CN110246076B - High dynamic range image watermarking method based on Tucker decomposition - Google Patents

Abstract

The invention discloses a high dynamic range image watermarking method based on Tucker decomposition, which comprises two parts of watermark embedding and watermark extraction, wherein in the watermark embedding process, a high dynamic range host image is expressed into a form of three-order tensor, then the high dynamic range host image is processed by Tucker3 decomposition, and an obtained first characteristic diagram of a core tensor is used as an embedding carrier of watermarking information, so that the first characteristic diagram of the core tensor covers the main energy of a high dynamic range host image, and the embedded watermarking information can be diffused into three channels of R, G and B of the high dynamic range watermarking image along with the inverse transformation of the decomposition, thereby effectively improving the robustness; in the watermark extraction process, an original host image with a high dynamic range is not needed, and blind extraction of watermark information is realized; in addition, the method of the invention can not damage the internal structure of the high dynamic range image and can obtain better effects in the aspects of invisibility and embedding capacity.

Description

High dynamic range image watermarking method based on Tucker decomposition

Technical Field

The invention relates to an image watermarking method, in particular to a high dynamic range image watermarking method based on Tucker decomposition.

Background

With the wide application of High Dynamic Range (HDR) imaging technology in the fields of consumer electronics, image production, virtual reality, remote sensing, medical detection, and the like, the issue of copyright protection of High Dynamic Range images is receiving increasing attention. Unlike traditional Low Dynamic Range (LDR) images, high Dynamic Range images are usually represented and stored as floating point type data, and their Dynamic Range can reach or exceed 9 orders of magnitude, which not only can improve the accuracy of scene brightness information to a certain extent, but also can bring richer color details and light and shade levels. However, since existing low dynamic range display devices can typically only display 3 orders of magnitude of dynamic range, tone Mapping (TM) preprocessing is often required for high dynamic range images in order to be able to present rich detailed information of the high dynamic range images on common display devices, which is undoubtedly a unique and unavoidable form of attack for copyright protection of high dynamic range images. In addition, through the analysis of the existing global tone mapping operator, it is found that tone mapping is a non-linear mapping process, which is specifically expressed as: after the high dynamic range image containing the watermark information is subjected to tone mapping processing, the watermark information embedded in the low brightness area is increased along with the amplification of the pixel value of the image, and the watermark information embedded in the high brightness area is reduced or even lost along with the compression of the pixel value of the image, so that the high brightness area of the image presents poorer robustness, namely presents different robustness in different brightness areas of the image. Although the conventional low dynamic range image watermarking technology has become mature, it is difficult to exhibit a good performance if the conventional low dynamic range image watermarking technology is simply transplanted to the high dynamic range image field in consideration of the characteristics of the high dynamic range image and the nonlinear characteristics of tone mapping attack.

Currently, research on high dynamic range image watermarking technology can be roughly divided into the following two categories:

one type is fragile watermarking, and the methods pay more attention to invisibility and embedding capacity, and watermark information is often embedded in a space domain by using a storage format of a high dynamic range image. Such as: yu, wang, chang and the like all use an index channel E in an RGBE storage format to guide lossless embedding of watermark information; cheng, li, etc. respectively combine Least Significant Bit (LSB) algorithm to embed watermark information on RGBE storage format or LogLuv (TIFF) storage format of high dynamic range image; lin et al uses 10-bit mantissa bits of high dynamic range images in the OpenEXR storage format to convey secret information.

The other type is robustness watermarking, and the method mostly considers the characteristics of the structure and the like of the high dynamic range image and embeds the watermark information in the transform domain of the image. Such as: guerrini et al designed a perception mask based on brightness, texture and edge information, and utilized Quantization Index Modulation (QIM) technique to embed watermark information in the low frequency sub-band of Discrete Wavelet Transform (DWT) domain featuring the kurtosis value, the algorithm tested 7 tone mapping attacks and 15 high dynamic range images, with certain robustness and invisibility, but the average bit error rate up to 29%(ii) a Xue et al successively proposed two schemes, one of which is to perform μ -Law-based tone mapping processing on a high dynamic range image to obtain a corresponding low dynamic range image, and then perform watermark information embedding in a DWT domain of the low dynamic range image, and the other is to perform logarithm preprocessing on the high dynamic range image, and use a bilateral filter to obtain a detail layer, and then perform watermark information embedding in the DWT domain of the detail layer, wherein both schemes embody better invisibility, but only test few high dynamic range images, and the error rate is still higher; wu et al, which is to embed watermark information into an image after known tone mapping processing in a Discrete Cosine Transform (DCT) domain, however, the algorithm only shows good performance for a predetermined tone mapping attack and its related parameters in the embedding process, which has great limitations in practical applications; the Solachidis et al embed watermark information in DWT domain in turn for low dynamic range images with different exposure degrees, although the idea of multiple embedding obtains better robustness, the invisibility is obviously reduced; in the same year, solachidis et al combined with Human Visual System (HVS) characteristics in DWT domain designed a perception mask based on Just Noticeable Distortion (JND) and Contrast Sensitivity Function (CSF) and selected proper embedding region and reasonable embedding strength based on the perception mask, the algorithm showed better robustness against 7 tone mapping attacks, but the embedding amount was only 128 bits; maiorana et al sequentially performs logarithm, DWT and RDCT processing on the high dynamic range image, and then utilizes a quantization index modulation technology to embed watermark information, and the algorithm tests 6 tone mapping attacks and 15 high dynamic range images, and has good invisibility, but the average error rate is still about 20%; anbarjafari et al first performs preprocessing such as blocking, DWT, chirp-Z transform (CZT), QR (orthogonal triangle) decomposition, singular Value Decomposition (SVD) and the like on a host image in sequence to obtain a Singular value matrix S of the host image, and then performs preprocessing on the original watermark messageSingular value decomposition is carried out to obtain S _w The watermark information is embedded by combining an additive embedding principle, the algorithm shows better robustness when resisting 14 tone mapping attacks, but the watermark extraction process is non-blind; bai et al propose a robust watermarking algorithm based on spatial activity, the algorithm first utilizes Non-subsampled Contourlet Transform (NSCT) and singular value decomposition to extract structural information representing an image as a watermark embedding carrier, and combines the provided concept of high dynamic range image watermarking activity to design a hierarchical embedding strength mechanism and a mixed perception mask to optimize the robustness and invisibility of the algorithm, and the algorithm presents better robustness against the existing 27 tone mapping attacks. In summary, although the existing high dynamic range image robustness watermarking algorithm has achieved certain effect in resisting the minority tone mapping attack, the algorithm does not fully consider the following two problems: firstly, the conventional data processing methods such as DCT, DWT, redundant Wavelet Transform (RDWT), NSCT, SVD, etc. all convert high-dimensional data into vectors for representation, but this not only causes the dimensionality of the data samples to be too high, but also destroys the internal structure of the data itself; secondly, tone mapping is a non-linear mapping process, that is, the watermark image shows inconsistent robustness in different brightness regions after being attacked by tone mapping. Therefore, it is especially important for copyright protection of high dynamic range images to research a high-robustness high-dynamic range image blind watermarking method which can effectively resist tone mapping attack and does not damage the internal structure of the image in the image processing process.

Disclosure of Invention

The invention aims to solve the technical problem of providing a high dynamic range image watermarking method based on Tucker decomposition, which cannot damage the internal structure of a high dynamic range image, has better robustness in resisting tone mapping attack, obtains better effects in the aspects of invisibility and embedding capacity, and extracts watermarks in a blind way.

The technical scheme adopted by the invention for solving the technical problems is as follows: a high dynamic range image watermarking method based on Tucker decomposition is characterized by comprising two parts of watermark embedding and watermark extracting;

the watermark embedding part comprises the following specific steps:

step 1_1: let I _host High dynamic range host image, I, representing information to be embedded with a watermark _host For RGB color images, I _host R, G, and B color channels of (1) are correspondingly denoted as I _{host_r} 、I _{host_g} And I _{host_b} (ii) a Wherein, I _host 、I _{host_r} 、I _{host_g} And I _{host_b} Are all M in width _host And the heights are all N _host ；

Step 1_2: will I _host Expressed as third order tensor, denoted A _host (ii) a Then using Tucker3 decomposition algorithm to pair A _host Performing tensor decomposition to obtain A _host Core tensor of (D), noted as B _host (ii) a And B is _host 1 st channel as I _host First characteristic diagram of (1), marked as B _{host_1} (ii) a B is to be _host The 2 nd channel of (2) is taken as I _host Second characteristic image of (1), noted as B _{host_2} (ii) a B is to be _host As the 3 rd channel of _host Third feature image of (1), noted as B _{host_3} (ii) a Wherein, A _host And B _host All have a size of M _host ×N _host ×3，B _{host_1} 、B _{host_2} And B _{host_3} Are all M in width _host And the heights are all N _host ；

Step 1 \ u 3: if M is _host And N _host All can be covered by N _block Integer division, then pair B _{host_1} 、I _{host_r} 、I _{host_g} And I _{host_b} Filling pixel points is not carried out, and B is added _{host_1} 、I _{host_r} 、I _{host_g} And I _{host_b} Remap is recorded as B' _{host_1} 、I' _{host_r} 、I' _{host_g} And l' _{host_b} ；

If M is _host Can be covered with N _block Trimming and removing deviceAnd N is _host Can not be covered by N _block Integer division, then pair B _{host_1} 、I _{host_r} 、I _{host_g} And I _{host_b} Filling pixel points at respective lower sides, and filling N _block -mod(N _host ,N _block ) A line and B _{host_1} The image obtained after the filling of the pixel points is recorded as B' _{host_1} Is shown by _{host_r} The image obtained after the filling of the pixel points is recorded as I 'again' _{host_r} Is shown by _{host_g} The image obtained after the filling of the pixel points is recorded as I 'again' _{host_g} A first reaction of _{host_b} The image obtained after the filling of the pixel points is recorded as I 'again' _{host_b} ；

If M is _host Can not be covered by N _block Integer division of N _host Can be covered with N _block Integer division, then pair B _{host_1} 、I _{host_r} 、I _{host_g} And I _{host_b} Filling pixel points on respective right sides, and filling N _block -mod(M _host ,N _block ) Column and B _{host_1} The image obtained after the filling of the pixel points is recorded as B' _{host_1} Is shown by _{host_r} The image obtained after the filling of the pixel points is recorded as I 'again' _{host_r} A first reaction of _{host_g} The image obtained after the pixel point is filled is recorded as I' _{host_g} A first reaction of _{host_b} The image obtained after the pixel point is filled is recorded as I' _{host_b} ；

