Robust Mesh watermarking

Before reading a paper titled "Robust Mesh watermarking", when looking up the data, I found a very similar "three-dimensional model digital watermarking system design and implementation" of Chinese paper, with the help of Chinese papers, finally to the grid watermark has a certain understanding, Simply tidy up a bit.

Due to the need of intellectual copyright protection, digital watermarking technology has emerged. At present, the research of image, video, audio and text watermarking is quite mature, but the research of three-dimensional model watermark is relatively scarce. However, with the increasing spread of three-dimensional model in the network, the protection of three-dimensional model knowledge copyright has a certain research significance. Due to the characteristics of the three-dimensional model, the watermark embedded in it is different from the traditional watermark:

• Robustness
• Can work on any grid
• Keep the original connection
• Not perceptible

The traditional watermark is usually divided into time/spatial watermark and frequency domain watermark. In the image, the spatial watermark is accomplished by directly changing the pixels of the image (for example, the LSB algorithm proposed earlier), which is of low complexity and high efficiency, but lacks robustness and is easily removed or destroyed.

The frequency domain (also called transform domain) is to embed the watermark information by changing some parameters in the transform domain by transforming the image into the transform domain. This kind of change mainly includes DCT, DFT, DWT and so on. This kind of algorithm is widely researched because of its high robustness.

For the grid, there is no frequency domain This representation, so we need to find a suitable representation of the frequency domain in the image, the author's starting point is to extend the spectrum representation of the image into the grid, their ideas are as follows:

lack of a natural parameterization method for frequency decomposition (no DCT, etc.) à Mesh Multi-resolution representation

no natural sampling. à Grid registration and resampling

The watermark generation, embedding and extraction methods mentioned in the paper are listed below.

Watermark Generation :

with original model file MD5 after encryption md5 Span style= "font-family: Microsoft Jacob Black;" The value as the key 0 , the variance is Span style= "Font-family:times New Roman;" >l M Span style= "font-family: Microsoft Jacob Black;" > a random real number as a watermark w = {w0,wl, ... wm-1},

Key = MD5 (models) ;

W = Random (key)

W ~ N ( 0 , 1 )

Watermark Embedding:

W : Watermark

Φ : Coefficient of base function

D : Watermark Embedding Direction

The Matrix form is: V ' = v + BW

The Matrix X component form is:

VX ': The x-coordinate of the mesh vertex after adding the watermark

VX: Original mesh vertex x coordinate

ε: User-defined global parameters to control the depth of watermark embedding

Φ: is a matrix of n x m, a matrix of base functions in which the items in the matrix represent the scalar coefficients of the base function φi at the vertex j

HDX: is a diagonal matrix of M x N, where DX is the X component of the global displacement Trend di, and hi is the "amplitude" of the I-base function

W: Watermark

The following introduction, Di, Hi Generation, because in the process of generating these values using the PM algorithm, before this is a simple introduction of the progressive grid (Progressive Meshes, PM) algorithm

For the edge collapse and the vertex splitting contrast chart, in the grid on the left, the edge motion between vertex Uvs is removed, the U point is merged to the V Point, the position between the original vertex and the new vertex is recorded during the edge collapse, and the connection relationship between the vertices is changed so that you can split the point by splitting the vertex v point on the right image. , and then restore the edges between the Uvs. The entire edge collapse is stripped of the energy-less edges in the original mesh, and the specific energy functions are not discussed here.

in each point splitting process, calculate the amplitude of the geometry H:

• First, the 1-field centroid of the current point is used to represent (predict) the newly created point after the current point split,
• Then, the surface normal vector is computed based on the 1-domain of the current point
• Finally, H is the point multiplication between the surface normal vector and the actual splitting of the new point coordinates to the left side of the predicted new point, i.e. H = surface normal vector. (Actual new point coordinates-predict new point coordinates)

Then, from a number of sub-point division operations (the author does not account for specific times), the first m times H Max Operation is selected, and the base function is generated on the original point corresponding to the M operation.

For each collapse, calculate "boundary" Bi: The Neighbor collection that is extended by the current neighbor of the collapse point I after the trace point split operation. Calculate radius Rji: For each vertex VJ, calculate the distance from the point CI within the boundary, when CI is in the center of the boundary, the radius is 0,ci on or outside the boundary, the radius is 1, and the other case is between 0 and 1, the formula is as follows:

where D (v,s) represents the minimum distance between the V and the number of vertices in S, using the Dijkstra shortest path algorithm

(Note: For the calculation of H and R a little concerned about the understanding of deviations, attach this part of the original English)

Based on Radius r, the base function is constructed as a Mexican straw hat function in order to achieve better results.

This function is selected because the function is continuous at the origin of the coordinates and the integral at the Origin is 0 , which does not cause a noticeable change in the model.

Watermark Extraction:

before watermark extraction , Pan, rotate, Uniformly indent when attacking Span style= "Font-family:times New Roman;" >, Span style= "font-family: Microsoft Jacob Black;" > The model needs to be brought back to its original location and scale reposition (registration)

Re-location : relocation can be understood as finding a transformation between two models , makes the two models between " Distance " Minimum

Get points v* on attacked mesh surface corresponding to original mesh vertices V

Use same basis functions F 1 ... F m and hence same matrix B

Resampling Choices:

• Closest Point Projection
• Ray-casting along local normal
• Global deformation of original

After completing these two steps (as the case may not necessarily be), you can extract the watermark from the suspect grid, according to the following formula

w* : the watermark extracted from the suspect model

v* : vertex coordinates in a suspicious grid

V : Vertex coordinates in the original mesh

Solving the problem of least squares can find out w*

Calculate the correlation between the two:

PFP computed from R and m using Student ' s t-test

Declare Watermark Present If

PFP < Pthresh (e.g. Pthresh = 10-6)

According to the author's experiments, the watermark can resist multiple attacks and has strong robustness. Please refer to the original text for specific experimental results.

Robust Mesh watermarking