Comparative Analysis of Substitutive 3D Models Fragile Watermarking Techniques

Abstract—

Due to the importance of multimedia data and the urgent need to use it in many fields such as industrial, medical and entertainment, protecting them becomes an important issue. Digital watermarking is considered as an efficient solution for multimedia security as it preserves the original media content's as it is. 3D Fragile watermarking aims to detect any attacks to 3D graphical models to protect the copyright and the ownership of the models. In this paper, we present a comparative analysis between two substitutive 3D fragile watermarking algorithms. The first based on adaptive watermark generation technique using the Hamming code, while the other uses Chaos sequence for 3D models fragile watermarking in the spatial domain. The study uses different assessment measures to show the points of strength and weaknesses of both methods.

Keywords—Adaptive watermarking, hamming code, Chaos sequence, tampering detection, authentication

Introduction

Information security refers to the protection of information from unauthorized access, use, modification, or destruction to achieve confidentiality, integrity, and availability of information. There are two types of information security; information hiding (Steganography) or information encryption (Cryptography). Encryption is the science of protecting information from unauthorized people by converting it into a form that is non-recognizable by its attackers. Information hiding embeds a message (watermark) over a cover signal such that its presence cannot be detected during transmission. There are two categories of information hiding: steganography and watermarking. The main goal of steganography is to protect the message itself and hide as much data as possible in the cover signal, while the goal of the watermarking is to protect the cover signal by hiding data (watermark) in it.

Watermarking may be used for a wide range of applications, such as Copyright protection and content authentication. There are three types of watermarking according to the goal to be achieved; robust watermarking, fragile watermarking and semi-fragile watermarking. The aim of the robust watermark is to protect the ownership of the digital media and keep the embedded watermark detectable after being attacked. On the other hand, the fragile watermark aims to be sensitive to any attack on the model and locate the changed regions and possibly predict how the model was before modification. Therefore, fragile watermarking is used for content authentication and verification. The semi-fragile watermark combines both the advantages of the robust watermark and the fragile watermark so that it is more robust than fragile watermark and less sensitive to classical user modifications that aims to discriminate between malicious and no malicious attack.

After the great interests and works for multimedia contents watermarking like in image, audio, video and text and with the growth of 3D graphical models generation, and the spread of using it in data representations of other applications like fuel or water transferring pip models, 3D cartoon models etc, recently, researchers have a great interest in watermarking of 3D models.

In this paper, we presented a comparative analysis of two adaptive fragile watermarking techniques [1, 2] and clarify their advantages and weakness area. The paper is organized as follows, section 2 previews the fragile watermarking from the state of the art. Section 3 briefly explains the methods used in this study. Section 4 shows the experimental result with empirical analysis. Finally, conclusions are provided in Section 5.

Related work

Watermark embedding strategies primarily are divided into two classes; additive and substitutive. In the case of additive strategy, a watermark is considered as a random noise pattern which is added to the mesh surface as in [3-6]. But in the case of substitutive, the watermark is embedded in the numerical values of the mesh elements by a selective bit substitution as in [1,2,7,8,9]. Based on this embedding style, the watermark may be embedded in different embedding primitives as follows:

A. Data file organization.

This category utilizes the redundancy of polygon models to carry information. Ichikawa et al [10] modified the order of the triangles (the order of the triplet of vertices forming a given triangle). They only use the redundancy of description. Wu et al [11] used the mesh partitioning to divide the mesh into patches with a fixed number of vertices. While the geometrical and topological information of each patch, as well as other properties (color, texture, and material), are used to produce the hash value which represents the signature embedded in the model. The goal of Bennour et al [12] was to protect the visual presentations of a 3D object in images or videos after it has been marked. They also proposed an extension of 2D contour watermarking algorithm to a 3D silhouette. Sales et al [13] presented a method based on the protection of the intellectual rights of 3D objects through their 2D projections.

