Watermarking and authentication of color images based on ...

Watermarking and authentication of color images based on segmentation of the xyY color space Ga¨el Chareyron, Dinu Coltuc and Alain Tr´emeau April 21, 2005 Abstract In this paper we propose a new strategy of watermarking which extends the principle of histogram specification to color histogram. The proposed scheme embeds into a color image a color watermark from either the xy chromatic plane or the xyY color space. The scheme resists geometric attacks (e.g., rotation, scaling, etc.,) and, within some limits, JPEG compression. The scheme uses a secret binary pattern, or combines some patterns generated by a secret key in order to modify the chromatic distribution of an image. By using the inverse pattern, the watermark is detected without knowing the original image. Examples of images and attacks are given to illustrate the relevance of the proposed approach, i.e., its invisibility and its robustness. In the second part of this paper we investigate the usefulness of our watermarking approach for color image authentication. Several experiments are presented to show that our scheme ensures image authentication, detects tampered regions in case of malicious attacks and ensures a certain degree of robustness to common image manipulations like JPEG compression, etc. Compared with other blind authentication schemes, the experiments show that, the detection ability, the invisibility, as well as the robustness to some common image processing are improved.

1

Introduction

Among the watermarking methods proposed so far, only few have been devoted to color images. Kutter[11], next Tao and Orchard[18], proposed to select the blue channel in order to minimize perceptual changes in the watermarked image. Van Schyndel[17] proposed to introduce watermarking in the hue angle of the HV S coded color image. One limit of such methods is that they embed only one dimensional color component. Thus, Kutter[11] embeds the blue component into the spatial domain, Voyatzis[22] embeds the intensity component with a binary logo into the spatial domain, Kim[9] embeds the saturation component into the spatial domain, Fleet[7] embeds the yellow-blue component into the frequency domain, Reed[15] embeds the yellow-blue component into the frequency domain, and Kundur[10] embeds the salient image components with a logo into the frequency domain. 1

The methods which embed color data either into the spatial domain or into the frequency domain are generally well-adapted to increase the robustness of the watermarking process [24, 16, 1, 21] but are not well-adapted to optimize both the invisibility (imperceptibility) of the watermark and the detection probability. For example, instead of taking advantage, only of the low sensitivity of the human visual system to high frequency changes along yellow-blue axis [2, 15], we strongly believe that it is more important to focuss on the low sensitivity of the human visual system to perceive small color changes whatever the hue of the color considered [8]. In this paper we propose a new watermarking strategy specifically designed for color images. Our approach extends the graylevel histogram specification watermarking proposed by Coltuc[4] to chromatic (2D) histogram and to color (3D) histogram. Rather than embedding only one color feature into the spatial or, equivalently, into the frequency domain, we place most of the watermark into the color domain. Watermarking imperceptibility is ensured by the low sensitivity of the human visual system to perceive small color differences. Meanwhile robust watermarks are designed to be detected even if attempts are made to remove them in order to preserve the information, fragile watermarks are designed to detect changes altering the image [12]. In the context robust/fragile, our watermarking strategy belongs to the semi-fragile category. It detects image alterations even after attacks such as geometric transforms and mild compression. In this paper we do not provide explicit comparisons with the other semi-fragile watermarking methods, such as the most recent ones proposed by Nikolaidis et al. [14], Yu et al. [26, 19], etc. Rather than comparing directly our method to the others, we provide several experimental data useful to evaluate the performance of our method. We mention that, from a theoretical point of view, our method is very different from the other semi-fragile methods reported in the literature. In the first part of this paper (Section 2), we present the process of embedding into a color image a color watermark from either the xy chromatic plane (Section 2.1.1) or the xyz color space (Section 2.2). The proposed method aims to introduce a color watermarking that resists space distortions (e.g., rotation and scaling) and cropping. In Section 2.1, we introduce the binary pattern used to modify the chromatic distribution of the image. The pattern is generated by a secret key. Next we explain how the chromatic values corresponding to the binary pattern are changed to insert the color watermark. In Section 2.3, we present the inverse strategy used to detect the binary pattern from the color watermarked image. Some examples of images and attacks are provided in Sections (2.1.2 and 2.2.1) to illustrate the invisibility and the robustness of the proposed approach. In the second part of this paper (Section 3), we discuss about the usefulness of proposed method for color image authentication. In the first stage (Section 3.1), we introduce the process of marking the image by using two complementary signatures. Next, in a second stage (Section 3.2), we present the detection strategy. Here again, examples are given, too. An extended discussion on the advantages of the proposed authentication method is given in Section 4. Finally, conclusions are drawn in Section 5.

2

2

Color Image Watermarking

2.1

Marking: Preparatory Stage

Watermarking techniques generally sign images by introducing changes that are imperceptible to the human visual system, but can be detected by a computer program. Consequently, secret keys are used to prevent malicious watermark removal. A secret key is also used in our approach to generate a binary pattern. This binary pattern can be approached as a 2D mask having square cells. Each cell is either black or white (Fig. 1).

