Piecewise Permutation Steganography for 3D Humanoid Mesh Models

Piecewise Permutation Steganography for 3D Humanoid Mesh Models Hsin-Chih Lin* and Shan-Jhu Lin Department of Information and Learning Technology National University of Tainan Tainan City, Taiwan * hclin@mail.nutn.edu.tw Abstract A new steganographic method for hiding secret information into a 3D humanoid mesh model is proposed in this study. First of all, the 3D humanoid mesh model is divided into several articulate segments. According to the mesh connectivity of each segment, the proposed method uses Bogomjakov et al. s permutation steganography [3] to hide messages in the index representation of the segment. We also present a new concept of piecewise hiding which embeds messages into segments in a specific order to raise security and applicability of the embedded messages. The proposed method is error-free since it does not modify the geometry of the cover model. Even if the stego-model has a different pose due to articulate motions, the embedded message can be extracted from the model with no errors since the topology of the cover model is not changed. Experiential results reveal the effectiveness of the proposed method. Keywords-permutation steganograph; information hiding; 3D humanoid mesh model. I. INTRODUCTION Steganography conceals the existence of secret messages, as shown in Fig.. Its benefit is that the secret message does not attract notice of attackers and even receivers. Watermarking is another technique to hide messages and it is often used to provide ownership on copyrighted media and to detect originators in illegal copies. An effective watermarking method must be robust against many kinds of attacks. In contrast to watermarking, steganography need to hide messages as much as possible and requires cover media with distortion as little as possible. Therefore, purposes of steganography and watermarking are quite different. Cover Work Source Embedding function Key Channel monitored Extraction function Key Figure. The procedure of steganography. Steganography is a technique of information hiding and consists of two branches, namely () technical steganography and (2) linguistic steganography [, 2]. Technical steganography hides a message by using scientific methods, This study was supported partially by the National Science Council, Taiwan, under the Grant NSC96-2422-E-024-00-MY2. such as invisible ink or pin punctures. Linguistic steganography hides a message by using language tricks, such as an arrangement of words within a harmless text. High security, high capacity, low distortion and limited robustness are required for steganographic methods [3-5]. Great deals of research works on information hiding have been proposed in last decades. Since its first proposal on the research domain, information hiding methods have become more and more sophisticated. Traditional steganographic methods try to embed secret messages in the noise of the media [4] by distorting the original media, while requiring unnoticeable distortions. These methods may, for example, modify the least significant bits in an image or a video. A general approach to embedding messages in a 3D model is to slightly perturb vertex positions. Recently, some researchers have proposed steganographic methods to hide secret messages in the representation domain. This kind of steganographic methods is distortion-free. To develop steganographic methods, researchers are interested in maximizing capacity and robustness, and reducing distortion. We describe some related steganographic algorithms as follows. Ohbuchi et al. [6, 7] discuss techniques for embedding messages into a 3D polygonal model. Their proposed triangle similarity quadrature (TSQ) algorithm is the first 3D model information hiding algorithm. TSQ is to mark similar triangles in the model and to embed messages into those triangles that are near the marked triangles. Cayre et al. [8, 9] presented a steganographic algorithm for 3D triangle meshes in the spatial domain. Their concept is to consider a triangle as a two-state (i.e., 0 and ) geometrical object. The position of the orthogonal projection of the triangle peak on the bottom edge is divided into the two states. The vertex is then modified according to the message to be embedded. Cayre et al. s algorithm uses the quantization index modulation (QIM) and its capacity is 0.5 bit per vertex. This algorithm is timeconsuming and usually cannot embed messages in all vertices of the model. Therefore, Wang & Cheng [0] proposed a multilevel embedding procedure (MLEP) to improve Cayre et al. s algorithm. They exploited the adaptability in representing polygon meshes to obtain more capacity. Wang & Cheng uses changing counterclockwise and clockwise orders of vertices to add an extra bit per triangle. Cheng & Wang [] proposed a modified multi-level embed procedure (MMLEP) to improve the MLEP algorithm [0]. This procedure could embed at least

