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OBTAINING AND ANALYZING OF MESHES OF MODELS 3D

E. Vélez Márquez, J. Moreno Sáenz, M. A. Molina Vilchis

[email protected]

ESIME Culhuacán-IPN

Abstract- Nowadays three-dimensional models or 3D are used on a large scale in different areassuch as medicine, entertainment, architecture, among others. As digital information is vulnerable toseveral attacks in the meshes as transformations, geometric or topologic alterations, and distortionswith malicious purposes, for this reason there is a need to protect these models using cryptographicor steganographic algorithms, such as fingerprints and watermarking. However, whatever theprotection strategy is, it is always necessary to determine the topology or geometry of the mesh ofthe model.This article presents a method for obtaining and analyzing 3D triangular mesh models, then makesan analysis of their properties and determine, according to its geometry and topology, the mostappropriate method for inserting a digital signature or watermark.Keywords: 3D model, mesh, topology, attacks.Resumen- En la actualidad los modelos tridimensionales o 3D son utilizados a gran escala endiferentes áreas tales como la medicina, el entretenimiento, la arquitectura, entre otras. Al serinformación digital son vulnerables a diversos ataques en las mallas como transformaciones,alteraciones geométricas o topológicas, y deformaciones con propósitos mal intencionados, poresta razón surge la necesidad de proteger dichos modelos utilizando algoritmos criptográficos oesteganográficos, tales como las huellas digitales y las marcas de agua. No obstante, cualquieraque sea la estrategia de protección, siempre será necesario determinar la topología o geometría dela malla del modelo.En este artículo se presenta un método para obtener y analizar mallas triangulares de modelos 3D,para luego hacer un análisis de sus propiedades y determinar, de acuerdo a su geometría y

topología, el método más adecuado para la inserción de una firma digital o una marca de agua.Palabras clave: modelo 3D, malla, topología, ataques.1. INTRODUCTION

Three-dimensional models (3D) in computer security, are found in a conceptual world of threedimensions that can be seen in two different ways depending on the need and use that the usersgive them, so that a 3D model is a schematic representation visible through set objects, elementsand properties that, once processed, will become an image or animation in three dimensions. Fromtechnical viewpoint, they are a set of formulas or mathematical representations which describes aworld on three dimensions [1].See Fig1.

(a) (b) (c) (d)

Fig. 1.Representation of the 3D model [2-4]. (a) Finished 3D model, (b) 3D object represented bymeshes to be modified subsequently (c) y (d) Models created from mathematical formulas.



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In recent years one of the impacts on computer technology have been the creating systems of 3Dmodels which contribute to increasingly credible simulation of reality [5], but this importantbreakthrough had its origin in big ideas produced during the last decades with three majorindustries [5-8]: a) Games, which originally were processed in large computer companies anduniversities, shortly after appearing on the market, the first console was based on analogictechnology in which a few programs were run whose feature were their simplicity and operationalgraphics. The increasing demand that year by year generates profits of billions of dollars, and thehuge competition that has occurred among manufacturers as well as technological advances in thisindustry evolve by leaps and bounds getting better, among other things, quality incorporating visualdynamic 3D models, which increase sales in the market. b) Virtual Reality, which has taken to 3Dmodels, being one of its main proponents Ivan Sutherland and Laboratories Lincoln of MIT, whoseresearch laid the foundation for Computer Graphics and Virtual Reality, widely used in computersystems for research, simulation and entertainment. And c) Internet, which emerged during the 60decade whose development has facilitated the emergence of new services that have been involvedimportantly 3D models, either for marketing or for integration into different applications usingprogramming languages such as VRML, XML and X3D.

The creation of 3D models has been developed in various areas in which vary the ways topresentation and interaction, in their development have been used electronic accessories such aspencils, three-dimensional mice, joysticks and electronics tablets, etc. To produce different effectsas the stereoscopic viewing that requires specialized devices and accessories such as 3D glassesused to view 3D anaglyphs, in order to trick the senses to perceive the images as they exist in thereal world.There are 3D modeling applications, which allow easy creation and modification of objects on threedimensions. These tools usually have polygonal basic objects (spheres, triangles, squares, etc.) inorder to assemble the model. Moreover, they often have tools for generating lighting effects,texturing, animation, transparency, etc. Some applications of modeling are 3D Studio Max, Alias,AutoCAD, Blender, Cheetah3D, Cinema 4D, Generative Components, Houdini, Java 3D,LightWave, Maya, MilkShape 3D, Modo Rhinoceros 3D, Poser, XSI Softimage, Solidworks, yZBrushTrueSpace, etc. [1].