(a) random pattern

(b) copyright logo

Figure 1: Two examples of binary patterns of size 1024 × 1024. Color images are usually represented as RGB data. Before the effective marking stage, image color coordinates are converted as follows: 1. RGB to XY Z conversion; 2. XY Z to xyz conversion. The XY Z system corresponds to the CIE 1931 XY Z color space [25]. Let us recall that the XY Z color space is based on the principle of the standard observer whose spectral response corresponds to the average response of the human visual system. It is also useful to recall that this 3D color space is linear. It is common to project this space to the x+ y + z = 1 plane. As x+ y + z = 1 rather than using the XY Z to xyz conversion, some prefers to use the XY Z to xyY conversion because this latter is directly reversible. The result is a 2D space known as the CIE xy chromaticity diagram. In Fig. 2, the test images Lighthouse, Colorbands and Parrots are represented in xyY space and in CIE xy chromaticity diagram. Finally, a look up table (LUT) is computed: for each color of the image an index value computed from its xyY coordinates is associated. 2.1.1

Color Watermarking by a 2D Binary Pattern (CW-2DBP)

The binary pattern previously defined is used to select color cells in CIE xy chromaticity diagram. Meanwhile pixels belonging to black cells keep their color, pixels belonging to white 3

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

Figure 2: Representation of images ”Lighthouse”, ”Colorbands” and ”Parrots” in xyY color space (d, e and f). Projection of color data in CIE xy chromaticity diagram (g, h and i) for Y = 50.

4

cells are changed. Thus, two categories of pixels can be considered: the unchanged pixels and the changed pixels. Unchanged pixels are by definition not modified. Changed pixels correspond to pixels category for which the color will be substituted by the color of a neighboring pixel belonging to the black cells set, i.e., to the unchanged pixels category. Among all the unchanged pixels candidates neighboring the pixel to be changed, the closest one considering its CIELAB ∆Eab color distance is selected.1 The L∗ a∗ b∗ color space is used because it is considered as uniform for the Human Visual System [25], namely the computed distances between colors are close to perceptive distances. In order to avoid false colors, i.e., the coming out of colors which do not belong to the color distribution of the original image, we take into account only colors belonging both to the black cells set and to the color distribution of the original image. Finally, a new image is generated in RGB color space by replacing, as described above, the changed pixels set. This is the marked image. The marking is summarized in Fig. 3. The example showed in Fig. 3 consideres a random binary pattern; other patterns, such as a logo (Fig. 1), have been used with similar results.

Figure 3: Strategy of watermark insertion. Only the cells inside the locus are embedded. Cells outside the horseshoe shape of the xy-locus are not taken into account. Only colors belonging to while cells are changed into function of colors of neighboring black cells belonging to the color distribution of the original image. 1

All colors are defined by three color coordinates XY Z. To compute L∗ a∗ b∗ color coordinates from XY Z color coordinates a non-linear transform is used.

5

Before going further a comment should be done. Since the distance between adjacent cells depends on the size of the cell, it clearly appears that the cell size is an important parameter of the method. Large cell size induces large distances in the considered color space and thus, visible distortions could appear. We have considered a 1 Mbit size binary pattern, i.e., a mask of 1024 × 1024 or, equivalenly, 10 bits/axis resolution in the chromatic plane. In this resolution the marking is completely imperceptible for the HVS. It further appears that the resolution of the chromatic plane can be decreased to 5 bits/axis (32 × 32 cell size), preserving the invisibility of the marking. On the other hand, the size of the cell determines the robustness of the watermarking. In increasing the size of the cells we increase the robustness of the watermarking process. To conclude, the cell size is an essential parameter which controls both the imperceptibility and the robustness of the watermarking. 2.1.2

CW-2DBP: Experimental Results

In order to evaluate the performance of the watermarking in terms of image quality or perceptiveness of color differences, we have considered two commonly used metrics: the Peak Signal-to-Noise Ratio (PSNR) and the CIELAB ∆Eab color distance. The metrics are defined as follows: ⎛

P SNR(dB) = 10 log10 ⎝

⎞

1 MN

M N i=1

j=1

2552 ⎠
j) − W
(i, j)||2 ||O(i,


j) is the original color where M, N is the number of columns and rows of the image. O(i, th
(i, j) is the corresponding color vector (e.g., [R(i, j), G(i, j), B(i, j)]) at (i, j) location and W vector of the watermarked image. ∆Eab =

M  N 1 
Lab (i, j) − W
Lab (i, j)||2 ||O MN i=1 j=1


Lab (i, j) is the color vector in L∗ a∗ b∗ color space (i.e., [L∗ (i, j), a∗ (i, j), b∗ (i, j)]) at the where O
Lab (i, j) is the corresponding color vector (i, j)th location of the original color image and W of the watermarked image. We notice that, on the contrary of the CIELAB ∆Eab color distance, the PSNR computed in RGB color space is not adequated with human perception of color difference. In a general way (see [13]), we have considered that if ∆Eab is greater than 2 a color difference is visible, while if ∆Eab is greater than 5 the watermarked image is very different from the original image. Thus, for a watermarked image, high fidelity means high PSNR and small CIELAB ∆Eab . We have tested the proposed method with several cell sizes for different types of images (presented in Fig. 4). The results are shown in Fig. 52 and Fig. 6. These tests have confirmed that increasing the size of cells we decrease the lower the perceptive quality of the watermarked image (see Fig. 6). The tests have also shown that, 2

see other xy projections vs pattern size at http://color-watermarking.gartworld.org