If M is _host Can not be covered by N _block Integer and N _host Can not be covered by N _block Integer division, then pair B _{host_1} 、I _{host_r} 、I _{host_g} And I _{host_b} Filling pixel points on respective right side and lower side, and filling N _block -mod(M _host ,N _block ) Column sum N _block -mod(N _host ,N _block ) A line and B _{host_1} The image obtained after the filling of the pixel points is recorded as B' _{host_1} Is shown by _{host_r} The image obtained after the filling of the pixel points is recorded as I 'again' _{host_r} Is shown by _{host_g} The image obtained after the filling of the pixel points is recorded as I 'again' _{host_g} Is shown by _{host_b} The image obtained after the pixel point is filled is recorded as I' _{host_b} ；

Above, N _block Is odd number, N _block >1，B' _{host_1} 、I' _{host_r} 、I' _{host_g} And l' _{host_b} Are all M 'in width' _host And the heights are all N' _host ，

(symbol)

Mod () represents the sign of the modulo operation for the sign of the rounding up operation;

step 1_4: b' _{host_1} B 'is embedded into carrier as watermark' _{host_1} Is divided into

A size of N _block ×N _block Image block of (1), will be to B' _{host_1} And recording image blocks with coordinate positions of (i, j) in all the divided image blocks as B' _{host_1} (i, j); wherein, the first and the second end of the pipe are connected with each other,

step 1 \ u 5: is prepared from' _{host_r} 、I' _{host_g} And I' _{host_b} Corresponds to as I' _host R, G, and B color channels; then obtain I' _host Has a width of

And has a height of

Brightness Mask, denoted Mask _lum And Mask _lum Storing as a secret Key Key 1; followed by masking _lum Whether the pixel value of each pixel point in the pixel list is B 'or not is judged' _{host_1} In the same coordinate position in the image blockWatermark information of B' _{host_1} (i, j), if Mask _lum (i, j) =0 is judged to be B' _{host_1} (i, j) is not embedded with watermark information, and B' _{host_1} (i, j) is defined as no processing block; if Mask _lum (i, j) =1 is judged to be B' _{host_1} (i, j) is embedded with watermark information, and B' _{host_1} (i, j) is defined as a block into which a watermark is to be embedded; wherein, I' _host Is M 'in width' _host And the height is N' _host ，Mask _lum (i, j) represents Mask _lum The pixel value of the pixel point with the middle coordinate position of (i, j);

step 1_6: in B' _{host_1} B 'is embedded in each block to be embedded with watermark' _{host_1} (i, j) is the block into which the watermark is to be embedded, then in B' _{host_1} The process of embedding watermark information in (i, j) is as follows: b' _{host_1} (i, j) the pixel value of the center pixel point is marked as G _t (i, j), mixing B' _{host_1} The pixel values of all the pixel points except the central pixel point in (i, j) are arranged in sequence to form a row vector, and the row vector is recorded as G _{host_1,i,j} B' _{host_1} (i, j) the predicted pixel value of the center pixel is marked as G _p (i, j); b' _{host_1} (i, j) after embedding watermark information, defining the embedded watermark block as B ^w _{host_1} (i, j) mixing B ^w _{host_1} (i, j) the pixel value of the center pixel point is recorded as

When the watermark information to be embedded is 1, if | G _t (i,j)|＞|G _p (i, j) | × (1 + T) then order

If G _t (i,j)|≤|G _p (i, j) | × (1 +T) then order

When the watermark information to be embedded is 0, if | G _t (i,j)|＜|G _p (i, j) | × (1-T) then order

If | G _t (i,j)|≥|G _p (i, j) | × (1-T) then order

Wherein G is _{host_1,i,j} Has a dimension of 1 (N) _block ×N _block -1)，G _p (i, j) is using the local correlation models Γ and G _{host_1,i,j} The result of the calculation is that,

m is a positive integer, m is an initial value of 1,1-N _block ×N _block -1，G _{host_1,i,j} (1, m) represents G _{host_1,i,j} The middle subscript is the element value of the element of (1, m), and the dimensionality of Γ is (N) _block ×N _block -1) × 1, storing Γ as a Key2, Γ (m, 1) representing an AR coefficient with subscript (m, 1) in Γ, "|" being an absolute value arithmetic symbol, T being watermark embedding strength,

"=" in (1) is an assigned symbol, sign () represents a function of taking a symbol;

step 1 \ u 7: to B' _{host_1} All unprocessed blocks and all watermark embedded blocks in the image block combination, and reconstructing to obtain an image containing watermark information, which is recorded as B' _{host_1_w} (ii) a Then according to the reverse process of step 1_3, to B' _{host_1_w} Processing the image to obtain an image with a width of M _host And a height of N _host And recording the processed image as B _{host_1_w} And is used as a first characteristic diagram containing watermark information; and then the inverse transformation pair B of the Tucker3 decomposition algorithm is utilized _{host_1_w} 、B _{host_2} And B _{host_3} Processing the image to obtain a watermark image marked as I _w (ii) a Wherein, I _w Has a width of M _host And a height of N _host ；

Step 1 \ u 8: the watermark embedding end sends a secret Key Key1 and a secret Key Key2 to the watermark extraction end;

the watermark extracting part comprises the following specific steps:

step 2_1: reading watermark image containing watermark information, recorded as I' _w (ii) a Wherein, I' _w Is an RGB color image, I' _w Has a width of M _host And a height of N _host ，I' _w The watermark image is the watermark image which is not attacked or the watermark image which is attacked by tone mapping;

step 2_2: is prepared from' _w Expressed as third order tensor, denoted A _w (ii) a Then using Tucker3 decomposition algorithm to pair A _w Performing tensor decomposition to obtain A _w Core tensor of (D), denoted as B _w (ii) a And B is _w Of 1 as I' _w Is marked as B _{w_1} (ii) a B is to be _w Of as l 'is the 2 nd channel of' _w Second characteristic image of (1), noted as B _{w_2} (ii) a B is to be _w Of as l' _w And a third characteristic image of (1), denoted as B _{w_3} (ii) a Wherein A is _w And B _w All being M _host ×N _host ×3，B _{w_1} 、B _{w_2} And B _{w_3} Are all M in width _host And the heights are all N _host ；

Step 2_3: if M is _host And N _host All can be covered by N _block Integer division, then pair B _{w_1} Filling pixel points is not carried out, and B is added _{w_1} Remap as B' _{w_1} ；

If M is _host Can be covered with N _block Integer and N _host Can not be covered by N _block Integer division, then pair B _{w_1} The lower side of the N-shaped substrate is filled with pixel points, and N is filled _block -mod(N _host ,N _block ) A line and B _{w_1} The image obtained after the filling of the pixel points is recorded as B' _{w_1} ；

If M is _host Can not be covered by N _block Integer and N _host Can be covered with N _block Integer division, then pair B _{w_1} The right side of the image is filled with pixel points, and N is filled _block -mod(M _host ,N _block ) Column and B _{w_1} The image obtained after the filling of the pixel points is recorded as B' _{w_1} ；

If M is _host Can not be covered by N _block Integer and N _host Can not be covered by N _block Integer division, then pair B _{w_1} The right side and the lower side are filled with pixel points, and N is filled _block -mod(M _host ,N _block ) Column sum N _block -mod(N _host ,N _block ) A line and B _{w_1} The image obtained after the filling of the pixel points is recorded as B' _{w_1} ；

Above, N _block Is odd number, N _block >1，B' _{w_1} Is M 'in width' _host And the height is N' _host ，

(symbol)

Mod () represents the sign of the modulo operation for the sign of the rounding up operation;

step 2_4: b' _{w_1} B 'is used as carrier for extracting watermark' _{w_1} Is divided into

A size of N _block ×N _block Image block of (1), will be to B' _{w_1} An image block with a coordinate position of (i, j) in all the divided image blocks is recorded as B' _{w_1} (i, j); wherein, the first and the second end of the pipe are connected with each other,

step 2 \ u 5: b 'is judged according to the pixel value of each pixel point in the secret Key Key 1' _{w_1} Whether watermark information is contained in image blocks of the same coordinate position in (B' _{w_1} (i, j), if the pixel value of the pixel point with the coordinate position of (i, j) in the Key Key1 is 0, judging B' _{w_1} (i, j) does not contain watermark information; b 'is judged if the pixel value of the pixel point with the coordinate position of (i, j) in the Key Key1 is 1' _{w_1} (i, j) contains watermark information, and B' _{w_1} (i, j) defining the watermark to be extracted block;

step 2_6: from B' _{w_1} B 'is set in each block to be extracted of the watermark' _{w_1} (i, j) is the block from which the watermark is to be extracted, then from B' _{w_1} The process of extracting the watermark information in (i, j) is as follows: b' _{w_1} (i, j) the pixel value of the center pixel point is marked as G _t '(i, j), mixing B' _{w_1} The pixel values of all the pixel points except the center pixel point in (i, j) are arranged in sequence to form a row vector and are marked as G' _{w_1,i,j} (ii) a Then utilizing keys Key2 and G' _{w_1,i,j} Calculating B' _{w_1} (i, j) the predicted pixel value of the center pixel, denoted as G _p '(i,j)，

Then according to G _t ' (i, j) and G _p '(i, j) from B' _{w_1} Extracting watermark information from (i, j), if G _t '(i,j)|＞|G _p If' (i, j) | holds, the extracted watermark information is 1, and if | G |, the extracted watermark information is 1 _t '(i,j)|≤|G _p If' (i, j) | is true, the extracted watermark information is 0; wherein, G' _{w_1,i,j} Has a dimension of 1 (N) _block ×N _block -1)，G' _{w_1,i,j} (1,m) represents G' _{w_1,i,j} The middle subscript is the element value of the element of (1,m).

In the step 1_3, the pair B _{host_1} 、I _{host_r} 、I _{host_g} And I _{host_b} The process of filling the pixel points at the respective lower sides is as follows: b is to be _{host_1} 、I _{host_r} 、I _{host_g} And I _{host_b} As a processed image; using the pixel value of each pixel point in the last row of the processed image as N of the filling _block -mod(N _host ,N _block ) Pixel values of pixel points in the same column in each row in the row;

to B _{host_1} 、I _{host_r} 、I _{host_g} And I _{host_b} The process of filling the pixel points on the respective right side is as follows: b is to be _{host_1} 、I _{host_r} 、I _{host_g} And I _{host_b} As a processed image; taking the pixel value of each pixel point in the last column of the processed image as the N of the filling _block -mod(M _host ,N _block ) And pixel values of pixel points in the same row in each column.