These models are no longer exclusive to the entertainment and research laboratories, now arewidely used in various fields such as medicine with representations of human body in 3D, educationfacilitating the learning of various disciplines, architecture complementing the design work replacingthe models, geography to the development of cartography, tourism through virtual tours toarchaeological sites and museums, and the study of physics for predictive purposes, among manyother applications. See Fig. 2.

(a) (b) (c)Fig. 2. 3D models for various applications [9-11]. (a) Model made in 3DMax to videogames (b)

Model made in Poser to explain the human body. (c) Model of Cheops pyramid made byDessaultSystemes in Solidworks.

3D models are considered like digital intellectual works, by what is stored and transmitted like anyother digital document, this makes them vulnerable to malicious attacks or unintentional such as



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transformations, manipulations or geometric alterations, distortions, unauthorized copies,including others violating copyright and distributed illegally by different media, so there is necessaryto protect this information using different methods and techniques based on steganographictechniques, like fingerprints and watermarking [12], which are generally based on the geometricmesh representing the model.This article presents a method for obtaining meshes from 3D models as an initial step to protectthem by watermarking techniques. This document has four sections, section II presents an overviewof the mesh representing the 3D models. In section III is presented the proposed method forobtaining the mesh. Finally, section IV presents the results of analysis of the mesh obtained toidentify the characteristics and properties usable for protection against geometric attacks.

2. RELATED WORK (STATE OF THE ART)

2.1 Concepts and overview of meshes.

A 3D model is formed by organized set of points that have numerical values in [13], and

these are linked together forming meshes characterized by having vertices and edges thatrepresent geometric shapes in different types as triangles, rectangles, quadrilaterals or fan, see Fig.3. These models are called polyhedral models [14], these meshes can be constructed from a cloudpoint, range data which are mainly numerical data with the location in the 3D plane, or isosurfaceextraction that are constant points mathematically describing the surface as a function of three-dimensional object [15], [6]. The mesh may or may not be. In structured meshes the connectivitycan be described by some indexing scheme, whereas in the unstructured one relationship does notexist and you need a special data structure to represent connectivity information [16]. Thesestructures have features which give them properties such as texture, color, tone, shade,transparency, reflection, translucency, refraction, lighting, depth etc. Each property providesinformation to join with the other properties is the model itself.

(a) (b) (c)

Fig. 3. 3D model representation using meshes [17], [18]. (a) Triangular, (b) Quadrilateral y (c)Polyhedral.

A mesh consists mainly of a) Vertex that determines the corners or intersections of geometricshapes that form the mesh in a 3D model, are also numerical information which represents thespatial location in the 3D plane. b) Edge that is the connection between vertices, it can have or notconnectivity to the mesh formation, the relationship between these two results c) Faces that areclosed sets and gain some form that together with other provide a topology either triangular, square,or polyhedral [19].



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Connectivity is very important because it gives form and related key parts of the mesh, a poorconnectivity would cause distortions and errors in the topology as in form. Each mesh has importantfeatures that are exploited for different purposes such as modification, analysis, protection, storageand export formats.

The main connections are:

a) Vertex-Vertex

In this one each vertex connects to its adjacent vertices, as shown in Fig 4. It provides a great easeof doing tours on the mesh, this type of connection is the simplest and is widely used in VRML andX3D formats, although operations at the edges and faces are not easy to perform [19] [20].

b) Face-Vertex

It is a simple connection and it is the most used, in this connection each vertex is linked to adjacentfaces. See Fig. 5., in this connection is easier to locate the corners of each side but there is noconcept of neighboring vertices through the faces, it is used in the file formats .obj [19] [20].

Fig. 4. Connectivity vertex-vertex representation.

http://en.wikipedia.org/wiki/File:Mesh_vv.jpg



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Fig. 5. Connectivity face-vertex representation.

c) Winged-Edge

This connectivity is widely used in modeling programs to provide flexibility in the changing dynamicsof the mesh geometry, because the split and merge operations can be done quickly. Its maindisadvantage is the large storage requirements and complexity, due to keep many indices, but alsoprovides greater mobility between their structures [19], [20]. See Fig.6. In this connectivity edgescan relate to all the essential parts of the mesh.

http://en.wikipedia.org/wiki/File:Mesh_fv.jpg



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Fig. 6. Representation of Winged-Edge connectivity.

In general, 3D modeling programs have extensive features to work with mesh due to the mainstructure, characteristics and resolution are involved with this, the more the mesh has polygons, themore the model has reality and resolution, but greater capacity and processing time required by thedevice running the model, these features must have a balance in the realism of the model(especially if it is got many curved shapes) and the number of polygons that are required dependingon the final application that will be given to the model [17].

