CN108564518B - Method for determining point cloud watermark based on radial distance and characteristic points - Google Patents
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Abstract
The invention discloses a method for determining cloud watermark based on radial distance and characteristic points, which specifically comprises the following steps: step 1, calculating the average curvature of each vertex in a three-dimensional point cloud model, and dividing the vertices in the model into two parts according to the average curvature calculation result; step 2, expressing all vertex coordinates in the model by newly established Cartesian coordinates of an invariant space, and converting all vertex coordinates into spherical coordinates; step 3, according to the number of the watermark embedding bits, performing equidistant ring division operation on the three-dimensional point cloud model with the transformed coordinates according to the vertex radial distance; a watermark bit is embedded in each ring, and the number of times of embedding the same watermark bit is controlled according to the number of characteristic points falling into the ring. The invention uses the peak with the average curvature smaller than 0 as the watermark embedding characteristic point to increase the invisibility of the watermark; embedding watermark bits multiple times according to the distribution of the feature points in the circular ring can improve the integrity of the watermark.
Description
Technical Field
The invention belongs to the technical field of three-dimensional point cloud watermarking, and particularly relates to a method for determining point cloud watermarking based on radial distance and feature points.
Background
In recent years, three-dimensional models are continuously appeared in the lives of people, and therefore, the protection of the copyright of the three-dimensional models is also emphasized.
The existing point cloud watermarking algorithms mainly comprise the following steps: the first method is a three-dimensional point cloud scheme for embedding watermarks by utilizing the high correlation of vertex neighborhoods, but has the defect that complete watermark bits cannot be extracted if an original model is attacked, namely the robustness is poor; the second method is a three-dimensional point cloud model watermarking algorithm based on local feature point extraction, wherein the watermark is embedded by changing the embedded vertex information, but the invisibility is poor. The third method is a new watermark algorithm embedded into the three-dimensional point cloud model based on distance normalization adjustment, and the watermark is embedded by adjusting the mean value of the distance after each watermark bit is normalized, but the algorithm has poor resistance to high-intensity noise attack and large-scale shearing, so that the research progress of the three-dimensional point cloud model watermark technology is slow.
Disclosure of Invention
The invention aims to provide a method for determining point cloud watermarking based on radial distance and characteristic points, and solves the problems that the existing point cloud watermarking algorithm is poor in robustness, weak in geometric attack capabilities such as rotation resistance and the like, poor in visibility and the like.
The technical scheme adopted by the invention is that the method for determining the cloud watermark based on the radial distance and the characteristic points specifically comprises the following steps:
step 1, calculating the average curvature of each vertex in a three-dimensional point cloud model, and dividing the vertices in the model into two parts according to the calculation result of the average curvature: a part of vertexes are used for establishing an invariant space, and a part of vertexes are used as characteristic points of the embedded watermark;
in the step 1, all vertexes are divided into two parts according to the average curvature size model: the C1 region represents the vertices with average curvature less than 0 for embedding the watermark; the C2 area represents the remaining vertices for building invariant space;
step 2, expressing all vertex coordinates in the model by newly established Cartesian coordinates of an invariant space, and converting all vertex coordinates into spherical coordinates;
in the step 2, the equation for calculating the coordinate of the invariant space origin is as follows:
wherein,
is the spherical coordinate of the ith non-characteristic point in the model,
the number of the model non-feature points is counted;
the calculation split ring formula is as follows:
wherein G isnIs the number of vertices in the nth ring, rn，jIs the jth vertex in the nth torus; step 3, according to the number of the watermark embedding bits, performing equidistant ring division operation on the three-dimensional point cloud model with the transformed coordinates according to the vertex radial distance; embedding a watermark bit in each ring, and controlling the times of embedding the same watermark bit according to the number of characteristic points falling into the ring;
step 4, normalizing the radial distance of the feature points to a range of [0, 1], so that the operation and the calculation are convenient;
step 5, adjusting the radial distance of the characteristic points according to the binary watermark bit content embedded at the position according to the histogram mapping function, and completing the watermark embedding of each ring;
in step 5, the histogram mapping formula is as follows:
wherein
For the adjusted value of the radial distance,
the normalized radial distance value is, alpha is a parameter;
step 6, the feature points with the adjusted radial distance after the watermark is embedded are inversely normalized to be an original radial distance range, and the spherical coordinates are converted into Cartesian coordinates;
and 7, reconstructing the vertex after the watermark is embedded and the vertex without the watermark to obtain a complete image after the watermark is embedded.