B. Topological data

These algorithms use the topology of the 3D object to embed the watermark which leads to change the triangulation of the mesh. Ohbuchi et al [14] presented two visible algorithms where the local triangulation density is changed to insert a visible watermark depending on the triangle similarity quadruple (TSQ) algorithm. Whereas the second is to embed a blind watermark by topological ordering TVR (Tetrahedral Volume Ratio) method. Mao et al ’method [15] triangulated a part of a triangle mesh to embed the watermark into the new positions of the vertices, this algorithm is considered a reversible as it allows a full extraction of the embedded information and a complete restoration of the cover signal.

C. Geometrical Data

Most of the 3D fragile watermarking algorithms embed the watermark by modifying the geometry of the 3D object either in the spatial domain or in the frequency domain. Yeo and Yeung [16] proposed the first 3D fragile watermarking algorithm where each of the vertex information is modified by slightly perturbing the vertex based on a pre-defined hash function to make all vertices valid for authentication. Lin et al. [4], and Chou et al. [17] solved the causality problem raised in Yeo’s method by setting both hash functions depending only on the coordinates of the current vertex [4] and proposed a multi-function vertex embedding method and an adjusting-vertex method [17]. With considering high-capacity watermarks, Cayre and Macq [18] considered a triangle as a two-state geometrical object and classify the triangle edges based on the traversal into entry edge and exit edge, where the entry edge is modulated using Quantization index modulation (QIM) to embed watermark bits.

To immune similarity transformation attacks, Chou et al [19] embedded watermarks in a subset of the model's faces so that any changes will ruin the relationship between the mark faces and neighboring vertices. Huang et al. [20] translated the 3D model into the spherical coordinate system, then used the QIM technique to embed the watermark into the r coordinate for authentication and verification. Xu and Cai [21] used the Principal Component Analysis PCA to generate a parameterized spherical coordinates mapping square-matrix to embed a binary image (watermark). Wang et al. [1] used the hamming code to calculate the parity bits that embedded in each vertex coordinate with the LSB substitution to achieve verification during the extraction stage. According to the problem of high collision characteristic of hash function used for generating the watermark from the mesh model Wang et al. [2] employed a chaotic sequence generator to generate the embedded watermark to achieve both the authentication and verification of the model.

Substitutive fragile watermarking techniques

Watermarking techniques can be classified into a different category depending on many attributes. Among the different attributes, watermark techniques can be classified according to watermark generation pattern which relays on the application type, the watermark may be an external information specific to the model - that must be kept secured - or may be an information that is not related to the model. Generally, there are two ways of watermark generation pattern:

1. Self-embedding: which means the watermark embedded in the cover model is a compressed version (the hash of the cover model or error correction code) of the same model by some embedding strategy.
2. External embedding: means that the watermark is an external information related or not related to the cover model. This external information could be text data, image data or pseudo-random bit sequence. And it is a need to transform the embedded data to binary bit sequence before embedding.

According to this classification, Wang [1, 2] proposed two fragile watermarking techniques based on substitutive embedding method. Where they used the Least Significant Bit (LSB) substitution embedding method. At first technique [1], an adaptive watermark is generated from each cover model by using the Hamming code technique for 3D objects verification. While the hamming code is used to generate three parity bits from each vertex, they are used for verification during the extraction stage. These three parity check bits P1, P2, and P3 are regarded as the watermark, which embedded in each vertex coordinate by the least significant bit (LSB) substitution. Leading to increasing the data hiding capacity but on the other hand, the embedding distortion to the model is uncontrollable. Authors claimed the method to be immune to the causality, convergence and embedding holes problems.

The second technique [2], proposed a novel Chaos sequence based fragile watermarking scheme for 3D models in the spatial domain. Where the authors used the chaotic sequence generated from the Chen-Lee system, which is considered as the embedded watermark. Then they embedded the watermark in each vertex coordinate according to a random sequence of integers generated by using a secret key K, to achieve both the authentication and verification. Instead of the hash function, the tampering region can be verified and located by the Chaos sequence-based watermark check.