2.2 Formats.

Currently in the world of 3D modeling has endless programs, formats and extensions which canwork but depends on each one will depend on user's necessity, its implementation or difficult towork, moreover, file extensions give a reference where they can be applied, so now 3D modelingprograms can export their original format to another one to include more areas, such as education,health, entertainment, communications etc. The Table 1 gives the comparison of most used fileextensions with the application with it is related.



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2.3 Handling of the mesh for purposes of protection.The methods of protection are extensive and the purpose of each one is to protect the integrity ofthe model, copyright and authorized distribution, these protection methods used as main disciplinethe steganography which studies the data hiding techniques. These techniques include fingerprintsand watermarking, both of them have advantageous features for protection, but their main goal is toinsert information (hidden or not) in the 3D model.Fingerprints mark uniquely the model for each user who purchases the product, because of thisthere cannot be two equal fingerprints, if it is not violated the distribution agreement, this will causea high level of security, but difficult to protect every distributed model with a unique identity.A watermark is an identification code, perceptible or preferably imperceptible, which is permanentlyembedded in the information (not disappear after decryption) and it may contain information aboutthe owner, copyrights, creator, authorized user, number of copies or authorized reproductions, soon. 3D models are marked in the same way protecting the copyrights of the product, any attack willbe reflected in the watermark that verifies the integrity of the model helping the user to know if youhave an illegal copy or not [12], [ 21].

Table 1. Examples of formats, programs and common applications to create 3D models.

Fileextension Program Internet Videogames Education Animation Virtual

realityMobile

Technology

.vrml Most ofthem x x

.obj Most ofthem x

.3ds 3D StudioMax x x x x

.jar Java 3D x x.mb Maya x.pcf Poser x x x

.sldprt Solidworks x

.blend Blender x x

.dwg AutoCAD x

Watermarking must have the following features to ensure their reliability:1. Undetectable: That is invisible to the observer.2. That does not degrade the object.3. Robustness: Elimination or reduction of the mark must be difficult or impossible without

degrading the quality of the digital object. It also must support common processes oftransformation (compression, filtering, format conversion, geometric distortion, etc.).

4. They cannot be ambiguous: The mark must clearly identify the copyright owner so that it

can claim ownership.These watermarking systems must be composed by two main modules, which perform theencoding (insertion or embedding) of the mark and decoding (extraction and identification) of it.Watermarking is an effective solution to protect 3D models. But protecting a three-dimensionalmodel is not easy due to the features of it, protecting a 3D model involves the collection andanalysis of mesh because of information security is inextricably embedded in the model.In order to embed the watermarking in the 3D model mesh is necessary to manipulate the meshinformation, namely, the vertices, the connections between vertices (topology), surface properties



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(textures, colors, so on). Having the 3D model mesh has a lot of possibilities for embeddingmethods, so that is preferable to make a choice on the set of model properties, such as:

1. Geometric features. The main geometric features of a mesh are the vertices in which canembed the watermarking, due to these attributed to the model location as well as shape.

2. Topological features. These features are related to the connectivity of the vertices of themesh, which can be redefined the topology in the process of watermark embedding.

Much of protection methods chooses to embed a protection code in the vertices of the mesh, due tothese are the main feature of the model, any change is reflected in the vertices of the mesh,because of these provide shape, topology, location and resolution as well as another attributes, andthe information which are integrated changes radically. The need arises methods for obtaining themeshes of 3D models as this would provide us more details about the model ensuring protectionfrom attacks by malicious users [22].Before protecting a 3D model must treat the mesh, either to improve the method of protection andprovide greater reliability and effectiveness. High resolution models are a great amount of verticesand edges, and other information of high priority to make sure their integrity, so that it results

tedious to embed watermarking in each of these properties and although in this case the watermarkresults robust, it would consume a lot of resources to embedding system or for its proof.The first step to make sure a 3D model through watermarking techniques starts with the selection ofstrategies to manipulate the mesh, the most common are:Mesh triangulation. This strategy subdivides each triangle of the mesh into a set of two or fourtriangles, the criterion for locating the new vertices created depend on the properties of the edgesand the amount of mark information. In [23] [24] are presented algorithms that employ thistechnique for either safety or attack model.Mesh partition. In [25-29] algorithms are proposed to embed watermarks based on initial selectionof a triangle mesh as a starting point to create subsets called sub regions of the mesh, consideringtheir topological and geometrical properties. The subsets created represent some parts of the 3Dmodel and only in these is embedded watermark.