6

Figure 4: 24 test images of sizes 512x768 or 768x512 pixels used in our experiments. These natural images belong to the Kodak PhotoCD.

when only one pattern is used to watermark the image, the signature is easily visible in CIE xy chromaticity diagram. To eliminate this drawback, we use two complementary signatures on two complementary parts of the image [3]. As for the CW-2DBP case a binary pattern should be defined. The modified watermarking proceeds as follows: 1. Partition image in two disjoint classes, where the partition is defined by a secret key; 2. Do CW-2DBP on one part of the image using the already defined binary pattern; 3. Do CW-2DBP on the other part of the image with the inverse binary pattern (i.e., black cells are changed into white cells and conversely). Let us call CW-2DTBP the modified watermarking procedure (Color Watermarking by Two 2D Binary Patterns). As we can see in Fig. 7, CW-2DTBP better protects the signature, namely the signature is considerably less visible in CIE xy chromaticity diagram. Lastly, we have tested different binary patterns with CW-2DBP. We have noticed that for binary patterns such as the one given in Fig. 1b, the signature is more perceptible in the CIE xy chromaticity diagram than for random binary patterns (see Fig. 8). This can be explained by the fact that the coherence of the pattern is somehow equivalent with a greater size of the cell. It should be stressed that regardless the binary pattern used, the watermarking remains invisible, i.e., we see no artifact in the marked image.

7

(a) Cell size: 2x2

(b) Cell size: 12x12 Figure 5: Impact of cell size of patterns with respect to perceptive quality of image. 8

(a) PSNR (in dB) vs cell size

(b) Average ∆Eab ± σ vs cell size

Figure 6: Impact of pattern size on image quality. Mean values and standard deviation values have been computed from image set of Fig. 4 and for a set of 100 different keys.

9

(a) First class of pixels to watermark.

(b) Original data in CIE xy chromaticity diagram

(c) Watermarked data in CIE xy chromaticity diagram

(d) Second class of pixels to watermark.

(e) Original data in CIE xy chromaticity diagram

(f) Watermarked data in CIE xy chromaticity diagram

(g) Final watermarked image.

(h) Original data in CIE xy chromaticity diagram

(i) Watermarked data in CIE xy chromaticity diagram

Figure 7: Representation of image ”Parrots” watermarked twice (cell size 16x16). Meanwhile some pixels (dark ones represented in (a) ) are watermarked with a secret pattern, other pixels (dark ones represented in (d) ) are watermarked with the inverse pattern.

10

(a) Original Image

(b) Watermarked Image

(c) Color data in CIE xy chromaticity diagram

(d) Detail of color data in CIE xy chromaticity diagram

Figure 8: Example of CW-2DBP watermarking (see full size images at http://colorwatermarking.gartworld.org) with the copyright logo given in Fig. 1b. 11

2.2

Color Watermark by 3D Binary Pattern (CW-3DBP)

Another way to improve the protection of the embedded signature is to use a 3D pattern. The idea of a 3D pattern occured to us in order to make the signature less visible not only in CIE xy chromaticity diagram, but also in the xyz color space. We have considered the following procedure to generate 3D patterns: 1. Several 2D binary patterns are generated in the CIE xy chromaticity diagram by using a secret key; 2. All the 2D binary patterns are piled (from lower to upper Y values). The color image watermarking using the 3D pattern generated as above will be called Color Watermark by Set of 2D Binary Patterns (abreviated CW-3DSBP). A slightly modified procedure generates only half of the 2D binary patterns. Furthermore, for each generated patterns, its inverse pattern is considered, too. The pairs pattern - inverse pattern are piled together as above (see Fig. 9). The order in the pile can be set by a secret key. We shall call CW-3DIBP (Color Watermarking by a set of 3D Inverse Binary Patterns) the resulted watermarking scheme.

y

Y pile order Y i+1 Yi

Y difference

x

Figure 9: The xyY 3D color space can be seen as a set (a pile) of CIE xy chromaticity diagram ordered from lower to upper Y values. In increasing the number of bits to digitize the Y component, we reduce the Y difference between each chromatic plane (Yi) and the following one (Yi+1 ) There are many other ways to generate 3D patterns, for instance, the 3D pattern can be generated completely by a pseudo-random sequence without any repetition of 2D patterns. The benefit of 3D watermarking clearly appears in Fig. 10. The test image Colorbands have been marked by using 1D, 2D and 3D color watermarking3 . As it can be seen, the 1D 3

The 1D strategy changes the Y values of cells selected to new Y values. As for 2D and 3D cases, two