three bits per vertex by modifying sliding, extending and arching in each triangle. Cheng & Wang also present a connectivity embedding scheme that raises the capacity by six bits per vertex. This scheme reorder vertices and faces to a reference ordering obtained from the mesh geometry. The place of a vertex or a face in the new ordering can be embedded one bit. Fig.2 is an example of a 3D model's dataset which contains vertex coordinates and faces. Each face is combined by three vertex indices. Cheng & Wang also use cyclic vertex moves on triangles to get another two bits per vertex. Their steganographic techniques are lossless because rearranging faces or vertices does not distort the geometry. Chao et al. [2] proposed a high-capacity and low-distortion steganographic scheme. This scheme is based on a novel multi-layered embedding scheme to hide secret messages in vertices of 3D polygon models. Vertices are modified slightly according to principal component analysis. The average capacity is about 2~33 bits per vertex, but the scheme is not robust to any geometric attack. Vertex coordinates Faces 2 3 4 5 6 7 2 3 4 5 6 7 8 9 0 The rest of this paper is organized as follows. In Section 2, we present an overview of the proposed method and then detail our steganographic algorithm. Experimental results are shown in Section 3. Conclusions and future works are given in Section 4. II. THE PROPOSED METHOD A. An overview The proposed steganographic method for 3D humanoid mesh models consists of two procedures, namely () piecewise embedding and (2) piecewise extraction. The embedding procedure is shown in Fig. 3. In the model segmentation step, the cover model is divided into several articulate segments. The initial segment is decided by a key. In the vertex traversal step, the reference order of triangles and vertices in each segment are established. Other neighboring segments are found and pushed into next-segment queue. In the permutation embedding step, the message is embedded into the dataset of each segment by permuting the reference orders. The last 0 bits of the message that are embedded into each segment are calculated in the decimal system and saved as IT value (initial triangle value) for the next segment. The order of non-initial segments to embed messages is decided by nextsegment queue. When the next segment is popped from nextsegment queue, the initial triangle in the segment is determined by IT value. The vertex traversal and permutation steps are repeated until the message is embedded into all segments. Key Cover Model Model Segmentation Figure 2. 3D model's dataset. Bogomjakov et al. [3] proposed a steganographic algorithm for 3D polygonal meshes to hide messages in the indexed representation of a mesh by re-permuting the order of faces and vertices. Their encoding and decoding algorithms consist of two steps: () A reference ordering of the mesh vertices and faces is computed. (2) The messages is encoded as a permutation of vertices and faces which depend on their reference order, or decoded by comparing the ordering present in the dataset to the reference one. Bogomjakov et al. s algorithm is lossless and can hide high capacity as much as 49.43 bits per vertex. In this study, we present a new steganographic method for hiding secret messages into a 3D humanoid mesh model. First of all, the 3D humanoid mesh model is divided into several segments. According to the mesh connectivity of each segment, the proposed method uses Bogomjakov et al. s permutation steganography [3] to hide messages in the index representation of the model. We also present a concept of piecewise steganography which embeds messages into segments in a specific order to raise security and applicability of the embedded messages. Initial Segment Initial Triangle Searching Vertex Traversal Reference order Permutation Embedding Stego-segments Stego-model Other Segments Initial Vertex Next Segment(s) Figure 3. Embedding procedure. Nextsegment Queue IT Value The extraction procedure, shown in Fig. 4, is very similar to the embedding procedure. The segments information is saved in the stego-model. We traverse each segment of the stegomodel and produce the reference order by the correct key and IT value from the last segment. In each segment, the message is extracted by matching the dataset and reference order.