The present invention is also characterized in that,
the coordinate transformation formula in step 2 is as follows:
wherein M (x)c，yc，zc) Representing the coordinates of the centre point of the model in a Cartesian coordinate system, Ai (x)i，yi，zi) Cartesian coordinates representing the ith vertex; r isiDenotes the radial distance, θ, of the ith vertex from the center point in spherical coordinatesiIs the included angle between the line segment from the vertex Ai to the center point of the model and the positive Z axis, and i is the included angle between the line segment from the projection point of Ai on the horizontal plane to the center point of the model and the positive X axis.
In step 4, the feature point normalization formula is as follows:
wherein
The normalized radial distance value of the jth characteristic point in the nth spherical ring is obtained,
and
the radial distance value of the maximum characteristic point and the minimum characteristic point in the nth spherical ring.
In step 6, the feature point inverse normalization formula and the spherical coordinate are converted into cartesian coordinate formulas which are respectively expressed as the following formulas (6) and (7):
In step 3, the number of the sub-rings is the bit size of the embedded watermark, namely 16 bits.
Step 5, utilizing a histogram mapping formula to adjust the radial distance, wherein if the parameter alpha is reduced, the radial distance of the feature point is increased, the average value is increased, and namely, the watermark bit 1 is embedded; conversely, if α increases, the feature point radial distance decreases, and the average value decreases, i.e., watermark bit 0 is embedded.
The method for determining the point cloud watermark based on the radial distance and the characteristic points has the advantages that the peak with the average curvature smaller than 0 is used as the watermark embedding characteristic point, so that the invisibility of the watermark can be increased; a point with the average curvature not less than 0 is used for establishing an invariant space for resisting geometric attacks such as rotation shearing and the like, so that the watermark robustness can be improved; embedding watermark bits multiple times according to the distribution of the feature points in the circular ring can improve the integrity of the watermark.
Drawings
FIG. 1 is a schematic diagram of rabbit model feature point selection in an embodiment of a method for determining point cloud watermarking based on radial distance and feature points according to the present invention;
FIG. 2 is a schematic diagram of the selection of feature points of a face model according to an embodiment of the method for determining a point cloud watermark based on radial distances and feature points of the present invention;
FIG. 3 is a schematic diagram of a rabbit model projection in a horizontal plane according to an embodiment of the method for determining a point cloud watermark based on radial distances and feature points;
FIG. 4 is a schematic diagram of a watermark embedding process of an embodiment of the method for determining a point cloud watermark based on radial distance and feature points according to the present invention;
FIG. 5 is a schematic diagram of a watermark extraction process according to an embodiment of the method for determining a point cloud watermark based on radial distances and feature points;
FIG. 6 is a rabbit three-dimensional point cloud original model based on an embodiment of a method for determining point cloud watermarking based on radial distances and feature points according to the present invention;
FIG. 7 is a human face three-dimensional point cloud original model of an embodiment of a method for determining a point cloud watermark based on radial distances and feature points according to the present invention;
FIG. 8 is a three-dimensional point cloud original model of a leopard in accordance with an embodiment of the present invention based on a method for determining a point cloud watermark using radial distances and feature points;
FIG. 9 is an ant three-dimensional point cloud original model according to an embodiment of the present invention, based on radial distances and feature points;
FIG. 10 is a model of a rabbit three-dimensional point cloud embedded watermark according to an embodiment of the method for determining point cloud watermark based on radial distance and feature points;
FIG. 11 is a model of a human face three-dimensional point cloud embedded watermark in an embodiment of a method for determining point cloud watermarking based on radial distance and feature points according to the present invention;
FIG. 12 is a model of a three-dimensional point cloud of leopard embedded with a watermark according to an embodiment of the method for determining a point cloud watermark based on radial distances and feature points;
FIG. 13 is a model of a method for determining a point cloud watermark based on radial distances and feature points according to an embodiment of the present invention, after a watermark is embedded in a three-dimensional point cloud of ants;
FIG. 14 is a rabbit three-dimensional point cloud original model according to an embodiment of the present invention based on radial distance and feature point determination point cloud watermarking method;