12

marking may be detected by looking the Y axis (Fig. 10 b)), while the 2D watermarking may be observed in the chromatic plane (Fig. 10 c)). On the contrary, in case of 3D marking, whatever the color representation considered (CIE xy chromaticity diagram or xyY color space (Fig. 10 c)) we can neither perceive nor detect any watermark embedded. To conclude, when watermarking strategy is based on Y or xy the signature is visible, whereas with the CW-3DBP watermarking strategy based on xyY the signature is imperceptible. 2.2.1

CW-3DBP: Experiments

In order to assess watermarking visual effects, we have computed for each pixel the CIELAB ∆Eab color distance between the original image and the watermarked image (see Fig. 11). In this figure, color changes are displayed with a black (smaller changes) and white (higher changes) logarithmic scale. We have also computed the mean and the standard deviation values of CIELAB ∆Eab . Let us recall that for CIELAB distance, ∆Eab < 2 means imperceptible to HSV, meanwhile CIELAB ∆Eab > 5 means strong color artifacts 4 . In order to compare CW-2DBP with CW-3DBP in terms of image quality, we have computed the PSNR and the CIELAB ∆Eab for several pattern sizes (see Fig. 12 and Fig. 6). The experimental results show that CW-3DBP outperforms CW-2DBP.

2.3

Color Image Watermarking: Detection

The watermark detection is blind, i.e., the original image is not needed. To decode the watermark, the user needs to know the secret key used to generate the pattern. The watermark detection proceeds as follows (see Fig. 13): 1. Generate the binary pattern BP; 2. Compute a look up table (LUT) for the colors of the watermarked image: for each color, an index value computed from its xyY coordinates is associated; 3. Search for each color pixel entry of the LUT if its xy color coordinates belong to a black cell or a white cell of the BP and count: (a) Nb : the number of pixels for which the color belongs to a black cell ; (b) Nw : the number of pixels for which the color belongs to a white cell ; 4. Compute the ratio

Nw Nb +Nw

and decide.

categories of pixels can be considered: the unchanged ones and the changed ones. Changed pixels correspond to pixels category for which the Y value will be substituted by the Y value of a neighborhood pixel belonging to black cells. 4 Other results, available at http://color-watermarking.gartworld.org, enable us to see the map of pixels for which color changes are too important (i.e. ∆Eab is greater than 5) in comparison to the map of pixels for which color changes are perceptible but not too important (i.e. ∆Eab is greater than 2 but lesser than 5).

13

(a) in CIE xy chromaticity diagram

(b) in xyY color space

(c) in CIE xy chromaticity diagram

(d) in xyY color space

(e) in CIE xy chromaticity diagram (f) in xyY color space Figure 10: Representation of image ”Colorbands” watermarked by : a 1D pattern applied to Y component (a, b) , a 2D pattern (CW-2DBP) applied to xy components (c, d), a 3D pattern (CW-3DIBP) applied to xyY components (e, f). 14

(a) cell size 02x02 : (b) cell size 04x04 : (c) cell size 08x08 : (d) cell size 16x16 : mean mean mean mean ∆Eab = 0.649569, ∆Eab = 0.641811, ∆Eab = 0.798739, ∆Eab = 1.0291, σ = 0.419291 σ = 0.433859 σ = 0.488431 σ = 0.58272

(e) cell size 32x32 : (f) cell size 64x64 : mean mean = 1.53645, ∆Eab = 2.47449, ∆Eab σ = 0.99099 σ = 1.68703

Figure 11: CIELAB ∆Eab color differences, displayed with a logarithmic scale space, computed between the original image and the CW-3DRBP watermarked image.

15

(a) PSNR (in dB) vs cell size

(b) Average ∆Eab ± σ vs cell size

Figure 12: Impact of cell size on image quality. Mean and standard deviation values have been computed from image set of Fig. 4 and for a set of 100 different keys.

16

Figure 13: Strategy of watermark detection.

If the image has been signed with the considered key (BP), then there is no point in the white zone, namely Nb = 100% and Nw = 0%. Obviously, in case of attack, these values can change. Therefore, we can decide if the image has been watermarked depending on the w value of NbN+N . In decreasing the ratio, we increase the probability that the image has been w watermarked. 2.3.1

Detection: Experimental Results

We tested several attacks on watermarked images by the CW-3DBP. All geometrical attacks tested affect the appearance of the image, but do not modify its color distribution (see Fig. 14). Thus, we can say that the proposed watermarking strategy resists the majority of geometrical attacks (provided that no interpolation or filtering is used). Indeed, even if these latter transforms do not generally modify the statistics of the image, they modify its color distribution (i.e., the number of colors and the value of these colors). Actually the signature essentially resists to deformation on image. In Fig. 14, some examples are given to illustrate the ratio of pixels matching the pattern used versus several attacks. Meanwhile this ratio remains equal to 100% when no filtering is used, the ratio of pixels matching the BP decreases proportionally to the strength of the filtering. For instance, for Gaussian filtering (σ = 0.391 for 3 × 3 mask and σ = 0.625 for 5 × 5) the watermark detection is impossible.