In the step 1_5, mask _lum The acquisition process comprises the following steps:

step 1_5a: calculating I' _{host_r} Corrected reflection-free map of (2), denoted MSF _r The MSF _r The pixel value of the pixel point with the middle coordinate position of (x, y) is recorded as MSF _r (x,y)，

Likewise, calculate l' _{host_g} Corrected reflection-free map of (2), denoted MSF _g The MSF _g The pixel value of the pixel point with the middle coordinate position of (x, y) is recorded as MSF _g (x,y)，

Calculating I' _{host_b} Corrected reflection-free map of (2), denoted MSF _b A MSF _b The pixel value of the pixel point with the middle coordinate position of (x, y) is recorded as MSF _b (x,y)，

Wherein x is more than or equal to 1 and less than or equal to M' _host ，1≤y≤N' _host ，I' _{host_r} (x, y) represents I' _{host_r} Pixel value, I 'of pixel point with middle coordinate position of (x, y)' _min (x,y)＝min(I' _{host_r} (x,y),I' _{host_g} (x,y),I' _{host_b} (x, y)), min () is the minimum value function, I' _{host_g} (x, y) represents I' _{host_g} The pixel value of the pixel point with the middle coordinate position of (x, y), I' _{host_b} (x, y) represents I' _{host_b} The pixel value of the pixel point with the middle coordinate position of (x, y),

step 1, u 5b: calculating l' _host And the difference graph between the corrected non-reflection graph and the corrected non-reflection graph is marked as d, the pixel value of the pixel point with the coordinate position of (x, y) in d is marked as d (x, y),

step 1_5c: d is subjected to binarization processing, and an image obtained after binarization processing is recorded as d _otsu D is mixing _otsu The pixel value of the pixel point with the middle coordinate position of (x, y) is recorded as d _otsu (x,y)，

Wherein th is the para-I 'by an OTSU method' _host Processing the obtained threshold value;

step 1 \ u 5d: will d _otsu Is divided into

The size of each non-overlapping is N _block ×N _block Image blocks of d _otsu And (3) recording the image block with the coordinate position of (i, j) in all the image blocks obtained after division as d _otsu (i, j); then obtain d _otsu Has a width of

And has a height of

Down-sampled image of (2), denoted as d _{otsu_sub} D is mixing _{otsu_sub} The pixel value of the pixel point with the middle coordinate position of (i, j) is recorded as d _{otsu_sub} (i, j), if d _otsu If the mean value of the pixel values of all the pixel points in (i, j) is 1, let d _{otsu_sub} (i, j) =1; if d is _otsu If the mean value of the pixel values of all the pixels in (i, j) is not 1, let d _{otsu_sub} (i,j)＝0；

Step 1, u 5e: to d _{otsu_sub} Performing morphological open/close processing, and using the image obtained after the morphological open/close processing as Mask _lum 。

In the step 1, G _p The acquisition process of (i, j) is as follows:

step 1 \ u 6a1: in B' _{host_1} Is filled with pixels having pixel values of 0 in k lines at B' _{host_1} Left side of andthe right side is respectively filled with k columns of pixel points with the pixel value of 0, and the image obtained after filling is recorded as B' _{host_1} (ii) a Wherein, k is a positive integer,

B” _{host_1} is M 'in width' _host +2k and height N' _host +2k；

Step 1, u 6a2: with the size of N _block ×N _block The square of (1) is a sliding window, and the number of pixels is B according to the step length " _{host_1} Middle sliding, sliding B " _{host_1} Is divided into M' _host ×N' _host The size of each overlap is N _block ×N _block Image block of (1), B " _{host_1} The s-th image block in (1) is denoted as B " _{host_1_s} (ii) a Wherein s is a positive integer, and the initial value of s is 1,1-M ≤' _host ×N' _host ；

Step 1, u 6a3: by using autoregressive prediction method, B' _{host_1} The pixel value of the central pixel point of each image block and N with the pixel point as the center _block ×N _block Local correlation between pixel values of all neighboring pixels within the neighborhood range, for B " _{host_1_s} Is prepared from B " _{host_1_s} The pixel value of the central pixel point is marked as G _s A is prepared from B' _{host_1_s} The pixel values of all the pixels except the central pixel are arranged in sequence to form a row vector and recorded as G _non,s (ii) a Will G _s And with B' _{host_1_s} N with central pixel as center _block ×N _block The local correlation between the pixel values of all neighboring pixels within the neighborhood range is described as:

wherein G is _non,s Has a dimension of 1 (N) _block ×N _block -1), m is a positive integer, m has an initial value of 1, 1. Ltoreq. M.ltoreq.N _block ×N _block -1，G _non,s (1, m) represents G _non,s The index is (1, m), Γ (m, 1) represents the AR coefficient of Γ with index (m, 1),Γ (m, 1) reflects G _s And G _non,s Correlation between (1, m), ε _s Represents B " _{host_1_s} Corresponding error term, ∈ _s Is close to 0;

step 1 \ u 6a4: b is prepared from " _{host_1} The pixel values of the central pixel points of all the image blocks in the image block are arranged in sequence to form a column vector, which is marked as G _{host_1_t} (ii) a B is prepared from " _{host_1} The row vectors formed by arranging the pixel values of all the pixel points except the central pixel point in all the image blocks in sequence are arranged in sequence to form a matrix and are marked as G _{host_1} ，

B is prepared from " _{host_1} The predicted pixel values of the central pixel points of all the image blocks in the image block are arranged in sequence to form a column vector, which is marked as G _{host_1_p} (ii) a Wherein G is _{host_1_t} Is of dimension (M' _host ×N' _host )×1，G _{host_1} Is of dimension (M' _host ×N' _host )×(N _block ×N _block -1)，G _nos,1 Represents B " _{host_1} 1 st image block B of (1) " _{host_1_1} In which the pixel values of all the pixels except its central pixel are arranged in sequence to form a row vector, G _non,s Represents B' _{host_1} Of the s-th image block B " _{host_1_s} The pixel values of all the pixel points except the central pixel point are arranged in sequence to form a row vector,

represents B " _{host_1} M 'of (1)' _host ×N' _host An image block

In which the pixel values of all the pixels except its central pixel are arranged in sequence to form a row vector, G _{host_1_p} Is of dimension (M' _host ×N' _host )×1；

Step 1 \ u 6a5: to make G _{host_1_p} And G _{host_1_t} Is minimized, and the optimum is estimated using the least square methodModel parameters of (a), denoted as Γ, Γ = ((G) _{host_1} ) ^T ×G _{host_1} ) ^-1 ×(G _{host_1} ) ^T ×G _{host_1_t} And taking gamma as a local correlation model; wherein the dimension of Γ is (N) _block ×N _block -1)×1，(G _{host_1} ) ^T Is G _{host_1} Transpose of (G) ((G) _{host_1} ) ^T ×G _{host_1} ) -1 is (G) _{host_1} ) ^T ×G _{host_1} The inverse of (1);

step 1, u 6a6: according to Γ and G _{host_1,i,j} Calculation of G _p (i,j)，

Wherein G is _{host_1,i,j} (1, m) represents G _{host_1,i,j} The middle subscript is the element value of the element of (1,m).

In step 1_6, the determination process of T is as follows:

step 1, u 6b1: setting the initial value of T to 0.5, and setting the decrement step length of T to 0.01; then according to the process from step 1 to step 1, I is obtained when each T value is taken _host Obtaining 50 high dynamic range watermark images in total according to the corresponding high dynamic range watermark images, and recording a set formed by the 50 high dynamic range watermark images as { I } _w1 ,I _w2 ,…,I _w50 }; wherein, I _w1 Represents that when the T value is taken as 0.5, I _host Corresponding high dynamic range watermark image, I _w2 Represents I when the T value is 0.49 _host Corresponding high dynamic range watermark image, I _w50 Represents I when the T value is 0.01 _host A corresponding high dynamic range watermark image;

step 1, u 6b2: calculation of { I _w1 ,I _w2 ,…,I _w50 The invisibility index of each high dynamic range watermark image in the { I } and the extraction error rate of the watermark information after resisting 5 different tone mapping attacks are calculated according to the { I } ratio _w1 ,I _w2 ,…,I _w50 The invisibility index of the q-th high dynamic range watermark image in the (1) and the extraction error rate of the watermark information after resisting the alpha tone mapping attack are correspondingly marked as VDP _q And BER _q,α (%); wherein the content of the first and second substances,q and alpha are positive integers, the initial values of q and alpha are both 1, 1-50, 1-5 _q And BER _q,α The value ranges of (%) are all [0,100]；

Step 1, u 6b3: let f _max ＝max(f ₁ ,f ₂ ,…,f ₅₀ ) (ii) a Then f is mixed _max The corresponding T value is taken as the final value of T; wherein f is _max 、f ₁ 、f ₂ 、f ₅₀ All are imported intermediate variables, max () is a max function,

VDP ₁ represents { I _w1 ,I _w2 ,…,I _w50 Invisibility index of 1 st high dynamic range watermark image in (1) }, VDP ₂ Represents { I } _w1 ,I _w2 ,…,I _w50 Invisibility index of 2 nd high dynamic range watermark image in (1) }, VDP ₅₀ Represents { I } _w1 ,I _w2 ,…,I _w50 The invisibility index, BER, of the 50 th high dynamic range watermark image in (1) _1,α Represents { I _w1 ,I _w2 ,…,I _w50 The extraction bit error rate, BER, of the watermark information after the 1 st high dynamic range watermark image resists the alpha tone mapping attack _2,α Represents { I } _w1 ,I _w2 ,…,I _w50 The 2 nd high dynamic range watermark image in the (1) resists the extraction bit error rate, BER of the watermark information after the alpha tone mapping attack _50,α Represents { I } _w1 ,I _w2 ,…,I _w50 And (4) extracting the bit error rate of the watermark information after the 50 th high dynamic range watermark image resists the alpha tone mapping attack.

Compared with the prior art, the invention has the advantages that:

1) The method of the invention considers that the use of Tucker decomposition can not only completely express high-dimensional data, but also effectively solve the characteristic that the internal structure in the traditional data processing method is damaged, the method of the invention expresses a colorful high dynamic range host image into a form of three-order tensor, then utilizes the Tucker3 decomposition to process the high dynamic range host image, and uses the first characteristic diagram of the obtained core tensor as an embedding carrier of watermark information, which not only covers the main energy of the high dynamic range host image, but also can diffuse the embedded watermark information into three channels of R, G and B of the high dynamic range watermark image along with the inverse transformation of the decomposition, thereby effectively improving the robustness of the method of the invention.

2) According to the method, the local correlation model is established on the first characteristic diagram of the core tensor by using the AR prediction method, and is transmitted as the secret key, so that the problem that the quality of the watermark image with the high dynamic range is reduced due to inaccurate prediction of the traditional prediction method is effectively solved, the invisibility is improved, and the safety of the method is improved.

3) Aiming at the nonlinear characteristic of tone mapping attack, the method designs a low-complexity brightness mask by referring to the extraction method of the over-exposure area in the low-dynamic-range image, thereby further optimizing the robustness of the method.

4) The method of the invention provides a simple watermark embedding strength calculation strategy for balancing invisibility and robustness and for adaptively selecting embedding strength aiming at different host images with high dynamic ranges.