Neighboring vertices. In [28], [30], [31] this strategy is used which consists in selecting a vertex vi =(xi, yi, zi) or centroid which is associated with a set of adjacent vertices N(vi), which are called"neighbors." In order to embed the watermark is randomly selected a vertex vi and from this it isfound the first node in the neighborhood, and through the recognition rule application neighboringvertices are selected, only in these vertices the watermarking is embedded. The number of verticesselected and the rule for recognition depends on the type and length of the pseudorandomsequence of the watermarking.

Clustering vertex. In dynamic models that will be animated, the clustering technique to embedwatermarks is adequate, especially in complex models like the human body. In [32], [33] groups canhave different topologies, such as mesh, star or triangle strips. The advantage of using clusters isthat is not necessary to compress the mesh to make the process of embedding marks.Knowing topology of the mesh let, later, embeds watermarks with different methods, for example in[34] it is done a spectral analysis of the mesh as a preliminary process to generate a Laplacianmatrix derived from the connectivity the vertices of the mesh.

3. OBTAINING MESH METHOD

There are different ways to represent a 3D model, as it is the case of a collection of surfaces orparametric curves, however, the most common and the most useful for our practical purposes is therepresentation by polygonal meshes. A mesh can be described as a list of ordered items is where a set of vertex or points in the three dimensional space and is theset coding adjacent vertices, edges and faces of the mesh. In other words, consists of subsets of



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of the three general component of the mesh: vertex , edges and faces[24].

In this section presents the methodology for obtaining the mesh of 3D models developed with3DMax Studio. From the meshes obtained will generate the parents of representation and paths,which can be used for later proceedings of embedded of watermarks. The method of production isbased on the following steps:1. Creation the model of three dimensional. For experimental purposes were created 3D models ofbasics forms such as the cube, as shown in the Fig. 7.

Fig. 7. Creation of a cube in 3D Studio Max

2. To get the vertices and faces is necessary that the model created has extension .wrl which willfacilitate the extraction of information. The file obtained contains the code to generate information ofthe vertices from the instruction point , as shown in Fig. 8, the vertices are presented in threegroups at coordinates ; separated by commas.

The instruction coordindex identifies the faces that are made up of closed paths between thevertices, these have three connections that are identified as triangles, each path that represents theface are divided by - 1, see Fig. 8.

#VRML V2.0 utf8

# Produced by 3D Studio MAX VRML97 exporter,Version 12, Revision 1.06# Date: Mon May 10 00:10:18 2010

DEF Box01 Transform {translation 4.25 0 0.498children [Shape {appearanceAppearance {materialMaterial {diffuseColor 0.6 0.894 0.722}}geometryDEF Box01-FACES IndexedFaceSet {ccw TRUEsolid TRUE



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coordDEF Box01-COORD Coordinate { point [-18.6 0 27.3, 18.6 0 27.3, -18.6 0 -27.3, 18.6 0 -27.3, -18.637.6 27.3,18.6 37.6 27.3, -18.6 37.6 -27.3, 18.6 37.6 -27.3]} coordIndex [0, 2, 3, -1, 3, 1, 0, -1, 4, 5, 7, -1, 7, 6, 4, -1, 0, 1, 5, -1,5, 4, 0, -1, 1, 3, 7, -1, 7, 5, 1, -1, 3, 2, 6, -1, 6, 7, 3, -1,2, 0, 4, -1, 4, 6, 2, -1]}}]}

Fig. 8. Code of the file with extension .wrl.

3. The variables face and vertex store information while the variable key stores the corresponding

identifiers, as shown in the Fig. 9.

key = 'point ['; % Identifier

vertex = []; % Creating vector called vertex that saved the information corner

key = 'coordIndex ['; % Identifier

face = []; % Creation of vector called face that kept the connectivity information

Fig. 9. Creation of vector called face that kept the connectivity information

4. The code to extract information from the vertices and faces to be stored in arrays of vertices. See Figs. 10 and 11.

while ( temp ~= -1)temp = fgets(fp);

if( ~isempty(findstr(temp,key)) )

[vertex,nc] = fscanf(fp,'%f%c', Inf); % extracts each number of the file and places it in annnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn column

vertex = reshape(vertex, [6,length(vertex)/6]); % remodel the vertex column

vertex([2 4 6],:) = []; % Delete rows spam

break;end

end Fig. 10. Identification and saved from the vertices.

while ( temp ~= -1)temp = fgets(fp);

if( ~isempty(findstr(temp,key)) )



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[face,nc] = fscanf(fp,'%d%c %d%c %d%c -1%c', Inf); % Data collection

face = reshape(face, [7,length(face)/7])+1;

face([2 4 6 7],:) = []; % Delete rows spam

endend

Fig. 11. Identification and saved faces.