Both techniques are simple to implement and don’t need the original model or the watermark for the 3D models verification and tampering detection localization, as they don’t depend on using the hash function for authentication and verification. Also they achieve high embedding capacity, since they used all the vertices of the model for embedding. For the second technique, from the security point of view, finding the Chaos sequence is a challenge for an attacker. Security was also achieved by using secret keys to embed the watermarks

Experimintal result and desscution

The two techniques of Wang et al [1, 2] are were implemented using a multi-paradigm numerical computing environment and a proprietary programming language developed by MathWorks (MATLAB R2018a).

Assessment Methods:

The main requirements to provide an effective watermark are imperceptibility, robustness against intended or non-intended attacks and capacity. Based on these requirements a series of experiments were conducted to measure the imperceptibility robustness. Table 1 illustrates the assessment measures needed to evaluate watermarking systems [22].

Performance Assessment measures used in mesh watermarking

Assessment Type

Assessment measure

Formula

Imperceptibility measures

Hausdorff

distance (HD)

Modified

Hausdorff distance (MHD)

Root mean

square error (RMSE)

Robustness measures

Correlation coefficient

Where, the RMSE measures the differences between the values predicted by the model or an estimator and the values observed. Lower values of RMSE indicate better fit. When the RMS values are small this indicates insignificant positional changes during the watermark embedding. The Hausdorff distance measures “how similar” two sets are in the metric sense. If two sets are in a small Hausdorff distance, they are supposed to “look” almost the same. The Modified Hausdorff distance computes the forward and reverse distances and outputs the minimum of both. The Correlation Coefficient (CC) measures the degree (strength) of the relationship between two variables. The range of values for the correlation coefficient is -1.0 to 1.0., whereby a correlation of -1.0 indicates a perfectly negative correlation and a correlation of 1.0 indicates a perfectly positive correlation. A value of zero indicates that there is no relationship between the two variables. Generally, the correlation coefficient used to measure the change in the bit values of the original watermark and the extracted watermark, meanly it measures how the watermark robust to the attacks. Since in the fragile watermark, the aim is to be sensitive to any attacks, and to detect any tempering to the model, we measured the CC metric between the original watermark W and the extracted watermark W’, and between the original model M and watermarked model M’.

We have applied the measures on both [1] and [2] techniques using 7 models. In the hamming code-based technique, the author normalized the 3D model into the range 0 to 1, to embed the watermark but they didn’t perform the denormalization after embedding. I our experiment, the algorithm has been used as mentioned in the paper [1] and after performing the denormalization step as well. the results of applying the technique on the models without the denormalization step is presented in Table 2. Table 3 shows the measurement metrics after applying denormalization to the 3D model, which obviously show that the values of the RMS are less than the first values which indicates minimal positional changes during the watermark embedding. Fig.1 shows the model before and after embedding the watermark without denormalization while Fig.2 shows the model before and after embedding the watermark after denormalization. Moreover, Fig.3 and Fig.4 show the difference between the X, Y, and Z values of the vertices of the original and the watermarked model without using normalization and with normalization respectively.

Table 4 shows the measurement metrics of the Chaos sequence based fragile technique [2]. Which illustrates that the imperceptibility measures are less than the previous technique. And this technique doesn’t distort the model after watermark embedding. Fig.5 shows the model before and after watermarking and the difference between the vertices I XYZ coordinate system.