5) The method does not need an original host image with a high dynamic range in the watermark information extraction process, and realizes the blind extraction of the watermark information.

6) Experiments are carried out on the method disclosed by the invention, and the method is high in embedding capacity and low in error rate.

Drawings

FIG. 1 is a block diagram of a general implementation of the watermark embedding portion of the method of the present invention;

FIG. 2 is a block diagram of a general implementation of the watermark extraction portion of the method of the present invention;

fig. 3 shows the results of the evaluation of 30 watermark images with respect to invisibility, obtained by the method of the present invention;

FIG. 4 shows the watermark extraction error rate (%) of 30 watermark images obtained by the method of the present invention when there is no tone mapping attack and the average watermark extraction error rate (%) when 27 tone mapping attacks are resisted respectively;

fig. 5 is a mean (%) of watermark extraction error rates of 27 tone mapping attacks respectively applied to 30 watermark images obtained by the method of the present invention.

Detailed Description

The invention is described in further detail below with reference to the accompanying examples.

The invention provides a high dynamic range image watermarking method based on Tucker decomposition.

As shown in fig. 1, the specific steps of the watermark embedding part are as follows:

step 1 \ u 1: let I _host High dynamic range host image, I, representing information to be embedded with a watermark _host For RGB color images, I _host R, G, and B color channels of (1) are correspondingly denoted as I _{host_r} 、I _{host_g} And I _{host_b} (ii) a Wherein, I _host 、I _{host_r} 、I _{host_g} And I _{host_b} Are all M in width _host And the heights are all N _host 。

Step 1 \ u 2: will I _host Expressed as third order tensor, denoted A _host (ii) a Then, the existing Tucker3 decomposition algorithm is utilized to carry out A _host Performing tensor decomposition to obtain A _host Core tensor of (D), denoted as B _host (ii) a And B is _host 1 st channel as I _host First characteristic diagram of (1), marked as B _{host_1} (ii) a B is to be _host As the 2 nd channel of _host Second characteristic image of (1), noted as B _{host_2} (ii) a B is to be _host As the 3 rd channel of _host And a third characteristic image of (1), denoted as B _{host_3} (ii) a Wherein, A _host And B _host All have a size of M _host ×N _host ×3，B _{host_1} 、B _{host_2} And B _{host_3} Are all M in width _host And all the height isIs N _host 。

Step 1 \ u 3: if M is _host And N _host All can be covered by N _block Integer division, then pair B _{host_1} 、I _{host_r} 、I _{host_g} And I _{host_b} Filling pixel points is not carried out, and B is added _{host_1} 、I _{host_r} 、I _{host_g} And I _{host_b} Remap is recorded as B' _{host_1} 、I' _{host_r} 、I' _{host_g} And l' _{host_b} 。

If M is _host Can be covered with N _block Integer division of N _host Can not be covered by N _block Integer division, then pair B _{host_1} 、I _{host_r} 、I _{host_g} And I _{host_b} Filling pixel points at respective lower sides, and filling N _block -mod(N _host ,N _block ) A line and B _{host_1} The image obtained after the filling of the pixel points is recorded as B' _{host_1} A first reaction of _{host_r} The image obtained after the filling of the pixel points is recorded as I 'again' _{host_r} A first reaction of _{host_g} The image obtained after the pixel point is filled is recorded as I' _{host_g} Is shown by _{host_b} The image obtained after the filling of the pixel points is recorded as I 'again' _{host_b} 。

If M is _host Can not be covered by N _block Integer and N _host Can be covered with N _block Integer division, then pair B _{host_1} 、I _{host_r} 、I _{host_g} And I _{host_b} Filling pixel points on respective right sides, and filling N _block -mod(M _host ,N _block ) Column, and B _{host_1} The image obtained after the filling of the pixel points is recorded as B' _{host_1} Is shown by _{host_r} The image obtained after the filling of the pixel points is recorded as I 'again' _{host_r} Is shown by _{host_g} The image obtained after the filling of the pixel points is recorded as I 'again' _{host_g} Is shown by _{host_b} The image obtained after the filling of the pixel points is recorded as I 'again' _{host_b} 。

If M is _host Can not be covered by N _block Integer and N _host Can not be covered by N _block Integer division, then pair B _{host_1} 、I _{host_r} 、I _{host_g} And I _{host_b} Filling pixel points on respective right side and lower side, and filling N _block -mod(M _host ,N _block ) Column sum N _block -mod(N _host ,N _block ) A line and B _{host_1} The image obtained after the filling of the pixel points is recorded as B' _{host_1} Is shown by _{host_r} The image obtained after the filling of the pixel points is recorded as I 'again' _{host_r} Is shown by _{host_g} The image obtained after the filling of the pixel points is recorded as I 'again' _{host_g} A first reaction of _{host_b} The image obtained after the pixel point is filled is recorded as I' _{host_b} 。

Above, N _block Is odd number, N _block >1 in this example, take N _block =5 pixels, B' _{host_1} 、I' _{host_r} 、I' _{host_g} And I' _{host_b} Are all M' _host And the heights are all N' _host ，

(symbol)

To round up the operation symbol, mod () represents the modulo operation symbol.

In this embodiment, in step 1, u 3, for B _{host_1} 、I _{host_r} 、I _{host_g} And I _{host_b} The process of filling the pixel points at the respective lower sides is as follows: b is to be _{host_1} 、I _{host_r} 、I _{host_g} And I _{host_b} As a processed image; using the pixel value of each pixel point in the last row of the processed image as N of the filling _block -mod(N _host ,N _block ) And the pixel value of the pixel point in the same column in each row in the row is the complete copy of the last row. To B _{host_1} 、I _{host_r} 、I _{host_g} And I _{host_b} The process of filling the pixel points on the respective right side is as follows: b is to be _{host_1} 、I _{host_r} 、I _{host_g} And I _{host_b} As a processed image; taking the pixel value of each pixel point in the last column of the processed image as the N of the filling _block -mod(M _host ,N _block ) And the pixel value of the pixel point of the same row in each column in the column is the complete copy of the last column.

Step 1_4: b' _{host_1} B 'is embedded into carrier as watermark' _{host_1} Is divided into

A size of N _block ×N _block Image block of (1), will be to B' _{host_1} And recording image blocks with coordinate positions of (i, j) in all the divided image blocks as B' _{host_1} (i, j); wherein, the first and the second end of the pipe are connected with each other,

step 1_5: is prepared from' _{host_r} 、I' _{host_g} And l' _{host_b} Corresponds to as I' _host R color channel, G color channel, and B color channel; then obtain I' _host Has a width of

And has a height of

Luminance Mask of (1), denoted Mask _lum And Mask _lum Storing as a Key Key 1; followed by masking _lum Whether the pixel value of each pixel point in the pixel array is judged to be B' _{host_1} In the image block with the same coordinate position, and for B' _{host_1} (i, j), if Mask _lum (i, j) =0 is judged to be B' _{host_1} (i, j) is not embedded with watermark information, and B' _{host_1} (i, j) is defined as no processing block; if Mask _lum (i, j) =1 is determined to be B' _{host_1} (i, j) is embedded with watermark information, and B' _{host_1} (i, j) is defined as a block into which a watermark is to be embedded; wherein, I' _host Is M 'in width' _host And the height is N' _host ，Mask _lum (i, j) represents Mask _lum And (5) the pixel value of the pixel point with the middle coordinate position (i, j).

In this embodiment, in step 1_5, mask _lum The acquisition process comprises the following steps:

step 1, u 5a: calculating l' _{host_r} The Modified Specular Free (MSF) map of (1), denoted MSF _r The MSF _r The pixel value of the pixel point with the middle coordinate position of (x, y) is recorded as MSF _r (x,y)，

Likewise, calculate I' _{host_g} Corrected reflection-free map of (2), denoted MSF _g A MSF _g The pixel value of the pixel point with the middle coordinate position of (x, y) is recorded as MSF _g (x,y)，

Calculating I' _{host_b} Corrected reflection-free map of (2), denoted MSF _b The MSF _b The pixel value of the pixel point with the middle coordinate position of (x, y) is recorded as MSF _b (x,y)，

Wherein x is more than or equal to 1 and less than or equal to M' _host ，1≤y≤N' _host ，I' _{host_r} (x, y) represents I' _{host_r} Pixel value, I 'of pixel point with middle coordinate position of (x, y)' _min (x,y)＝min(I' _{host_r} (x,y),I' _{host_g} (x,y),I' _{host_b} (x, y)), min () is the minimum value function, I' _{host_g} (x, y) represents I' _{host_g} Pixel value, I 'of pixel point with middle coordinate position of (x, y)' _{host_b} (x, y) represents I' _{host_b} The pixel value of the pixel point with the middle coordinate position of (x, y),

step 1, u 5b: calculating l' _host And correction ofThe difference graph between the reflection graphs is marked as d, the pixel value of the pixel point with coordinate position (x, y) in d is marked as d (x, y),

。

step 1, u 5c: d is subjected to binarization processing, and an image obtained after binarization processing is recorded as d _otsu D is mixing _otsu The pixel value of the pixel point with the middle coordinate position of (x, y) is recorded as d _otsu (x,y)，

Wherein th is the para-I 'by the OTSU (Nobuyuki Otsu) method' _host And processing the obtained threshold value.

Step 1 \ u 5d: will d _otsu Is divided into

The size of each non-overlapping is N _block ×N _block Image blocks of d _otsu And (c) recording image blocks with coordinate positions (i, j) in all the image blocks obtained after division as d _otsu (i, j); then obtain d _otsu Has a width of

And has a height of

Down-sampled image of (2), denoted as d _{otsu_sub} D is mixing d _{otsu_sub} The pixel value of the pixel point with the middle coordinate position of (i, j) is recorded as d _{otsu_sub} (i, j) if d _otsu If the mean value of the pixel values of all the pixels in (i, j) is 1, let d _{otsu_sub} (i, j) =1; if d is _otsu If the mean value of the pixel values of all the pixel points in (i, j) is not 1, let d _{otsu_sub} (i,j)＝0。

Step 1, u 5e: to d _{otsu_sub} Performing morphological open-close processing, and using the image obtained after the morphological open-close processing as Mask _lum 。

Step 1_6: in B' _{host_1} B 'is set for each watermark to be embedded block to embed watermark information' _{host_1} (i, j) is the block into which the watermark is to be embedded, then in B' _{host_1} The process of embedding watermark information in (i, j) is as follows: b' _{host_1} (i, j) the pixel value of the center pixel point is marked as G _t (i, j), mixing B' _{host_1} The pixel values of all the pixel points except the central pixel point in (i, j) are sequentially arranged to form a row vector, and the row vector is recorded as G _{host_1,i,j} Prepared from B' _{host_1} (i, j) the predicted pixel value of the center pixel is recorded as G _p (i, j); b' _{host_1} (i, j) after embedding watermark information, defining the embedded watermark block as B ^w _{host_1} (i, j) mixing B ^w _{host_1} (i, j) the pixel value of the center pixel point is recorded as

When the watermark information to be embedded is 1, if | G _t (i,j)|＞|G _p (i, j) | × (1 + T) then order

If G _t (i,j)|≤|G _p (i, j) | × (1 +T) then order

When the watermark information to be embedded is 0, if | G _t (i,j)|＜|G _p (i, j) | × (1-T) then order

If | G _t (i,j)|≥|G _p (i, j) | × (1-T) then

Wherein G is _{host_1,i,j} Has a dimension of 1 (N) _block ×N _block -1)，G _p (i, j) is using the local correlation models Γ and G _{host_1,i,j} The result of the calculation is that,

m is a positive integer, m is an initial value of 1,1-N _block ×N _block -1，G _{host_1,i,j} (1, m) represents G _{host_1,i,j} The middle subscript is the element value of the element of (1, m), and the dimensionality of Γ is (N) _block ×N _block -1) × 1, storing Γ as a Key2, Γ (m, 1) representing an AR coefficient with subscript (m, 1) in Γ, "|" being an absolute value operator, T being the watermark embedding strength, T being adaptively selected for different high dynamic range host images according to the respective corresponding high dynamic range host images in this embodiment,

"=" in (1) is an assigned symbol, and sign () represents a function taking a symbol.