Key Initial Segment Stego-model Initial Triangle Searching Vertex Traversal Reference order Other Segments Initial Vertex Permutation Extraction Nextsegment Queue Next Segment(s) IT Value Key: Initial segment: Head Initial triangle: The 5th Triangle list The 5th triangle 2 3 4 5 6 Dataset # object body to come... # object head to come... # v -7.825284-0.924872 79.33688 v -6.60775-0.79843 79.24283 # 004 vertices g head f 992 948 938 f 949 963 05 f 987 942 94 f 540 943 942 f 942 987 540 f 943 285 965 # 884 faces Figure 6. The initial triangle and the initial vertex. Figure 4. Extraction procedure. B. Model segmentation In this study, we propose a concept of piecewise hiding to raise security and applicability of the embedded messages. An example is shown in Fig. 5. The cover model is divided to six segments and the segment order keys are decided by a traversal algorithm. s can be embedded into six segments by different keys. Figure 5. An example of piecewise hiding. The piecewise hiding technique is presented in Sections 2.2~2.5. The initial segment and the initial triangle of the initial segment are decided by a key. The initial vertex is the first vertex of the initial triangle in the model dataset. Shown in Fig. 6 is an example of the initial triangle and the initial vertex. The initial segment that the key decided is "Head". The initial triangle is the 5-th triangle in dataset and its first vertex (with index 942) is the initial vertex. C. Vertex traversal As long as the traversal algorithm is based on the mesh connectivity, it can be used in our method. This property makes our method robust on condition that the topology of the stegomodel is unchanged. Once the initial vertex and edge are selected, the whole traversal is uniquely defined. And the traversal path is regarded as a reference order. The breadth-first traversal algorithm proposed by Cheng & Wang [4] is used in this study. This traversal algorithm is inspired by the concept of epidemics to traverse the mesh, producing a traversal path, as shown in Fig. 7. The initial vertex is defined as a virus vertex. The initial edge is defined as a virus edge. The initial triangle is defined as a virus triangle. All vertices are considered healthy except those of the initial triangle. The virus edge is taken as the medium for infection. A triangle would be infected by the shared virus edge. A triangle that has not been infected is called susceptible. The susceptible triangle is infected by one shared virus edge and in turn become incubative. When all healthy vertices in an incubative triangle become virus ones, the triangle becomes infective and then can infect susceptible neighbor triangles. Finally, when all neighboring triangles have been infected, the originally infective triangle does not infect other triangles anymore and then becomes immune. The four states repeat until all triangles of the mesh are immune. not yet infected Susceptible has susceptible neighbor Infective infected all neighbors have been infected has health vertex Incubative all vertices are virus Immune Figure 7. The four states of a triangle in contagious diffusion.

In the vertex traversal process, if a neighboring segment is near a virus edge, we push the segment into the next-segment queue and find the ITS triangle of the segment. Shown in Fig. 8a is an example of ITS triangle. Vt and Vs are virus vertices. The virus edge of Ti in segment A is near segment B. In Fig. 8b, TB_ITS that shares the same edge with Ti is the ITS triangle of segment B. In the step of initial triangle searching, the initial triangle is determined by the ITS triangle. Segment A V t T i Segment B V s Segment A V t T B_ITS Figure 8. ITS triangle of segment B. V s Segment B D. Permutation embedding In this study, we use Bogomjakov et al. s permutation steganographic algorithm [3] to hide messages in each segment. The message is embedded in each segment by permuting reference order. The permutation order which is the result of permuting reference order saved in dataset. The permutation embedding proceeds as follows. Step : Assume there are n vertices in the segment and the number of permuting vertices is i. The number of bits to be embedded is k = log 2 (n - i). Step 2: Late b and b' be decimal values of the next k and k+ bits, respectively, of the message. Step 3: If n - i > b' 2 k, the vertex which is b'-th vertex in reference order is saved in the permutation order. The (n-i-)-th vertex of reference order replaces the b'-th vertex of reference order. Otherwise, the vertex which is b-th vertex in reference order is saved in the permutation order. The (n-i-)th vertex of reference order replaces the b-th vertex of reference order. Step 4: Repeat Steps ~3 until all vertices in the segment are embedded the message. F. Permutation extraction In the extraction procedure, each segment of the stegomodel is traversed and produced the reference orders by a correct key and the IT value. In each segment, the message is extracted by matching dataset and reference order. The permutation extraction proceeds as follows. Step : Assume there are n vertices in the segment and the number of permuting vertices is i. The number of bits to be embedded is k = log2(n - i). Step 2: According permutation order from dataset, the vertex of permutation order is matched with reference order. The vertex of permutation order is the b-th vertex of reference order. Step 3: If b 2 k, b is calculated into binary system by k bits. Otherwise, b is calculated into binary system by k+ bits. Step 4: The (n-i-)-th vertex of