17

Original image

Nw = 50% - Watermark can not be detected

Watermarked image

Nw = 0% - The watermark is detected

Scale 50% or Scale 200% (none intepola- Nw = 0% - The watermark is detected tion)

Wave effect on image

Nw = 0% - The watermark is detected

Cropping

Nw = 0% - The watermark is detected

Free rotation

Nw = 0% - The watermark is detected

Screenshot

Nw = 0% - The watermark is detected

Figure 14: Example of attacks on image ”Parrots”. Percentage of Nw = 0% versus varoius attacks. In decreasing the percentage of pixels belonging to a white cell (Nw ) we increase this probability.

18

We have tested the robustness of our watermarking process to JPEG attack. The experiments have shown that, at a high compression quality factor between 100% and 96 % (see Fig. 15), in almost all cases, the watermark is detected. On the other hand, for lower JPEG compression quality factor, i.e., for higher JPEG compression ratio, the performance of the detection process decreases rapidly, the detection being quite impossible. Intrinsically to the proposed method, for a random BP, the ratio of unchanged pixels (for a 2 × 2 pattern) is near 50% (see Fig. 17). On the other hand, compressing a watermarked image with a quality factor (97%) by JPEG, we find a ratio of unchanged pixels near 50%. Thus, it is impossible to say if the image has been watermarked with the random BP, or has not been watermarked at all. When we use a larger size for cells (such 16 × 16 or 32 × 32), the watermarking resists a little bit more JPEG compression, but the probability of false detection is more important than in case of a small pattern. It seems that with the 2D strategy (see Fig. 15) the robustness to JPEG compression scheme is higher than with the 3D strategy (see Fig. 16); inversely the quality of the watermarked image seems to be higher with the 3D strategy than with the 2D strategy. Consequently, a compromise needs to be found between the robustness and the invisibility when an image compression is foreseen. From our experiments, it follows that for a size of cells 2 × 2, we can decide that if Nb > 75% (see the results given Fig. 15 and Fig. 17) then the image has been watermarked. If we increase the size of cells we have to increase the decision threshold should be increased. For example, for a size of cells 8 × 8, we should take Nb > 90% to decide that the image has been marked.

Figure 15: Impact of JPEG compression on watermark detection (2D Pattern) wich varying cell sizes. Mean values have been computed from image set of Fig. 4 and for a set of 100 different keys. We have also studied the rate of false alarms associated to this watermarking method. In a first time, we have watermarked an image and we have computed the number of pixels 19

Figure 16: Impact of JPEG compression on watermark detection (3D Pattern) wich varying cell sizes. Mean values has been computed from images set of Fig. 4 and from a set of 100 different keys.

detected as watermarked. Next, the original non-watermarked image has been watermarked with another key and, as above, the number of pixels detected as marked have been counted. Finally, the number of detected pixels for this two watermarking processes have been compared to the number of pixels detected as marked for the original non-marked image. Let us consider that the rate of false alarms corresponds to the number of non-watermarked pixels detected as watermarked. We have observed that the ratio of false alarms is better with a 3D method, such as CW-3DBP, than with a 2D method, such as CW-2DBP. This can be observed by comparing Fig. 18 (computed with a 3D pattern), with Fig. 17 (computed with a 2D pattern). We can see in these figures that, with the 3D process, the shape of the distribution of detected pixels is always Gaussian. With the 2D watermarking, the distribution of detected pixels is more irregular and it is worsen as the size of the pattern increases. Meanwhile, in case of 2D watermarking, the rate of false alarms is less than 10% only for a 2x2 pattern. In case of 3D watermarking, the rate of false alarms is less than 10% for BP up to 8x8. We have also observed that the number of holes in the pattern (i.e., the percentage of white cells where there is no color belonging to the color distribution of the watermarked image) increases the rate of false alarms. Thus, we have observed that, when the size of the pattern increases, if we increase the density of the color distribution then we increase the rate of false alarms. For instance see the color distribution of ”Parrots” (Fig. 2 (i) ) and of ”Lighthouse” (Fig. 2 (g) ), with a pattern of size 2 × 2 and with CW-3DBP, for ”Parrots” the detection rate of watermarked pixels is equal to 49.9 % 5 with a standard deviation equal to 0.97, meanwhile for ”Lighthouse” this rate is equal to 49.9% with a standard deviation 5

This result has been obtained from an experiment done with 100 different keys.

20

(a) 2x2 cells

(b) 4x4 cells

(c) 8x8 cells

(d) 16x16 cells

(e) 32x32 cells

(f) 64x64 cells

Figure 17: Percentage of pixels detected as watermarked for a given set of images ( see Fig. 4), with a random key and different sizes of 2D pattern.

21

(a) 2x2 cells

(b) 4x4 cells

(c) 8x8 cells

(d) 16x16 cells

(e) 32x32 cells

(f) 64x64 cells

Figure 18: Percentage of pixels detected as watermarked for a given set of images ( see Fig. 4), with a random key and different sizes of 3D pattern.