In this embodiment, step 1, U6, G _p The acquisition process of (i, j) is as follows:

step 1, u 6a1: to B' _{host_1} Is filled with pixels having pixel values of 0 in k lines at B' _{host_1} Respectively filling k columns of pixel points with pixel values of 0, and recording the filled image as B " _{host_1} (ii) a Wherein, k is a positive integer,

B” _{host_1} is M 'in width' _host +2k and height N' _host +2k。

Step 1, u 6a2: with the size of N _block ×N _block The square of (A) is a sliding window, and the step length is 1 pixel point at B' _{host_1} Middle sliding, sliding B " _{host_1} Is divided into M' _host ×N' _host The size of each overlap is N _block ×N _block Image block of, will B " _{host_1} The s-th image block in (1) is denoted as B " _{host_1_s} (ii) a Wherein s is a positive integer, and the initial value of s is 1, 1-M ≦ s' _host ×N' _host 。

Step 1, u 6a3: b is established by using the existing Auto-regression (AR) prediction method " _{host_1} The pixel value of the central pixel point of each image block and N with the pixel point as the center _block ×N _block Local correlation between pixel values of all neighboring pixels within the neighborhood, for B " _{host_1_s} Is prepared from B " _{host_1_s} The pixel value of the central pixel point is marked as G _s Is prepared from B " _{host_1_s} The pixel values of all the pixels except the central pixel are arranged in sequence to form a row vector and recorded as G _non,s (ii) a G is to be _s And with B' _{host_1_s} N with central pixel as center _block ×N _block The local correlation between the pixel values of all neighboring pixels within the neighborhood range is described as:

wherein, G _non,s Has a dimension of 1 (N) _block ×N _block -1), m is a positive integer, m has an initial value of 1, 1. Ltoreq. M.ltoreq.N _block ×N _block -1，G _non,s (1, m) represents G _non,s The element value of an element whose middle subscript is (1, m), Γ (m, 1) represents an AR coefficient whose middle subscript is (m, 1), Γ (m, 1) reflects G _s And G _non,s Correlation between (1, m), ε _s Represents B " _{host_1_s} Corresponding error term, ∈ _s Is close to 0, e.g. by ε _s ＝0.0000001。

Step 1, u 6a4: b is prepared from " _{host_1} The pixel values of the central pixel points of all the image blocks in the image block are arranged in sequence to form a column vector, which is marked as G _{host_1_t} (ii) a B is prepared from " _{host_1} The row vectors formed by arranging the pixel values of all the pixel points except the central pixel point in all the image blocks in sequence are arranged in sequence to form a matrix and are marked as G _{host_1} ，

B is prepared from " _{host_1} The predicted pixel values of the central pixel points of all the image blocks in the image block are arranged in sequence to form a column vector, which is marked as G _{host_1_p} (ii) a Wherein G is _{host_1_t} Is of dimension (M' _host ×N' _host )×1，G _{host_1} Is (M' _host ×N' _host )×(N _block ×N _block -1)，G _nos,1 Represents B " _{host_1} 1 st image block B of (1) " _{host_1_1} In which the pixel values of all the pixel points except its central one are arranged in sequence to form a row vector G _non,s Represents B' _{host_1} Of the s-th image block B " _{host_1_s} The pixel values of all the pixel points except the central pixel point are arranged in sequence to form a row vector,

represents B " _{host_1} M 'of (1)' _host ×N' _host An image block

In which the pixel values of all the pixels except its central pixel are arranged in sequence to form a row vector, G _{host_1_p} Is (M' _host ×N' _host )×1。

Step 1, u 6a5: to make G _{host_1_p} And G _{host_1_t} The optimal model parameters are estimated by the existing least square method, and are denoted as Γ, Γ = ((G) _{host_1} ) ^T ×G _{host_1} ) ^-1 ×(G _{host_1} ) ^T ×G _{host_1_t} And using gamma as a local correlation model; wherein the dimension of gamma is (N) _block ×N _block -1)×1，(G _{host_1} ) ^T Is G _{host_1} Transpose of (G) ((G) _{host_1} ) ^T ×G _{host_1} ) ^-1 Is (G) _{host_1} ) ^T ×G _{host_1} The inverse of (c).

Step 1 \ u 6a6: according to gamma and G _{host_1,i,j} Calculating G _p (i,j)，

Wherein G is _{host_1,i,j} (1, m) represents G _{host_1,i,j} The middle subscript is the element value of the element of (1,m).

In this embodiment, in step 1_6, the determination of T is as follows:

step 1, u 6b1: the initial value of T is set to 0.5, and the decreasing step size of T is set to 0.01(ii) a Then according to the process from step 1 to step 1, I is obtained when each T value is taken _host Obtaining 50 high dynamic range watermark images in total according to the corresponding high dynamic range watermark images, and recording a set formed by the 50 high dynamic range watermark images as { I _w1 ,I _w2 ,…,I _w50 }; wherein, I _w1 Represents I when the T value is 0.5 _host Corresponding high dynamic range watermark image, I _w2 Represents that when the T value is taken as 0.49, I _host Corresponding high dynamic range watermark image, I _w50 Represents I when the T value is 0.01 _host A corresponding high dynamic range watermark image.

Step 1, u 6b2: calculation of { I _w1 ,I _w2 ,…,I _w50 The invisibility index of each high dynamic range watermark image in the { I } and the extraction error rate of the watermark information after resisting 5 different tone mapping attacks are calculated according to the { I } ratio _w1 ,I _w2 ,…,I _w50 The invisibility index of the q-th high dynamic range watermark image and the extraction error rate of the watermark information after resisting the alpha tone mapping attack are correspondingly recorded as VDP _q And BER _q,α (%); wherein q and alpha are positive integers, the initial values of q and alpha are both 1, 1-50, 1-5 _q And BER _q,α The value ranges of (%) are all [0,100](ii) a The 5 different tone mapping attacks in this example are DragoTMO, durandTMO, fattalTMO, pattanaikVisualTMO, and ReinhardDevlinTMO, respectively.

Step 1, u 6b3: let f _max ＝max(f ₁ ,f ₂ ,…,f ₅₀ ) (ii) a Then f is mixed _max The corresponding T value is taken as the final value of T; wherein, f _max 、f ₁ 、f ₂ 、f ₅₀ All are imported intermediate variables, max () is a function taking the maximum value,

VDP ₁ represents { I } _w1 ,I _w2 ,…,I _w50 Invisibility of high dynamic Range watermark image No. 1 in }Index, VDP ₂ Represents { I _w1 ,I _w2 ,…,I _w50 Invisibility index of 2 nd high dynamic range watermark image in (1) }, VDP ₅₀ Represents { I } _w1 ,I _w2 ,…,I _w50 The invisibility index, BER, of the 50 th high dynamic range watermark image in (1) _1,α Represents { I _w1 ,I _w2 ,…,I _w50 The extraction bit error rate, BER, of the watermark information after the 1 st high dynamic range watermark image resists the alpha tone mapping attack _2,α Represents { I } _w1 ,I _w2 ,…,I _w50 The 2 nd high dynamic range watermark image in the image resists the extraction bit error rate, BER of the watermark information after the alpha tone mapping attack _50,α Represents { I _w1 ,I _w2 ,…,I _w50 And (4) extracting the bit error rate of the watermark information after the 50 th high dynamic range watermark image resists the alpha tone mapping attack.

Step 1 \ u 7: to B' _{host_1} All unprocessed blocks and all watermark embedded blocks in the image block group are merged and reconstructed to obtain an image B 'containing watermark information' _{host_1_w} (ii) a Then according to the reverse process of step 1_3, to B' _{host_1_w} Processing the image to obtain an image with a width of M _host And a height of N _host And recording the processed image as B _{host_1_w} And is used as a first characteristic diagram containing watermark information; then, the inverse transformation pair B of the existing Tucker3 decomposition algorithm is utilized _{host_1_w} 、B _{host_2} And B _{host_3} Processing the image to obtain a watermark image marked as I _w (ii) a Wherein, I _w Has a width of M _host And a height of N _host 。

Step 1 \ u 8: the watermark embedding end sends the secret Key Key1 and the secret Key Key2 to the watermark extracting end.

As shown in fig. 2, the watermark extraction section specifically includes the steps of:

step 2_1: reading watermark image containing watermark information, and recording as I' _w (ii) a Wherein, I' _w Is an RGB color image, I' _w Has a width of M _host And a height of N _host ，I' _w Is not under any attackThe watermark image is the watermark image after the tone mapping attack.