reference order replaces the b- th vertex of reference order. Step 5: Repeat Steps ~4 until the message embedded in all vertices of the segment are extracted. Finally, all pieces of message which are extracted from all segments are combined to form the complete message. III. EXPERIMENTAL RESULTS Our experiments were implemented on a personal computer with a 3.4 GHz processor and.5gb memory. The operate system is Microsoft Windows XP Service Pack 2. We implemented the proposed scheme using C++ programming language. The analyses of our steganographic system are based on the following three goals: high capacity, lossless, and high security. There are five triangle mesh models, as show in Figs. 9a~9e, to be tested in this study. The five models dataset are.obj. First of all, we use 3DS Max to divide these models into several articulate segments, as shown in Fig. 9. The last 0 bits of the message that are embedded into the segment are regarded as an IT value. The initial triangle of the next segment is searched by the IT value. E. Initial triangle search In the embedding order of non-initial segments, the next segment is popped from next-segment queue. The initial triangle in the next segment is searched by the ITS triangle and tit value which is from last segment. The traversal algorithm proposed by Cheng & Wang [4] starts from the ITS triangle. When the IT-th vertex is traversed, the vertex is defined as the initial vertex of the segment and the triangle is defined as the initial triangle of the segment. (c) (d) (e) Figure 9. The divisions of experimental models. The model detail and capacity is listed in Table I, where S init (=2) is initial segment, T Sinit (=5) is initial triangle of initial segment. The average capacity is 7.76~27.70 bits per

vertex. We could discover that the average capacity is high when the number of vertices is large. The capacity is s ( log 2( vi ) + log 2( ( fi! )) + vi + fi + ) i=!, where s is the number of segments, v i is the number of vertices in the i-th segment, f i is the number of triangles in the i-th segment. TABLE I. MODEL DETAIL AND CAPACITY. Model Capacity [bits] name #vertices #faces #segments total bit/vertex rabbit 680 248 8 2,076 7.76 spider 2,073 3,960 9 46,003 22.9 goldfish 2,246 4,240 7 59,628 26.55 human 4,77 9,68 6 29,72 27.50 barosaur 6,9 2,040 7 7,45 27.70 S init = 2, T Sinit = 5 TABLE III. DIFFERENT NUMBERS OF SEGMENTS. Model Capacity [bits] name #segments total bits/vertex human 6 29,72 27.50 human 20,659 25.58 S init = 2, T Sinit = 5 To analyze the relationship between the model pose and the robustness, the pose of the stego-model is changed and then we extract the message from the model. Fig. a is original pose and Fig. b is the pose after articulate motions. The result is shown in Table IV. The normalized correlation (NC) is to estimate the correlation of the message that is extracted from stego-model. When NC is, the message is not lossless. If NC is smaller, the message is loss a lot. From Table IV, the NC of the changed model is so the message is lossless. It means that different poses of the stego-model does not affect the completeness of the embedded message. To analyze the relationship between the key and the capacity, we use different keys to hide messages in the human model. The results are listed in Table II. From experimental results, we can find that the average capacity of the model is similar. It means that the use of different keys affects the capacity slightly. TABLE II. S init USING DIFFERENT KEY TO EMBED MESSAGE. Capacity [bits] T Sinit total bits/vertex 2 5 29,72 27.50 2 25 29,72 27.50 4 25 29,70 27.50 6 25 28,725 27.29 2 5 29,72 27.50 Model: human.obj To analyze the relationship between the number of segments and the capacity, the human model is divided to different number of segments and then embedded the same message. Figs. 0a and 0b show the human model with 6 and segments, respectively. The capacity is listed in Table III. The average capacity is 27.50 bits and 25.58 bits per vertex, respectively. From experimental results, we find that if a model is divided to more segments, the capacity would be lower. Figure 0. Human models with different segmentations. TABLE IV. Figure. Different poses of model. DIFFERENT POSES OF THE STEGO-MODEL. name #segments Pose change NC human 6 Yes human 6 No S init = 2, T Sinit = 5 IV. CONCLUSIONS AND FUTURE WORK In this study, we have presented a new steganographic method for 3D humanoid mesh models. The concept of piecewise hiding is also presented. The message can be embedded into 3D model s dataset by permuting the index of vertices and the index of faces. From experiment results, our method has high capacity and is distortion-free. By the concept of piecewise hiding, the security and applicability of the embedded messages can be raised significantly. In the future, we can combine the concept of piecewise hiding with those of access rights and public key infrastructure (PKI), as shown in Fig. 2. In this figure, different keys mean different access rights. Si denotes the message embedded in the i-th segment; K i denotes the i-th key used to encrypt S i. There are four concepts of access rights. In Fig. 2a, only when S has be decrypted by K, S 2 can be decrypted by K 2 and S, and so on. In Fig. 2b, different messages can be encrypted and decrypted by different keys independently. In Fig. 2c, only when S and S 2 have been encrypted by K and K 2, respectively, S 3 can be decrypted by K 3, S and S 2. In Fig. 2d, only when S

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