3D MODELLING AND WATERMARKING

The title suggests 3D Modelling and Watermarking, the blog will brief you about both the concepts and suggest a few algorithms as well. Initially, let’s start with what does 3D modelling mean?

The definition of 3D modelling is the process of developing a mathematical representation of any surface of an object (either inanimate or living) in three dimensions via specialized software. The product obtained is called a 3D model. A physical body using a collection of points in 3D space, connected by various geometric entities such as triangles, lines, curved surfaces, etc is represented by 3D model. They can be created manually or algorithmically. 3D models are basis for physical devices that are built with 3D printers or CNC machines.

      Now that we are writing a blog on this topic, it must have some significant uses. A few are listed below:

·       The medical industry uses detailed models of organs that may be created with multiple 2D image slices from an MRI or CT scan.

·       The Movie or Film industry uses them as characters and objects for animated and real-life motion pictures.

·       Used as assets for Computer and video games by the Video game industry

·       Highly detailed models of chemical compounds are used in science sector.

·       Used in Architecture industry to demonstrate proposed buildings and landscapes in lieu of traditional, physical architectural models.

·       Uses as designs of new devices, vehicles and structures as well as a host of other uses by engineering sector.

·     Earth science industry has taken initiative for constructing 3D geological models as a standard practice.

       

One must be wondering, how can you represent something 3D, how do we get in the third dimension unlike our generic 2 dimensions. Here’s the answer, 3D models can be displayed as a two-dimensional image through a process called 3D rendering or used in a computer simulation of physical phenomena. The models can also be physically created using 3D printing devices.

Almost all 3D models can be divided into two categories namely:

1.       Solid :

 These models define the volume of the object they represent (like a rock).

Used in Engineering and medical simulation. They are usually built with constructive solid geometry.

2.      Shell / Boundary:

These models represent the surface, i.e. the boundary of the object, not its volume (like an infinitesimally thin eggshell).

Used in games and film are shell models.

Let’s move to next part of our topic, i.e. Watermarking. We all have an idea of what a general watermark is, but what is different in this blog is that a watermark is applied to a 3 dimensional object.

The formal definition is, Watermarking is the process of hiding digital information in a carrier signal; the hidden information should, but does not need to, contain a relation to the carrier signal.  A digital watermark is a kind of marker covertly embedded in a noise-tolerant signal such as audio, video or image data. Digital watermarking is a passive protection tool because the digital copy of data is same as the original one. Digital watermark marks the data but it neither degrade it nor control access to the data.

As we saw some significant uses for 3D Modelling, let us take a look on uses or applications of Watermarking:

•        Copyright protection[2].
•         For source tracking. In source tracking different recipients get differently watermarked content.
•   For Broadcast monitoring (television news includes watermarked video from different  international agencies).
•         Video authentication.
•         Software crippling on screen casting and video editing software programs, to encourage users to purchase the full version to remove it.
•         ID card security.
•         Fraud and Tamper detection.
•         Content management on social networks.
•         Digital cinematography.

                 Let us go through one algorithm for image(2D) integrity verification[3].

                

               The watermark in this algorithm is capable of detecting any change made to an image, including changes in pixel values and image size. This watermarking algorithm is important for several imaging applications, including trusted camera, medical archiving of images, legal usage of images, news reporting, commercial image transaction, and other applications.

                In this algorithm following steps are taken:

      1. Cosider the grayscale image X of size (mXn).   

      2. Take the binary image A to watermark on image X .

      3. Resize the image A in (mXn) by tiling into image B(mXn) .   

      4. Partition the image B(mXn) into small blocks of size (i X j).

      5. Each block from image B will be inserted into corresponding block of image X

      6. This will create watermarked image Y(mXn).

Embedded watermarks can be used to enforce copyright, data authentication or to add information to the data. Ideally, the watermark should not interfere with the intended purposes of the data.

A watermarking technique has two stages, namely watermark embedding and watermark detection respectively. Most of the research until now has been performed on watermarking is concentrated on watermarking audio data, still images, or video. We consider a 3D model that is to be watermarked as a wire-frame whose nodes are represented by vertices. A graphical object is described by a set of vertices which are defined as 3D vectors, and a set of surfaces, each delimited by a group of vertices. As the watermark has to be applied to different types of data, algorithms employed in still 2D images cannot be used in a straight forward way for graphical objects. Obviously, we have to add a whole new dimension here, to convert it into 3D.

Now, when we look at both the techniques i.e. 3D modelling and watermarking, we can proceed to next stage and that is, applying a watermark to a 3D model!

Yes! For this purpose to get accomplished, we referred research papers and studied what scientists or developers have done so far. Just to give an idea, we will write about one algorithm from a paper in short. The watermarking technique is studied by us in detail, which is applied locally and it is essentially geometrical in nature[1].

 We identified two main steps in the watermarking algorithm as mentioned earlier. In the first step of embedding watermark, a chain of vertices and their neighborhoods are selected from the object data which in our case is the 3D model. The neighborhoods are chosen such that we achieve a minimal visibility of the modifications to be performed in the geometry of the object thus working well with the safety application. The selected vertices are ordered according to a distance criterion.

In the second stages, bounding volumes are modeled from the selected neighborhoods and the corresponding vertices are moved inside the bounding volume when embedding a 1 bit or outside, respectively, for embedding a bit of 0. The Fig. 1 just gives a visual glimpse of embedding bit 1 in the vertex[1]. 

In the detection stage of the watermark, i.e. while detecting the presence of watermark, the embedded bits are retrieved by checking their relative location with respect to the bounding volumes. The sequence of retrieved bits is matched against the given watermark code. Vertices and their neighbourhoods that do not fulfil the selection condition are not suitable to embed the watermarking code. The proposed watermarking algorithm in the paper can be used as a public key watermarking technique.

Hardly any visible differences can be observed between the watermarked and the original graphical objects which can be seen below. The Fig. 2 given below can be referred to check the differences observed.

 Can you really make out any difference? No, not really. However, due to the geometrical nature of the watermarking algorithm, the watermark can be recovered after scaling, rotation or combinations of geometrical transformations. 

A copyright protection watermarking algorithm can employ modifications in the histograms of 3D object surface normal. Watermarking of 3D polygonal meshes in spectral domain has been shown to be robust under various attacks. However, these approaches need the original object in the detection stage. Such watermarking algorithms can be used only for private key watermarking systems.

This blog was an overview of 3D modelling, watermarking and watermarking a 3D model. We have tried to put in information in a simple yet effective way for our users. These modern technical advancements and approaches definitely help for the security of our data, which is the base of all technological advancements in recent times.

References:

[1] Thomas Harte and Adrian G. Bors, “Watermarking 3D Models”, Department of Computer Science University of York, York YO10 5DD, U.K.

[2] F. Hartung and M. Kutter, “Multimedia watermarking techniques,” Proceedings of the IEEE, vol. 87, no. 7, pp. 1079– 1107, July 1999.

[3] Ping Wah Wong Hewlett Packard Company, “A Public Key Watermark for Image Verification and Authentication”  11000 Wolfe Road Cupertino, CA 95014.