Step 2_2: is prepared from' _w Expressed as third order tensor, denoted A _w (ii) a Then, the existing Tucker3 decomposition algorithm is utilized to pair A _w Carrying out tensor decomposition to obtain A _w Core tensor of (D), denoted as B _w (ii) a And B is _w 1 channel of (a) as l' _w Is marked as B _{w_1} (ii) a B is to be _w Of 2 as I' _w Second characteristic image of (1), noted as B _{w_2} (ii) a B is to be _w Of as l' _w And a third characteristic image of (1), denoted as B _{w_3} (ii) a Wherein A is _w And B _w All being M _host ×N _host ×3，B _{w_1} 、B _{w_2} And B _{w_3} Are all M in width _host And the heights are all N _host 。

Step 2_3: if M is _host And N _host All can be covered by N _block Integer division, then pair B _{w_1} Filling pixel points is not carried out, and B is added _{w_1} Remap as B' _{w_1} 。

If M is _host Can be covered with N _block Integer and N _host Can not be covered by N _block Integer division, then pair B _{w_1} Filling the lower side of the N-shaped substrate with N _block -mod(N _host ,N _block ) A line and B _{w_1} The image obtained after the filling of the pixel points is recorded as B' _{w_1} 。

If M is _host Can not be covered by N _block Integer and N _host Can be covered with N _block Integer division, then pair B _{w_1} The right side of the image is filled with pixel points, and N is filled _block -mod(M _host ,N _block ) Column, and B _{w_1} The image obtained after the filling of the pixel points is recorded as B' _{w_1} 。

If M is _host Can not be covered by N _block Integer and N _host Can not be covered by N _block Integer division, then pair B _{w_1} The right side and the lower side of the frame are filled with pixel points, and N is filled _block -mod(M _host ,N _block ) Column sum N _block -mod(N _host ,N _block ) A line and B _{w_1} The image obtained after the filling of the pixel points is recorded as B' _{w_1} 。

Above, N _block Is odd number, N _block >1 in this example, take N _block =5 pixels, B' _{w_1} Is M 'in width' _host And the height is N' _host ，

(symbol)

To round up the operation symbol, mod () represents the modulo operation symbol.

Step 2_4: b' _{w_1} B 'is used as carrier for extracting watermark' _{w_1} Is divided into

A size of N _block ×N _block Image block of (1), will be to B' _{w_1} An image block with a coordinate position of (i, j) in all the divided image blocks is recorded as B' _{w_1} (i, j); wherein the content of the first and second substances,

step 2_5: b 'is judged according to the pixel value of each pixel point in the secret Key Key 1' _{w_1} Whether watermark information is contained in image blocks at the same coordinate position in (B' _{w_1} (i, j), if the pixel value of the pixel point with the coordinate position of (i, j) in the Key Key1 is 0, judging B' _{w_1} (i, j) does not contain watermark information; b 'is judged if the pixel value of the pixel point with the coordinate position of (i, j) in the Key Key1 is 1' _{w_1} (i, j) contains watermark information, and B' _{w_1} (i, j) is defined as the block where the watermark is to be extracted.

Step 2 \ u 6: from B' _{w_1} B 'is set in each block to be extracted of the watermark' _{w_1} (i, j) is the block from which the watermark is to be extracted, then from B' _{w_1} (i, j) extraction ofThe process of watermarking information is as follows: b' _{w_1} (i, j) the pixel value of the center pixel point is marked as G _t '(i, j), mixing B' _{w_1} The pixel values of all the pixel points except the center pixel point in (i, j) are arranged in sequence to form a row vector and are marked as G' _{w_1,i,j} (ii) a Then utilizing keys Key2 and G' _{w_1,i,j} Calculating B' _{w_1} (i, j) the predicted pixel value of the center pixel point, denoted as G _p '(i,j)，

Then according to G _t ' (i, j) and G _p '(i, j) from B' _{w_1} Extracting watermark information from (i, j), if G _t '(i,j)|＞|G _p If' (i, j) | holds, the extracted watermark information is 1, and if | G |, the extracted watermark information is 1 _t '(i,j)|≤|G _p If' (i, j) | is true, the extracted watermark information is 0; wherein, G' _{w_1,i,j} Has a dimension of 1 (N) _block ×N _block -1)，G' _{w_1,i,j} (1,m) represents G' _{w_1,i,j} The middle subscript is the element value of the element of (1,m).

To further illustrate the feasibility and effectiveness of the method of the invention, experiments were conducted.

In this example, a total of 30 high dynamic range host images and 27 tone mapping operators were selected for testing. Wherein, 30 high dynamic range host images are respectively from: [1] a Greg Ward website; [2] image Gallery website; [3] a TMQI database; the 27 tone mapping attacks are selected from the HDR Toolbox for Matlab toolkit. Table 1 gives detailed information of 30 high dynamic range host images; table 2 gives details of the 27 tone mapping attacks.

TABLE 1 details of the 30 high dynamic range host images

TABLE 2 details of Tone Mapping (TM) attacks

The method of the invention is utilized to respectively execute the concrete steps of the watermark embedding part and the watermark extracting part on 30 host images with high dynamic range. Here, the invisibility of the method of the present invention is evaluated by using three indexes, namely, the existing Signal-to-Noise Ratio (SNR), the Structural Similarity Index (SSIM) and HDR-VDP-2.2; the robustness of the method is measured by Bit Error Rate (BER); the watermark embedding capacity of the inventive method is expressed by the embedding amount (bit) and embedding rate (bpp). Besides the bit error rate, the higher the value is, the better the performance of the watermarking method is represented by other evaluation indexes, and the lower the value is, the higher the robustness is represented by the bit error rate.

The embedding capacity of the method of the invention mainly depends on the size N of the image block in the image processing process _block (in this example, N _block Fetch 5) and luminance Mask _lum The distribution ratio of the middle pixel value 0 and the pixel value 1. Table 3 shows the embedding capacity of the obtained 30 watermark images, the average embedding amount of the 30 watermark images is up to 47644 bits, the average embedding rate is about 0.0290bpp, and is significantly higher than most of the existing high dynamic range image robustness watermarking methods. Furthermore, the method of the invention is also valid for other image block sizes and follows the image block size N _block The embedding capacity tends to decrease while the invisibility appears to gradually increase. Table 4 gives the image block size N for the high dynamic range host image with image number "29 _block The embedding amount (bit), the embedding ratio (bpp), the SNR, SSIM, VDP, BER values in the case of no tone mapping attack (represented by BER0 (%)) and average BER values in the case of 27 tone mapping attacks (represented by BER1 (%)) were taken at 3, 5 and 7 times, respectively.

TABLE 3 embedding Capacity of 30 watermark images

TABLE 4 contrast data for high dynamic range host image with image number "29" at different image block sizes

For the invisibility and the robustness of the method, fig. 3 shows the evaluation result of 30 watermark images about the invisibility, fig. 4 shows the watermark extraction error rate (%) of the 30 watermark images when the 30 watermark images are subjected to the tone-free mapping attack and the average watermark extraction error rate (%) when the 30 watermark images respectively resist 27 tone mapping attacks, fig. 5 shows the average value of the watermark extraction error rates after each tone mapping attack respectively acts on the 30 watermark images, and the total 27 attack types are provided. Since the selected 30 high dynamic range host images contain different scene information and indoor and outdoor environments, different high dynamic range host images can show different robustness and invisibility by observing data in fig. 3, 4 and 5, however, the average SNR of the 30 watermark images is about 53.2654dB, the average SSIM is 1.0000, the average VDP can be as high as 91.5311, and the average bit error rate of the 30 high dynamic range host images is only 0.44% when the watermark images are not subjected to tone mapping attack, and the average bit error rate of the 30 high dynamic range host images is only 7.13% when the watermark images are respectively subjected to 27 tone mapping attacks, so that the method of the invention shows higher robustness and better invisibility as a whole.

In order to further prove the superiority of the method of the present invention, the factors such as the practicability, the effectiveness and whether the extraction process is blind detection are comprehensively considered, the method respectively compares the selected data with the prior art methods such as the BER (robust High dynamic range image watermarking algorithm for resisting tone mapping) proposed by Guerrini et al, "High-performance watermarking of High dynamic range images" (High-capacity watermarking algorithm for High dynamic range images) proposed by Mairiana et al and "hardware a tone mapping-hardware watermarking algorithm for High dynamic range image base on specific activity" proposed by Bai et al, and the BER et al compares the selected data with the prior art methods such as the BER (BER 5) and the BER (%) of the present invention and the BER of the present invention.

TABLE 5 comparative data of the method of the invention with Guerrini et al, bai et al regarding the amount of embedding (bit) and BER (%)

TABLE 6 comparison data of the method of the invention with Maiorana et al, bai et al regarding the amount of embedding (bit) and BER (%)

Analyzing the data listed in tables 5 and 6, it can be seen that the embedding capacity of the method of the present invention is about 15 times of the watermarking method proposed by guerrii et al, maiorana et al, and is equivalent to the watermarking method proposed by Bai et al; regarding robustness, although individual images show a higher bit error rate (%) when subjected to tone mapping attack than the existing methods, the bit error rate (%) of watermark information extraction under most tone mapping attacks is still significantly lower than the watermarking methods proposed by Guerrini et al and Maiorana et al. In addition, table 7 shows the comparison result of the comprehensive performance of the method of the present invention and the existing three watermarking methods.

TABLE 7 comparison of the overall Performance of the watermarking methods

From the overall performance comparison data given in table 7, it can be seen that the method of the present invention tests more high dynamic range host images and more tone mapping attack types, and has higher embedding capacity and better robustness.

Claims (5)

1. A high dynamic range image watermarking method based on Tucker decomposition is characterized by comprising two parts of watermark embedding and watermark extracting;

the specific steps of the watermark embedding part are as follows:

step 1 \ u 1: let I _host High dynamic range host image, I, representing information to be embedded with a watermark _host For RGB color images, I _host R, G, and B color channels of (1) are correspondingly denoted as I _{host_r} 、I _{host_g} And I _{host_b} (ii) a Wherein, I _host 、I _{host_r} 、I _{host_g} And I _{host_b} Are all M in width _host And the heights are all N _host ；

Step 1 \ u 2: will I _host Expressed as third order tensor, denoted A _host (ii) a Then, the Tucker3 decomposition algorithm is used for A _host Performing tensor decomposition to obtain A _host Core tensor of (D), noted as B _host (ii) a And B is _host 1 channel of (a) as I _host Is marked as B _{host_1} (ii) a B is to be _host The 2 nd channel of (2) is taken as I _host Second characteristic image of (1), noted as B _{host_2} (ii) a B is to be _host As the 3 rd channel of _host Third feature image of (1), noted as B _{host_3} (ii) a Wherein A is _host And B _host All being M _host ×N _host ×3，B _{host_1} 、B _{host_2} And B _{host_3} Are all M in width _host And the heights are all N _host ；

Step 1_3: if M is _host And N _host All can be covered by N _block Integer division, then pair B _{host_1} 、I _{host_r} 、I _{host_g} And I _{host_b} Filling pixel points is not carried out, and B is added _{host_1} 、I _{host_r} 、I _{host_g} And I _{host_b} Remap as B' _{host_1} 、I' _{host_r} 、I' _{host_g} And l' _{host_b} ；

If M is _host Can be covered with N _block Integer division of N _host Can not be covered by N _block Integer division, then pair B _{host_1} 、I _{host_r} 、I _{host_g} And I _{host_b} Filling pixel points at the lower sides of the two groups of the pixel points, and filling N _block -mod(N _host ,N _block ) A line and B _{host_1} The image obtained after the filling of the pixel points is recorded as B' _{host_1} Is shown by _{host_r} The image obtained after the pixel point is filled is recorded as I' _{host_r} Is shown by _{host_g} The image obtained after the filling of the pixel points is recorded as I 'again' _{host_g} Is shown by _{host_b} The image obtained after the filling of the pixel points is recorded as I 'again' _{host_b} ；