22

equal to 1.34. On the other hand, with a 16 × 16 pattern, meanwhile the detection rate of watermarked pixels decreases imperceptibly to 49.5% for ”Parrots” with a standard deviation equal to 3.40 , for ”Lighthouse” this rate decreases perceptibly to 49.1% and the standard deviation increases significantly to 6.2 .

3

Color Image Authentication

3.1

Color Image Authentication: Marking

We investigated, in the sequel, the usefulness of our watermarking approach for color image authentication. The proposed scheme extends and ameliorates the exact histogram specification method proposed by Coltuc et al., in [5, 6]. The exact histogram specification method marks a set of sentinel pixels, uniformly spread over the image. The watermark consists in sparse and symmetric histograms (for instance, graylevels multiple of a certain prime number). Image authentication immediately follows if the histogram of sentinel pixels is exactly recovered. In case of attack, obviously some sentinel pixels are modified. Since sentinel pixels have only some predefined graylevels, any graylevel change of a sentinel pixel is easily detected. It is therefore possible to locate all areas where image has been altered by malicious editing. The same idea was used as well for color image authentication by marking the intensity component in the HSI color space. While in the original method only a small subset of pixels was marked, the new method extends the marking to the entire image pixel set. Two complementary signatures are used. Thus, the unchanged pixels and changed pixels are evenly treated. The authentication watermarking scheme proceeds as follows: 1. Divide color space into 2 disjoint sets of color cells: C1 and C2 ; 2. Segment image into 2 disjoint classes of pixels: S1 and S2 ; 3. Mark all image pixels. These three stages are described in the following sections. 3.1.1

Color sets

C1 and C2 are selected by using a secret key. The color space is divided in ”fine grains”, i.e., around each C1 cell there are cells belonging to C2 and, conversely. So far, we have used equal sized cells. As stated in Section 2, the cell size is a very important parameter. A small cell size value gives a very safe tampering detection and the watermarking is certainly invisible, but does not ensure any robustness. A large cell size gives robustness, but color artifacts such as false colors may appear.

23

3.1.2

Pixel classes

In order to prevent watermark removal, S1 and S2 are selected by using a secret key, as well. Opposite to [5, 6] (where sentinels are selected as isolated pixels uniformly spread over the entire image), no special constraints are imposed on S1 and S2 selection. We have considered, however, a ”fine grain” selection of the two sets. 3.1.3

Marking

The marking follows the color watermarking principle introduced in Section 2. If the color
c of a pixel p ∈ Si , i = 1, 2 belongs to Ci , no modification is done; otherwise change color to
c∗ ∈ Cj , j = 3 − i. The new color is selected such as CIELAB ∆Eab between
c and
c∗ is minimal. Obviously, if we increase the granularity of the color space partition is fine, then we increase the invisibility of the watermark. Since changed pixels for one set of pixels (e.g., C1 ) are unchanged pixels for the other set (e.g., C2 ) and conversely, all pixels are marked by this watermarking method. Besides, the color distribution of the watermarked image is preserved. For exemple, see the watermarked images of Fig. 19. As it can be seen, no visual artifact appears on watermarked images. The shape and the content of all color distributions seems preserved in L∗ a∗ b∗ color space. Let us call CW-TCBP this Color Watermarking based on Two Complementary Binary Patterns. Unlike to CW-2DTBP (see Section 2.1.2) all pixels are marked by CW-TCBP. Since two complementary signatures are used to watermark the image, the invisibility of CW-TCBP is better ensured than for CW-2DTBP. This can be seen by comparing the 3D-representations of Fig. 19 for CW-TCBP with the 2D-representations of Fig. 7 for CW-2DTBP. Let us note that, unlike to CW-2DTBP which uses only one binary pattern applied to the color space, the CW-TCBP uses two binary patterns. Meanwhile one pattern is applied to the color space, another one is applied to the image.

3.2

Color Image Authentication: Detection

During the detection, the color distribution of S1 and S2 classes are analyzed. If all pixel belonging to S1 have only colors in C1 set and all pixel belonging to S2 have only colors in C2 set, then the image is authenticated. If not, an error map is computed. The error map is obtained simply by setting to zero all pixels violating the color membership stated above. Since all pixels have been marked, the detection process is able to locate all areas where the image has been altered by malicious attacks. The detection is blind. Image validation should be tackled by a trustworthy content verification system (CVS). Since customers must not have access to secret keys, the appropriate solution is to create network servers [23]. The watermarked image is submitted to CVS server which either authenticates the image, or computes an error map6 . 6

As Tsai et al. did in [20] for edge detection

24

(a) ”Parrots”

(b) xyY colorspace representation

(c) ”Colorbands”

(d) xyY colorspace representation

(e) ”Lighthouse”

(f) xyY colorspace representation

Figure 19: Some examples of fragile watermarked images.

25

An example is provided in Fig. 20. A malicious attack has been simulated on the watermarked image. The attack is done by using data blocks of the image itself. Such attacks usually are, by far, more difficult to be trapped than simple pixel editing ones. The proposed scheme detects immediately the tampered region.

(a) Original watermarked image. (b) Attacked watermarked image. The tip of beak have been erased.

