Geodesic-based robust blind watermarking method for three-dimensional mesh animation by using mesh segmentation and vertex Trajectory

Before the test, interrupted the work of the laboratory, now the examination is over, can not be wasted.

recently read an article about the sequence watermark, the general idea is: for a grid sequence, first processing the first frame, on the first frame, the mesh segmentation algorithm (SDF) to divide the mesh into several meaningful regions. In each area, the geodesic distance of the point-to-region boundary in the area is computed, and the points in the area are divided into different sets according to the geodesic distance, and then the average distance of geodesic distances in the set is kept within the specified range, thus embedding the watermark.

The following describes the practice.

     Span style= "font-family: Microsoft Jacob Black;" > watermark sequence : +1 -1 sequence, generated by a pseudo-random function

Mesh Segmentation algorithm:Shape Diameter Function (SDF). SDF as a local feature can be thought of as the diameter of the corresponding shape in the region of each point. Three-dimensional model in the attack, such as translation, rotation, simplification, noise, posture changes, etc., generally can maintain the original shape characteristics, as the local features of SDF can be saved after the attack, so SDF And its distribution has a certain robustness.

SDF There are three steps to the practice:

Step1 : Calculate shape diameter value

for a patch, make a cone with the center of the patch centered as the cone vertex and its normal vector in the direction of the center line, from which the rays from the cone range are drawn to the surface meshes of the model, and the X-ray intersecting with the mesh is computed by constructing the eight-fork tree structure to remove the same ray as the vertex normal direction. ( the angle is less than .) That is the same direction ), take the remaining length of all ray length within the standard deviation of the median of the ray as a weighted average, that is, the SDF value of the vertex .

STEP2 : Gmm-em Clustering.

Use maximum expectation(Exception-Maximization,EM)algorithm to construct three-dimensional model patchesSDFhistogram of values, with a Gaussian mixture model(Gaussian mixture model,GMM)Getka Gaussian distribution, all the patches of the mesh model are clustered intokcluster, which is represented as a number of tiles on the model view, i.e. the grid is given aka coarse chunk of the hierarchy.

STEP3 : Cutting boundary refinement.

Another important problem for meaningful segmentation is the smoothness of the segmentation boundary and the

whether the local characteristics of the class are preserved, using the extended Alpha Graph-cutting algorithm (Alpha expansion

graph-cut algorithm) Minimize the energy function to determine the ownership of the patch and get the final boundary.

Embedding watermarks:

( 1 ) using SDF splits the first frame of the mesh into different regions

( 2 ) in SDF each of the vertices in the region, for each vertex in the vj1 , calculate vj1 The average of the geodesic distance to the point on the boundary line of the area to which it is located, DJB, according to the size of the DJB, divides the points in the area into NW different sets, each set as

Where DMax is the highest value of all DJB in the region, and 1≤I≤NW.

(3) Each watermark will be embedded in the I=1 to I=NW collection. For the I-set, calculate the average UD for all DJB and check the size relationship between UD and Ki, as defined by Ki:

[0,0.5]

if and wi=+1 Span style= "font-family: Microsoft Jacob Black;" You would otherwise need to increase the dmax ud ki The relationship, until the conditions are met.

Similarly, when ud<ki and wi=-1

( ) depending on the trajectory of the vertex, you can ensure that the other frames are split as the first frame. In the third step, the difference between the original vertex of the vertex selected for the adjusted position and the adjusted new vertex is recorded as δ j The remaining frames can be directly based on the δ j and wi wi=+1 j wi=-1 j

watermark Extraction: The algorithm presented in this paper is blind watermarking algorithm, so the original sequence is not needed at the time of extraction, and the detection steps are as follows.

(1) Enter the watermark sequence anddivide the first frame of the sequence according to the embedded step (1).

(2) The first frame of the sequence is divided according to theembedded step (2).

(3) Extract the watermark from each set, according to the following formula to determine the extracted watermark value

which

is the maximum value of the distance from the area boundary geodesic in the collection.

(4) The same as the Step (4) Embedding the watermark, the remaining frames can be divided into the same meaningful region as the first frame through the vertex trajectory. The watermark is then extracted by step (3).

(5) In order to verify the version information, calculate the bit error rate (BER) between the embedded watermark W and the extracted watermark W ', if the BER is smaller than the predetermined threshold, it proves that there is an embedded watermark in a set.

Geodesic-based robust blind watermarking method for three-dimensional mesh animation by using mesh segmentation and vertex Trajectory