If M is _host Can not be covered by N _block Integer and N _host Can be covered with N _block Integer division, then pair B _{host_1} 、I _{host_r} 、I _{host_g} And I _{host_b} Filling pixel points on respective right sides, and filling N _block -mod(M _host ,N _block ) Column and B _{host_1} The image obtained after the filling of the pixel points is recorded as B' _{host_1} Is shown by _{host_r} The image obtained after the filling of the pixel points is recorded as I 'again' _{host_r} Is shown by _{host_g} The image obtained after the filling of the pixel points is recorded as I 'again' _{host_g} Is shown by _{host_b} The image obtained after the pixel point is filled is recorded as I' _{host_b} ；

If M is _host Can not be covered by N _block Integer and N _host Can not be covered by N _block Integer division, then pair B _{host_1} 、I _{host_r} 、I _{host_g} And I _{host_b} Filling pixel points on respective right side and lower side, and filling N _block -mod(M _host ,N _block ) Column sum N _block -mod(N _host ,N _block ) A line and B _{host_1} The image obtained after the filling of the pixel points is recorded as B' _{host_1} A first reaction of _{host_r} The image obtained after the pixel point is filled is recorded as I' _{host_r} A first reaction of _{host_g} The image obtained after the pixel point is filled is recorded as I' _{host_g} Is shown by _{host_b} The image obtained after the filling of the pixel points is recorded as I 'again' _{host_b} ；

Above, N _block Is odd number, N _block >1，B' _{host_1} 、I' _{host_r} 、I' _{host_g} And I' _{host_b} Are all M 'in width' _host And the heights are all N' _host ，

(symbol)

To round up the operation symbol, mod () represents the modulo operation symbol;

step 1_4: b' _{host_1} B 'is embedded as watermark carrier' _{host_1} Is divided into

The size of each non-overlapping is N _block ×N _block Image block of (1), will be to B' _{host_1} And recording image blocks with coordinate positions of (i, j) in all the divided image blocks as B' _{host_1} (i, j); wherein the content of the first and second substances,

step 1_5: i' _{host_r} 、I' _{host_g} And l' _{host_b} Corresponds to as I' _host R, G, and B color channels; then obtain I' _host Has a width of

And has a height of

Brightness Mask, denoted Mask _lum And Mask is formed _lum Storing as a secret Key Key 1; followed by masking _lum Whether the pixel value of each pixel point in the pixel list is B 'or not is judged' _{host_1} In the image block with the same coordinate position, and for B' _{host_1} (i, j), if Mask _lum (i, j) =0 is judged to be B' _{host_1} (i, j) is not embedded with watermark information, and B' _{host_1} (i, j) is defined as no processing block; if Mask _lum (i, j) =1 is judged to be B' _{host_1} (i, j) is embedded with watermark information, and B' _{host_1} (i, j) is defined as a block into which a watermark is to be embedded; wherein, I' _host Is M 'in width' _host And is N 'in height' _host ，Mask _lum (i, j) represents Mask _lum The pixel value of the pixel point with the middle coordinate position of (i, j);

step 1_6: to B' _{host_1} B 'is embedded in each block to be embedded with watermark' _{host_1} (i, j) is the block into which the watermark is to be embedded, then in B' _{host_1} The process of embedding watermark information in (i, j) is as follows: b' _{host_1} (i, j) the pixel value of the center pixel point is marked as G _t (i, j), mixing B' _{host_1} The pixel values of all the pixel points except the central pixel point in (i, j) are arranged in sequence to form a row vector, and the row vector is recorded as G _{host_1,i,j} Prepared from B' _{host_1} (i, j) the predicted pixel value of the center pixel is marked as G _p (i, j); b' _{host_1} (i, j) after embedding watermark information, defining the embedded watermark block as B ^w _{host_1} (i, j) mixing B ^w _{host_1} Of central pixel of (i, j)The pixel value is noted as

When the watermark information to be embedded is 1, if | G _t (i,j)|＞|G _p (i, j) | × (1 + T) then order G _t ^w (i,j)＝G _t (i, j), if | G _t (i,j)|≤|G _p (i, j) | × (1 + T) then order

When the watermark information to be embedded is 0, if | G _t (i,j)|＜|G _p (i, j) | × (1-T) then order

If G _t (i,j)|≥|G _p (i, j) | × (1-T) then

Wherein G is _{host_1,i,j} Has a dimension of 1 (N) _block ×N _block -1)，G _p (i, j) is using the local correlation models Γ and G _{host_1,i,j} The result of the calculation is that,

m is a positive integer, and m is equal to or greater than 1,1 and equal to or less than N _block ×N _block -1，G _{host_1,i,j} (1, m) represents G _{host_1,i,j} The middle subscript is the element value of the element of (1, m), and the dimensionality of Γ is (N) _block ×N _block -1) × 1, storing Γ as a Key2, Γ (m, 1) representing AR coefficient with subscript (m, 1) in Γ, "|" being absolute value arithmetic sign, T being watermark embedding strength,

"=" in (1) is an assigned symbol, sign () denotes a signed function;

step 1_7: to B' _{host_1} All unprocessed blocks and all watermark embedded blocks in the image block combination, and the image block combination is reconstructed to obtain the image block containingImage of watermark information is marked as B' _{host_1_w} (ii) a Then according to the reverse process of step 1_3, to B' _{host_1_w} Processing the image to obtain an image with a width of M _host And a height of N _host Recording the processed image as B _{host_1_w} And is used as a first characteristic diagram containing watermark information; and then the inverse transformation pair B of the Tucker3 decomposition algorithm is utilized _{host_1_w} 、B _{host_2} And B _{host_3} Processing to obtain watermark image marked as I _w (ii) a Wherein, I _w Has a width of M _host And a height of N _host ；

Step 1 \ u 8: the watermark embedding end sends a secret Key Key1 and a secret Key Key2 to the watermark extraction end;

the watermark extracting part comprises the following specific steps:

step 2_1: reading watermark image containing watermark information, recorded as I' _w (ii) a Wherein, I' _w Is an RGB color image, I' _w Has a width of M _host And a height of N _host ，I' _w The watermark image is the watermark image which is not attacked or the watermark image which is attacked by tone mapping;

step 2_2: is prepared from' _w Expressed as third order tensor, denoted A _w (ii) a Then using Tucker3 decomposition algorithm to pair A _w Carrying out tensor decomposition to obtain A _w Core tensor of (D), denoted as B _w (ii) a And B is _w Of 1 as I' _w Is marked as B _{w_1} (ii) a B is to be _w Of 2 as I' _w Second feature image of (1), noted as B _{w_2} (ii) a B is to be _w Of as l' _w Third feature image of (1), noted as B _{w_3} (ii) a Wherein A is _w And B _w All have a size of M _host ×N _host ×3，B _{w_1} 、B _{w_2} And B _{w_3} Are all M in width _host And the heights are all N _host ；

Step 2_3: if M is _host And N _host All can be covered by N _block Integer division, then pair B _{w_1} Filling pixel points is not carried out, and B is added _{w_1} RemapIs recorded as B' _{w_1} ；

If M is _host Can be covered with N _block Integer and N _host Can not be covered by N _block Integer division, then pair B _{w_1} Filling the lower side of the N-shaped substrate with N _block -mod(N _host ,N _block ) A line and B _{w_1} The image obtained after the filling of the pixel points is recorded as B' _{w_1} ；

If M is _host Can not be covered by N _block Integer and N _host Can be covered with N _block Integer division, then pair B _{w_1} The right side of the image is filled with pixel points, and N is filled _block -mod(M _host ,N _block ) Column, and B _{w_1} The image obtained after the filling of the pixel points is recorded as B' _{w_1} ；

If M is _host Can not be covered by N _block Integer and N _host Can not be covered by N _block Integer division, then pair B _{w_1} The right side and the lower side of the frame are filled with pixel points, and N is filled _block -mod(M _host ,N _block ) Column sum N _block -mod(N _host ,N _block ) A line and B _{w_1} The image obtained after the filling of the pixel points is recorded as B' _{w_1} ；

Above, N _block Is odd number, N _block >1，B' _{w_1} Is M 'in width' _host And is N 'in height' _host ，

(symbol)

To round up the operation symbol, mod () represents the modulo operation symbol;

step 2_4: b' _{w_1} B 'is used as carrier for extracting watermark' _{w_1} Is divided into

A size of N _block ×N _block Of (2)Block, will be to B' _{w_1} An image block with a coordinate position of (i, j) in all the divided image blocks is recorded as B' _{w_1} (i, j); wherein the content of the first and second substances,

step 2_5: b 'is judged according to the pixel value of each pixel point in the secret Key Key 1' _{w_1} Whether watermark information is contained in image blocks of the same coordinate position in (B' _{w_1} (i, j), if the pixel value of the pixel point with the coordinate position of (i, j) in the Key Key1 is 0, judging B' _{w_1} (i, j) does not contain watermark information; b 'is judged if the pixel value of the pixel point with the coordinate position of (i, j) in the Key Key1 is 1' _{w_1} (i, j) contains watermark information, and B' _{w_1} (i, j) defining a watermark block to be extracted;

step 2 \ u 6: from B' _{w_1} B 'is set for extracting watermark information from each watermark block to be extracted' _{w_1} (i, j) is the block from which the watermark is to be extracted, then from B' _{w_1} The process of extracting watermark information in (i, j) is as follows: b' _{w_1} (i, j) the pixel value of the center pixel point is marked as G _t '(i, j), mixing B' _{w_1} The pixel values of all the pixel points except the center pixel point in (i, j) are arranged in sequence to form a row vector and are marked as G' _{w_1,i,j} (ii) a Then utilizing keys Key2 and G' _{w_1,i,j} Calculating B' _{w_1} (i, j) the predicted pixel value of the center pixel, denoted as G _p '(i,j)，

Then according to G _t ' (i, j) and G _p '(i, j) from B' _{w_1} (i, j) extracting watermark information, if | G _t '(i,j)|＞|G _p If' (i, j) | holds, the extracted watermark information is 1, and if | G |, the extracted watermark information is not included in the watermark information _t '(i,j)|≤|G _p If' (i, j) | is true, the extracted watermark information is 0; wherein, G' _{w_1,i,j} Has a dimension of 1 (N) _block ×N _block -1)，G' _{w_1,i,j} (1,m) represents G' _{w_1,i,j} The middle subscript is the element value of the element of (1,m).