(c) Map of attacked area.

(d) Map of attacked area after JPEG compression of watermarked image (100% quality factor. Between original watermarked image and JPEG watermarked image P SN R = 48.42dB)

Figure 20: Example of image attack on fragile watermarked image.

3.2.1

Semi-fragility

The proposed watermarking scheme appears to be semi-fragile. By common image processing, pixels are modified. However some of the modified pixels preserve an allowed color: either they keep their color or they have a very close one. This is due to the correlation

26

between the original image and the processed ones. The number of pixels detected as having correct colors depends on the size of the color cells, as well. An interesting feature of the proposed scheme is that the correct pixels appears to be uniformly distributed over the image. Therefore, if a malicious attack has been performed on the image, the attacked region appears to be less populated by correct detected pixels; we can then observe higher density of erroneus pixels. In Fig. 20, errors detection after malicious attack and JPEG compression is shown. Obviously, the attacked region still can be identified.

4

Authentication: Some Comments

At a first sight, the proposed method appears to be very similar to the exact histogram specification method proposed by Coltuc et al. in [5, 6]. Allowed graylevels are replaced by allowed colors and, instead of specifying allowed graylevels (or colors) only for a set of pixels, i.e., the sentinel pixels, we have to specify allowed colors for the other set, as well. Besides, the former scheme was extended as well to color images. It should be noticed, however, that color image authentication by marking the intensity component in the HSI color space is near graylevel marking. In fact, even if the basic principle is the same, the watermarking in the chromatic domain completely changes the behavior of the scheme. Some arguments are given below.

4.1

Imperceptibility versus sentinel density

The number of sentinel pixels of [5, 6] is highly limited by the histogram specification procedure. Exact histogram specification excellently performs when applied on the entire image. Regional histogram specification performs very well if regions are separated by image contours. When the regions are highly interleaved, as for authentication watermarking, exact histogram specification can introduce noise. If we restrict to at most 5% sentinel pixels, we avoid noise. However, if we try to mark 1 pixel out of 9 or 1 pixel out of 4 (i.e., 25% of the total number), the marking is no more invisible. The newly proposed scheme yields invisible watermarking when 1 pixel out of 2 is marked (see Section 2.1.1) or even when all pixels are marked (see Section 3.1.3).

4.2

Sentinel density versus attack tracking

We can argue that a sentinel density of 2 − 10% is high enough to detect image malicious attacks. Since 2% means 2 pixels out of a square of 10×10 pixels and, even better, 10% means about a pixel out of a 3 × 3 area, obviously, this is enough for almost all cases. However, we can easily imagine cases where such assertion is no longer true. For instance, for an image representing written text, the modification of very few pixels can completely change the meaning of the text. Similarly, modifying a simple digit, we can drastically modify the resulted number. Such an example is given in Fig. 21. Other examples can be given as well. 27

(a) Watermarked image.

(b) Attacked watermarked image. Some words (see item 2) and numbers (see items 3 and 4) have been modified.

(c) Detection of attacks (all pixels detected as attacked are displayed in white)

Figure 21: Example of fragile watermark on a Driver’s license. In this experiment, the sentinel density is equal to 100%, and the detection threshold Nb is equal to 100%.

28

4.3

Fragility versus semi-fragility

As the original graylevel method, the proposed method is a fragile one. It should be noticed that, opposite to the original method, it exhibits a certain degree of robustness. We have presented an example where attack detection was possible after image compression. For a subtle attack as discussed in the above paragraph, certainly the attack remains undetected. However, the degree of robustness represents an improvement with respect to the original scheme.

5

Conclusions

In this paper we have introduced a new watermarking method for color images. We have proposed different strategies to optimize this method. We have presented a new CW-3DBP strategy which ameliorates the previous CW-2DBP strategy. We have shown that this new strategy not only improves the invisibility, but also the robustness of the watermarking. We have shown that this method resists geometrical deformations and, within limits, to JPEG compression. That is, it remains fragile to major color histograms changes. We have also shown that the proposed watermarking method is very efficient for color image authentication. Several results have been given to show that our scheme ensures image authentication, detects tampered regions in case of malicious attacks (even very subtle ones) and ensures a certain degree of robustness against JPEG compression. In comparison with other blind authentication schemes, we have shown that the detection ability and the invisibility have been improved, likewise the robustness to some common image processing has been improved. Other comparisons are actually under study to show the quality and other advantages of these watermarking and authentication methods. Further research is in progress to improve the resistance of our method to a higher number of attacks. Another improvement will consist in extending the watermark process to other color spaces like L∗ a∗ b∗ or Y Cr Cb color space used in JPEG and MPEG standards. Another improvement will consist in optimizing the signature from new patterns as, for instance, to avoid the marking of the central region in xyY color space because this latter is achromatic.

References [1] P. Campisi, D. Kundur, D. Hatzinakos, and A. Neri. Hiding-based compression for improved color image coding. In SPIE Proceedings, volume 4675, pages 230–239, January 2002. [2] J.J. Chae, D. Murkherjee, and B.S. Manjunath. Color image embedding using multidimensional lattice structures. In Proceedings of IEEE, Forum on Research and Technology Advances in Digital Librarie, pages 319–326, Santa Barbara, CA, Apr 1998.