Hamming code based fragile technique mesurments without Denormalization

Model

No. vertices/

faces

Imperceptibility measures

Robustness measure

HD

MHD

RMSE

CC (M,M’)

CC (W,W’)

Cow

2904/ 5804

0.9043

0.4848

0.4965

0.8995

1.0000

Casting

5096/ 10224

1.1005

0.4039

0.4912

0.9008

1.0000

Bunny

1355/ 2641

1.2419

0.6803

0.5303

0.9765

1.0000

Bunny_

bent

1355/ 2641

1.4291

0.6760

0.5450

0.9549

1.0000

hemi_

bumpy

1441/ 2816

1.5671

0.7331

0.5592

0.7941

1.0000

Bunny

34835/ 69666

0.9822

0.5176

0.4866

0.9544

1.0000

hand

36619/ 72958

1.0941

0.4169

0.4811

0.8988

1.0000

Hamming code based fragile technique mesurments - After Denormalization

Model

No. vertices/

faces

Imperceptibility measures

Robustness measure

HD

MHD

RMSE

CC (M,M’)

CC (W,W’)

Cow

2904/

5804

1.5685e-15

5.0240e-16

3.4358e-16

1.0000

-0.0050

Casting

5096/

10224

1.8388e-15

5.3842e-16

3.6531e-16

1.0000

0.0056

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Bunny

1355/

2641

1.9375e-15

7.2551e-16

4.7291e-16

1.0000

-0.0253

Bunny_

bent

1355/

2641

2.4139e-15

8.4952e-16

5.5116e-16

1.0000

-0.0057

hemi_

bumpy

1441/

2816

3.1563e-15

9.8454e-16

6.5371e-16

1.0000

0.0048

Bunny

34835/

69666

1.7844e-15

5.2505e-16

3.4298e-16

1.0000

0.0011

hand

36619/

72958

1.8113e-15

5.1365e-16

3.5427e-16

1.0000

0.0117

[image: c1][image: c2]

(a) (b)

(a) Original Caw model, (b) Stego Caw model after implementing Hamming technique without denormalization

[image: c1] [image: c2]

(a) (b)

(a) Original Caw model, (b) Stego Caw model after implementing Hamming technique after denormalization

[image: c3][image: c4][image: c5]

(a) (b) (c)

Change in x,y and z coordinates after applying Hamming code technique [1] without denormalization

[image: c3][image: c4][image: c5]

(a) (b) (c)

Change in x,y and z coordinates after applying Hamming code technique [1] then applying the denormalization

Chaos sequence based fragile technique mesurments

Model

No. vertices/

faces

Imperceptibility measures

Robustness measure

HD

MHD

RMSE

CC (M,M’)

CC (W,W’)

Cow

2904/ 5804

8.9034e-16

2.8523e-16

1.9411e-16

1

1

Casting

5096/ 10224

1.0270e-15

2.7498e-16

1.8997e-16

1

1

Bunny

1355/ 2641

3.9374e-16

1.5555e-15

2.6232e-16

1

1

Bunny_

bent

1355/ 2641

4.0792e-16

1.6542e-15

2.8374e-16

1

1

hemi_

bumpy

1441/ 2816

1.6514e-15

5.3170e-16

3.5182e-16

1

1

Bunny

34835/ 69666

9.0876e-16

2.3628e-16

1.6133e-16

1

1

hand

36619/ 72958

8.7595e-16

2.4214e-16

1.6964e-16

1

1

[image: ][image: ]

(a) (b)

[image: ][image: ][image: ]

(c) (d) (e)

(a) Original Caw model, (b) Stego Caw model after implementing Chaos based technique, (c) , (d) and (e) the change in x,y and z coordinates.

By analyzing these techniques we found that they achieved high embedding capacity as they used all of vertices for embedding that also leads to high distortion. To avoid this distortion, we suggested selecting the best vertices for embedding by using one of computational intelligent CI techniques named neural network.

Conclusion

In this paper, we presented a comparative analysis between two substitutive fragile watermarking algorithms, by clarifying the points of strength and weaknesses. The main requirements to design an effective watermark are imperceptibility, robustness against intended or non-intended attacks and capacity. We have used the RMSE, HD, and MHD to measure the imperceptibility, and the Correlation Coefficient was often used to measure the robustness of the watermark, but we use it to measure the sensitivity of the watermark as shown in the experiment result.

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