2. The method for watermarking a high dynamic range image based on Tucker decomposition as claimed in claim 1, wherein in step 1 \, pair B _{host_1} 、I _{host_r} 、I _{host_g} And I _{host_b} The process of filling the pixel points at the respective lower sides is as follows: b is to be _{host_1} 、I _{host_r} 、I _{host_g} And I _{host_b} As a processed image; using the pixel value of each pixel point in the last row of the processed image as N of the filling _block -mod(N _host ,N _block ) Pixel values of pixel points in the same column in each row in the rows;

to B _{host_1} 、I _{host_r} 、I _{host_g} And I _{host_b} The process of filling the pixel points on the respective right side is as follows: b is to be _{host_1} 、I _{host_r} 、I _{host_g} And I _{host_b} As a processed image; taking the pixel value of each pixel point in the last column of the processed image as the N of the filling _block -mod(M _host ,N _block ) And pixel values of pixel points in the same row in each column.

3. The Tucker decomposition-based high dynamic range image watermarking method according to claim 1 or 2, wherein in the step 1 \ u 5, mask _lum The acquisition process comprises the following steps:

step 1, u 5a: calculating l' _{host_r} Corrected reflection-free map of (2), denoted MSF _r A MSF _r The pixel value of the pixel point with the middle coordinate position of (x, y) is recorded as MSF _r (x,y)，

Likewise, calculate l' _{host_g} Corrected reflection-free map of (2), denoted MSF _g The MSF _g The pixel value of the pixel point with the middle coordinate position of (x, y) is recorded as MSF _g (x,y)，

Calculating l' _{host_b} Corrected reflection-free map of (2), denoted MSF _b The MSF _b The pixel value of the pixel point with the middle coordinate position of (x, y) is recorded as MSF _b (x,y)，

Wherein x is more than or equal to 1 and less than or equal to M' _host ，1≤y≤N' _host ，I' _{host_r} (x, y) represents I' _{host_r} The pixel value of the pixel point with the middle coordinate position of (x, y), I' _min (x,y)＝min(I' _{host_r} (x,y),I' _{host_g} (x,y),I' _{host_b} (x, y)), min () is the minimum value function, I' _{host_g} (x, y) represents I' _{host_g} Pixel value, I 'of pixel point with middle coordinate position of (x, y)' _{host_b} (x, y) represents I' _{host_b} The pixel value of the pixel point with the middle coordinate position of (x, y),

step 1, u 5b: calculating l' _host And the difference value graph between the corrected reflection-free graph and the corrected reflection-free graph is marked as d, the pixel value of the pixel point with the coordinate position of (x, y) in the d is marked as d (x, y),

step 1_5c: d is subjected to binarization processing, and an image obtained after binarization processing is recorded as d _otsu D is mixing _otsu The pixel value of the pixel point with the middle coordinate position of (x, y) is recorded as d _otsu (x,y)，

Wherein th is the para-I 'by an OTSU method' _host Processing the obtained threshold value;

step 1 \ u 5d: will d _otsu Is divided into

A size of N _block ×N _block Image blocks of d _otsu Coordinates in all image blocks obtained after divisionThe image block with position (i, j) is denoted as d _otsu (i, j); then obtain d _otsu Has a width of

And has a height of

Down-sampled image of (2), denoted as d _{otsu_sub} D is mixing d _{otsu_sub} The pixel value of the pixel point with the middle coordinate position of (i, j) is recorded as d _{otsu_sub} (i, j) if d _otsu If the mean value of the pixel values of all the pixel points in (i, j) is 1, let d _{otsu_sub} (i, j) =1; if d is _otsu If the mean value of the pixel values of all the pixel points in (i, j) is not 1, let d _{otsu_sub} (i,j)＝0；

Step 1, u 5e: to d _{otsu_sub} Performing morphological open-close processing, and using the image obtained after the morphological open-close processing as Mask _lum 。

4. The Tucker decomposition-based high dynamic range image watermarking method as claimed in claim 1, wherein in step 1 \ u 6, G is _p The acquisition process of (i, j) is as follows:

step 1, u 6a1: to B' _{host_1} Is filled with pixels having pixel values of k lines of 0 at B' _{host_1} Respectively filling k columns of pixel points with pixel values of 0, and recording the filled image as B " _{host_1} (ii) a Wherein k is a positive integer,

B” _{host_1} is M 'in width' _host +2k and height N' _host +2k；

Step 1, u 6a2: with the size of N _block ×N _block The square of (A) is a sliding window, and the step length is 1 pixel point at B' _{host_1} Middle sliding, slide B' _{host_1} Is divided into M' _host ×N' _host The size of each overlap is N _block ×N _block Image block of, will B " _{host_1} The s-th image block in (1) is denoted as B " _{host_1_s} (ii) a Wherein s is a positive integer, and the initial value of s is 1,1-M ≤' _host ×N' _host ；

Step 1, u 6a3: by using autoregressive prediction method, B' _{host_1} The pixel value of the central pixel point of each image block and N with the pixel point as the center _block ×N _block Local correlation between pixel values of all neighboring pixels within the neighborhood, for B " _{host_1_s} Is prepared from B " _{host_1_s} The pixel value of the central pixel point is marked as G _s A is prepared from B' _{host_1_s} The pixel values of all the pixels except the central pixel are arranged in sequence to form a row vector and recorded as G _non,s (ii) a G is to be _s And with B' _{host_1_s} Is centered at the center pixel point of N _block ×N _block The local correlation between pixel values of all neighboring pixel points within the neighborhood range is described as:

wherein G is _non,s Has a dimension of 1 (N) _block ×N _block -1), m is a positive integer, m has an initial value of 1, 1. Ltoreq. M.ltoreq.N _block ×N _block -1，G _non,s (1, m) represents G _non,s The element value of the element with the middle subscript of (1, m), Γ (m, 1) represents the AR coefficient with the middle subscript of (m, 1), Γ (m, 1) reflects G _s And G _non,s Correlation between (1, m), ε _s Represents B " _{host_1_s} Corresponding error term, ∈ _s Is close to 0;

step 1 \ u 6a4: b' _{host_1} The pixel values of the central pixel points of all the image blocks in the image block are arranged in sequence to form a column vector, which is marked as G _{host_1_t} (ii) a B' _{host_1} The row vectors formed by arranging the pixel values of all the pixel points except the central pixel point in all the image blocks in sequence are arranged in sequence to form a matrix and are marked as G _{host_1} ，

B is prepared from " _{host_1} The predicted pixel values of the central pixel points of all the image blocks in the image block are arranged in sequence to form a column vector, which is marked as G _{host_1_p} (ii) a Wherein G is _{host_1_t} Is of dimension (M' _host ×N' _host )×1，G _{host_1} Is of dimension (M' _host ×N' _host )×(N _block ×N _block -1)，G _nos,1 Represents B " _{host_1} The 1 st image block B in (1)' _{host_1_1} In which the pixel values of all the pixel points except its central one are arranged in sequence to form a row vector G _non,s Represents B' _{host_1} Of the s-th image block B " _{host_1_s} The pixel values of all the pixel points except the central pixel point are arranged in sequence to form a row vector,

represents B " _{host_1} M 'of (1)' _host ×N' _host An image block

In which the pixel values of all the pixel points except its central one are arranged in sequence to form a row vector G _{host_1_p} Is (M' _host ×N' _host )×1；

Step 1 \ u 6a5: to make G _{host_1_p} And G _{host_1_t} The optimal model parameters are estimated by the least square method, and are recorded as gamma, gamma = ((G) _{host_1} ) ^T ×G _{host_1} ) ^-1 ×(G _{host_1} ) ^T ×G _{host_1_t} And taking gamma as a local correlation model; wherein the dimension of gamma is (N) _block ×N _block -1)×1，(G _{host_1} ) ^T Is G _{host_1} Transpose of (G) ((G) _{host_1} ) ^T ×G _{host_1} ) ^-1 Is (G) _{host_1} ) ^T ×G _{host_1} The inverse of (c);

step 1 \ u 6a6: according to Γ and G _{host_1,i,j} Calculation of G _p (i,j)，

Wherein, G _{host_1,i,j} (1, m) represents G _{host_1,i,j} The middle subscript is the element value of the element of (1,m).

5. The Tucker decomposition-based high dynamic range image watermarking method according to claim 1 or 4, wherein in the step 1_6, the determination process of T is:

step 1, u 6b1: setting the initial value of T to 0.5, and setting the decrement step length of T to 0.01; then according to the process from step 1 to step 1, I is obtained when each T value is taken _host Obtaining 50 high dynamic range watermark images in total according to the corresponding high dynamic range watermark images, and recording a set formed by the 50 high dynamic range watermark images as { I _w1 ,I _w2 ,…,I _w50 }; wherein, I _w1 Represents that when the T value is taken as 0.5, I _host Corresponding high dynamic range watermark image, I _w2 Represents that when the T value is taken as 0.49, I _host Corresponding high dynamic range watermark image, I _w50 Represents I when the T value is 0.01 _host A corresponding high dynamic range watermark image;

step 1, u 6b2: calculation of { I _w1 ,I _w2 ,…,I _w50 The invisibility index of each high dynamic range watermark image in the { I } and the extraction error rate of the watermark information after resisting 5 different tone mapping attacks are calculated according to the { I } ratio _w1 ,I _w2 ,…,I _w50 The invisibility index of the q-th high dynamic range watermark image and the extraction error rate of the watermark information after resisting the alpha tone mapping attack are correspondingly recorded as VDP _q And BER _q,α (%); wherein q and alpha are positive integers, the initial values of q and alpha are both 1, 1-50, 1-5 _q And BER _q,α The value ranges of (%) are all 0,100]；

Step 1, u 6b3: let f _max ＝max(f ₁ ,f ₂ ,…,f ₅₀ ) (ii) a Then f is mixed _max The corresponding T value is taken as the final value of T; wherein, f _max 、f ₁ 、f ₂ 、f ₅₀ Are all imported intermediate variables, max () is takenThe function of the maximum value is a function of,

VDP ₁ represents { I _w1 ,I _w2 ,…,I _w50 Invisibility index of 1 st high dynamic range watermark image in (1) }, VDP ₂ Represents { I _w1 ,I _w2 ,…,I _w50 Invisibility index of 2 nd high dynamic range watermark image in (1) }, VDP ₅₀ Represents { I } _w1 ,I _w2 ,…,I _w50 The invisibility index, BER, of the 50 th high dynamic range watermark image in (1) _1,α Represents { I _w1 ,I _w2 ,…,I _w50 The extraction bit error rate, BER, of the watermark information after the 1 st high dynamic range watermark image resists the alpha tone mapping attack _2,α Represents { I } _w1 ,I _w2 ,…,I _w50 The 2 nd high dynamic range watermark image in the (1) resists the extraction bit error rate, BER of the watermark information after the alpha tone mapping attack _50,α Represents { I _w1 ,I _w2 ,…,I _w50 And (4) extracting the bit error rate of the watermark information after the 50 th high dynamic range watermark image resists the alpha tone mapping attack.

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