according to claim 1, is characterized in that, this embedding supplementary step comprises:

Replace least significant bit (LSB): calculate supplementary length, extract the least significant bit (LSB) of the front and supplementary equal length number pixel of image, and replace by supplementary;

Embed least significant bit (LSB): the least significant bit (LSB) sequence extracted be embedded in the later pixel of the last embedded block of data.

5. reversible data concealing method according to claim 1, is characterized in that, the supplementary in this embedding supplementary step comprises: the location drawing and supplementary mark.

6. a restoration methods for hiding reversible data, is characterized in that, comprising:

Read supplementary step, after receiving the image of embed watermark information, read and obtain complete supplementary, this supplementary comprises the location drawing and supplementary mark;

Pre-treatment step, carries out piecemeal by the image of embed watermark information and sorts by gray-scale value in block;

Identification of steps, is undertaken the sequence after sequence detecting, identifying and identification characteristics class block;

Treatment step, the secondary maximum that decompresses out from location drawing value location of pixels figure, determines each piece of location drawing, identification block type; Determine secondary maximum value pixel: according to the secondary maximum value location of pixels figure decompressed, determine the secondary maximum value pixel of each piece, be called secondary maximum base pixel; Calculate the difference of the large pixel of secondary maximum base grey scale pixel value and secondary maximum base pixel, difference is 1 extraction watermark information 0, and grey scale pixel value is constant; Difference is 2 extraction watermark informations 1, and grey scale pixel value subtracts 1; Difference is greater than 2 marks without embedding information, and grey scale pixel value is constant; From the pixel that the last embedded block of data is later, extract the least significant bit (LSB) sequence of embedding, and be substituted in the pixel that supplementary takies;

Extract watermark information and Recovery image step, duplicate marking step and treatment step, process each block successively and extract watermark information and each maximum pixel gray-scale value in recovery block, obtainoriginal image.

7. restoration methods according to claim 6, is characterized in that, this feature class block comprises: k ₁class block, k ₂class block and mixing k class block.

8. restoration methods according to claim 7, is characterized in that, this k ₁class block is minimum gray-value pixel quantity is 1, equivalent greatly number of gray values 1<n _p-max≤ n-1, wherein k ₁=n _p-maxand 1<k ₁≤ n-1;

When identifying k ₁during class block, in the case, i ∈ 1,2 ..., n}, the information bit extracted is:

$b={\tilde{p}}_i^s-({p^s}_{n-k_1}+1),$

Image recovery scheme is:

${p^s}_i=\left\{\begin{array}{ccc}{\tilde{p}}_i^s& if& 1\&le;i\&le;n-k_1\\ {\tilde{p}}_i^s-b& if& n-k_1+1\&le;i\&le;nand{\tilde{e}}_{\max }^k\&Element;\{1,2\}\\ {\tilde{p}}_i^s-1& if& n-k_1+1\&le;i\&le;nand{\tilde{e}}_{\max }^k>2\end{array}\right.$

The image intensity value recovered is:

${p^s}_i={\tilde{p}}_i^s-b={\tilde{p}}_i^s-({\tilde{p}}_i^s-({p^s}_{n-k_1}+1\left)\right)={p^s}_{n-k_1}+1.$

9. restoration methods according to claim 7, is characterized in that, this k ₂class block is very big gray-value pixel quantity is 1, equivalent minimum number of gray values 1<n _p-min≤ n-1, wherein k ₂=n _p-minand 1<k ₂≤ n-1;

When identifying k ₂during class block, in the case, i ∈ 1,2 ..., n}, the information bit extracted is:

$b=({p^s}_{k_2}-1)-{\tilde{p}}_i^s$

Image recovery scheme is:

${p^s}_i=\left\{\begin{array}{ccc}{\tilde{p}}_i^s& if& k_2+1\&le;i\&le;n\\ {\tilde{p}}_i^s+b& if& 1\&le;i\&le;k_{2}and{\tilde{e}}_{\max }^k\&Element;\{-1,-2\}\\ {\tilde{p}}_i^s+1& if& 1\&le;i\&le;k_{2}and{\tilde{e}}_{\min }^k<-2\end{array}\right.$

The image intensity value recovered is:

${p^s}_i={\tilde{p}}_i^s+b={\tilde{p}}_i^s+\left(\right({p^s}_{k_2}-1)-{\tilde{p}}_i^s)={p^s}_{k_2}-1.$

10. restoration methods according to claim 7, is characterized in that, this mixing k class block is equivalent greatly gray-value pixel quantity 1<n _p-max≤ n-1, equivalent minimum number of gray values 1<n _p-min≤ n-1, wherein k ₁=n _p-max, k ₂=n _p-min, and k ₁+ k ₂≤ n-1;

When identifying mixing k class block, in the case, i ∈ 1,2 ..., n}, ${\tilde{e}}_{max}^k={\tilde{p}}_{n-k_1+1}^s-{p^s}_{n-k_1},{\tilde{e}}_{min}^k={\tilde{p}}_{k_2}^s-{p^s}_{k_2+1},$ The information bit that equivalent maximum value place extracts is:

$b_1={\tilde{p}}_i^s-({p^s}_{n-k_1}+1)$

The information bit that equivalent minimal value place extracts is:

$b_2=({p^s}_{k_2}-1)-{\tilde{p}}_i^s$

Image recovery scheme is:

${p^s}_i=\left\{\begin{array}{ccc}{\tilde{p}}_i^s& if& k_2+1\&le;i\&le;n-k_1\\ {\tilde{p}}_i^s-b_1& if& n-k_1+1\&le;i\&le;nand{\tilde{e}}_{\max }^k\&Element;\{1,2\}\\ {\tilde{p}}_i^s-1& if& n-k_1+1\&le;i\&le;nand{\tilde{e}}_{\max }^k>2\\ {\tilde{p}}_i^s+b_2& if& 1\&le;i\&le;k_{2}and{\tilde{e}}_{\min }^k\&Element;\{-1,-2\}\\ {\tilde{p}}_i^s+1& if& 1\&le;i\&le;k_{2}and{\tilde{e}}_{\min }^k<-2\end{array}\right.$

The image intensity value recovered is:

${p_i}^s={\tilde{p}}_i^s-b={\tilde{p}}_i^s-({\tilde{p}}_i^s-({p^s}_{n-k_1}+1\left)\right)={p^s}_{n-k_1}+1.$