5. The results of the previous steps are 2 matrices that contain closed paths that form the facesand vertices. See Figs. 12 and 13.

Fig. 12. Obtained array representing the vertices in the 3D drawing.

Fig. 13. Obtained array representing the closed paths between each vertex to form the faces of the3D model.

6. From this information can be obtained the mesh and the three dimensional model with itstriangular topology, for this can be used the program as Matlab using graficacion tools can obtainmodels as seen in the Fig. 14, In this case was obtained a mesh of 8 vertices and 12 faces.



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Fig. 14. Obtaining the mesh and the 3D model.

4. MESH ANALYSIS

Once created and exported the file to. Wrl can verify its integrity by opening the file like a textdocument, which will contain very important parts that can be seen in Fig. 8., This type of formathas characteristics much as a 3D model, textures, lighting, shapes, location, connectivity, size, coloretc., but the ones we are interested to obtain meshes of 3D models are created before the locationin the 3D map of the vertices and faces.At this point we turned to a program that allow us to have enough tools to get and manipulate datafiles regardless of the format, and allows viewing graphics in 3D with the data for this applicationwas chosen the program MatLab, since as shown in the procedure described in the previoussection, allows opening files and extract data from great importance, these data are the vertex andthe paths that make up the faces of the model, these are saved in two variables.

In the previous section the vertices are stored neatly in the matrix with name "vertex" each columnrepresents a new vertex and each row represent the coordinates in the Cartesian 3D plane in theform which we can see in the Figs. 15 and 16.

Fig. 15. Mathematical representation of the matrix vertex .



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In the matrix "vertex" the unique size of rows is 3 and is determined by the coordinates thatdetermine the position of a point at the 3D, while is determined by the complexity of the model, togreater complexity greater numbers of vertex will have.

In the variable " face" saves the relationship of each vertex in closed trajectories that shaped thefaces of the 3D model connectivity.As you can see in the Fig. 17, each column represents one face, the total number of columnsrepresents the number of faces that possesses the 3D model, and each face is showed by 3vertices that connect each and that governing complies a closed path forming the face model, these3 vertices are due to its triangular, since 3 edges or connections needed to render a single triangletopology.

With these matrices and with help of MatLab charting tools you can display the three-dimensionalmodel with its characteristic mesh, see Fig. 15.Below in Table 2 shows the results obtained by the method, for different models 3D. All tests wereperformed using a PC with AMD Sempron processor at 1.6 GHz, 1 GB RAM memory running underthe Windows XP operating system. The models were developed in 3D Max Studio and exported tocode VRML97, and implementations of the models were made in MatLab 7.

Table. 2. Results obtained from different 3D models .

Name of the3D model

Model 3D done in 3DMax Studio

Numberof

verticesobtained

Numberof facesobtained

Model and mesh obtained

Fig. 16. Matrix obtained that represents the vertices denoted with their respective attributes.

Fig. 17. Matrix obtained by representing the faces.



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Cylinder 110 216

Pyramid 5 8

Cone 146 288

Sphere

162 320

Teapot 530 1024

5. CONCLUSIONS

The 3D models are widely used in different areas of study, education and entertainment, with theInternet are accessible to everyone, so may be object of manipulation, and unauthorized copies, toprotect them have been proposed various strategies steganographic as marks of water from themeshes can embed copyright information or proprietary or copy control mechanisms, so it isimportant to have a method to obtain the mesh from the models mentioned.This paper presents the results of the method proposed for the obtaining of the mesh from VRMLcode regardless of the complexity of the 3D models. The information of the vertices and edges ofthe mesh are stored in arrays for further processing in security processes.



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As future work the meshes obtained will be object of experimentation in the laboratory for testing ofattack and protection by watermarks.

6. ACKNOWLEGMENTS

EVM, JMS and MAMV thanks for the support of the Secretaría de Investigación y Posgrado (SIP-IPN) to the project 20100682 and the financial support received by Comisión de Operación yFomento de Actividades Académicas (COFAA-IPN).

EVM y JMS thank the financial support received by IPN through Programa Institucional deFormación de Investigadores (PIFI-IPN).

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[33] Puneet Maheshwari, Parag Agarwal, Balakrishnan Prabhakaran,” Progressive Compression Invariant Semi-Fragile Watermarks for 3D Meshes ”, Department of Computer Science,University of Texas at Dallas.

[34] Ryutarou Ohbuchi, Shigeo Takahashi, Takahiko Miyazawa, Akio Mukaiyama,” Watermarking 3DPolygonal Meshes in the Mesh Spectral Domain”, Computer Science Department, YamanashiUniversity, Takeda, Yamanashi-shi, Japan.

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