29

[3] G. Chareyron, B. Macq, and A. Tr´emeau. Watermaking of color images based on segmentation of the xyz color space. In Proceedings of CGIV Conference, pages 178– 182, Aachen (GE), april 2004. IS & T. [4] D. Coltuc and Ph. Bolon. Robust watermarking by histogram specification. In Proceedings of the IEEE Workshop on Multimedia and Signal Processing, 1999. [5] D. Coltuc, J.M. Chassery, and Ph. Bolon. Image authentication by histogram specification. In Proceedings of the IEEE Workshop on Multimedia and Signal Processing, pages 499–504, 2001. [6] D. Coltuc, J.M. Chassery, and Ph. Bolon. Fragile and robust watermarking by histogram specification. In SPIE Conf. on Security and Watermarking of Multimedia Contents IV, SPIE Proceedings, volume 4657, pages 701–710, 2002. [7] D. Fleet and D. Heeger. Embedding invisible information in color images. In Proc. 4th IEEE International Conference on Image Processing (ICIP’97), volume 1, pages 532–535, Santa Barbara, USA, 1997. [8] S.L. Hayden and D.P. Oulton. The quantification of small visual colour differences. Journal of SDC, 10:104–111, march 1994. [9] H. S. Kim, H. K. Lee, H. Y. Lee, and Y. H. Ha. Digital watermarking based on color differences. In Proc. SPIE Internet Imaging II, volume 4314, pages 10–17, San Jose, California, 2001. [10] D. Kundur and D. Hatzinakos. Toward robust logo watermarking using multiresolution image fusion principles. IEEE Trans. on Multimedia, 6(1):185–198, Feb 2004. [11] M. Kutter. Digital signature of color images using amplitude modulation. In Proceedings of the SPIE, volume 3022, pages 518–525, 1997. [12] E.T. Lin, C.I. Podilchuk, and E.J. Delp. Detection of image alterations using semifragile watermarks. In Proceedings of SPIE, International Conference on Security and Watermarking of Multimedia Contents II, volume 3971, San Jose, CA, Jan 2000. [13] M. Mahy, E. Van Eyckden, and O. Oosterlink. Evaluation of uniform color spaces developed after the adoption of cielab and cieluv. Color Research and Application, 19(2):105–121, 1994. [14] N. Nikolaidis and I. Pitas. Robust image watermarking in the spatial domain. Signal processing, 66:385–403, 1998. [15] A. Reed and B. Hanningan. Adaptive color watermarking. In SPIE Proceedings, volume 4675, pages 222–229, January 2002.

30

[16] M. Saenz, P. Salama, K. Shen, and E. J. Delp. An evaluation of color embedded wavelet image compression techniques. In Proceedings of the SPIE/IS & T Conference on Visual Communications and Image Processing (VCIP), pages 282–293, San Jose, CA, Jan 1999. [17] G. Van Schyndel. Data hiding in angle quantisation. In SPIE Security and Watermarking of Multimedia Contents III, pages 544–554, 2001. [18] B. Tao and M. T. Orchard. Coding and modulation in watermarking and data hiding. In SPIE Conference on Security and Watermarking of Multimedia Contents, volume 3657, pages 503–510, 1999. [19] H. H. Tsai, P. T. Yu, and C. C. Chang. A color image watermarking scheme based on color quantization. Signal processing, 84:95–106, 2004. [20] P. Tsai, C. C. Chang, and Y. C. Hu. An adaptive two-stage edge detection scheme for digital color images. Real-Time Imaging, 8:329–343, 2002. [21] J. Vidal, M. Madueno, and E. Sayrol. Color image watermarking using channel-state knowledge. In SPIE Proceedings, volume 4675, pages 214–221, January 2002. [22] G. Voyatzis and I. Pitas. Digital image watermarking using mixing systems. Computer and Graphics, 22(4):405–416, 1998. special issue on data security in image communication and networking. [23] G. Voyatzis and I. Pitas. The use of watermarks in the protection of multimedia products. In Proceedings of the IEEE Workshop on Multimedia and Signal Processing, volume 87, pages 1197–1207, 1999. [24] R.B. Wolfgang, C.I. Podilchuk, and E.J. Delp. The effect of matching watermark and compression transforms in compressed color images. In Proceedings of the IEEE International Conference on Image Processing (ICIP), Chicago, Illinois, Oct. [25] G. Wyszecki and W. S. Stiles. Color science: concepts and methods, quantitative data and formulae, second edition. J. Wiley publisher, 1982. [26] P. T. Yu, H. H. Tsai, and J. S. Lin. Digital watermarking based on neural networks for color images. Signal processing, 81:663–671, 2001. Acknowledgements: The authors would like to thank the anonymous referee for his helpfull suggestions and remarks. All captures of colorspace had been done with ColorSpace Software by Philippe COLANTONI - http://www.couleur.org.

31