FIG. 15 is a schematic view of a rabbit model rotated 90 degrees along the Y-axis according to an embodiment of the method for determining point cloud watermarking based on radial distance and feature points of the present invention;
FIG. 16 is a schematic view of a rabbit model rotated 45 degrees along the Z-axis according to an embodiment of the method for determining point cloud watermarking based on radial distance and feature points.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention relates to a method for determining cloud watermark based on radial distance and characteristic points, which specifically comprises the following steps:
step 1, calculating the average curvature of each vertex in a three-dimensional point cloud model, and dividing the vertices in the model into two parts according to the calculation result of the average curvature: a part of vertexes are used for establishing an invariant space, and a part of vertexes are used as characteristic points of the embedded watermark;
in the step 1, all vertexes are divided into two parts according to the average curvature size model: the C7 region represents the vertices with average curvature less than 0 for embedding the watermark; the C2 area represents the remaining vertices for building invariant space;
step 2, expressing all vertex coordinates in the model by newly established Cartesian coordinates of an invariant space, and converting all vertex coordinates into spherical coordinates;
in the step 2, the equation for calculating the coordinate of the invariant space origin is as follows:
wherein,
is the spherical coordinate of the ith non-characteristic point in the model,
the number of the model non-feature points is counted;
the calculation split ring formula is as follows:
wherein G isnIs the number of vertices in the nth ring, rn，jIs the jth vertex in the nth torus;
the coordinate transformation formula in step 2 is as follows:
wherein M (x)c，yc，zc) Representing the coordinates of the centre point of the model in a Cartesian coordinate system, Ai (x)i，yi，zi) Cartesian coordinates representing the ith vertex; r isiDenotes the radial distance, θ, of the ith vertex from the center point in spherical coordinatesiIs the included angle between the line segment from the vertex Ai to the center point of the model and the positive Z axis, and i is the included angle between the line segment from the projection point of Ai on the horizontal plane to the center point of the model and the positive X axis.
Step 3, according to the number of the watermark embedding bits, performing equidistant ring division operation on the three-dimensional point cloud model with the transformed coordinates according to the vertex radial distance; embedding a watermark bit in each ring, and controlling the times of embedding the same watermark bit according to the number of characteristic points falling into the ring;
in step 3, the number of the sub-rings is the bit size of the embedded watermark, namely 16 bits.
Step 4, normalizing the radial distance of the feature points to a range of [0, 1], so that the operation and the calculation are convenient;
in step 4, the feature point normalization formula is as follows:
wherein
The normalized radial distance value of the jth characteristic point in the nth spherical ring is obtained,
and
the radial distance value of the maximum characteristic point and the minimum characteristic point in the nth spherical ring.
Step 5, adjusting the radial distance of the characteristic points according to the binary watermark bit content embedded at the position according to the histogram mapping function, and completing the watermark embedding of each ring;
in step 5, the histogram mapping formula is as follows:
wherein
For the adjusted value of the radial distance,
the normalized radial distance value is, alpha is a parameter; step 5, utilizing a histogram mapping formula to adjust the radial distance, wherein if the parameter d is reduced, the radial distance of the feature point is increased, the average value is increased, and namely the watermark bit 1 is embedded; conversely, if α increases, the feature point radial distance decreases, and the average value decreases, i.e., watermark bit 0 is embedded.
Step 6, the feature points with the adjusted radial distance after the watermark is embedded are inversely normalized to be an original radial distance range, and the spherical coordinates are converted into Cartesian coordinates;
in step 6, the feature point inverse normalization formula and the spherical coordinate are converted into cartesian coordinate formulas which are respectively expressed as the following formulas (6) and (7):
And 7, reconstructing the vertex after the watermark is embedded and the vertex without the watermark to obtain a complete image after the watermark is embedded.
The invention discloses a fixed point cloud watermarking method based on radial distance and characteristic points, which utilizes an index stretching method to realize the embedding of watermark information, classifies all vertexes of a point cloud model by calculating an average curvature value in the process of selecting the characteristic points, and then selects points with the value less than 0 as watermark embedding points; when the radial distance position is adjusted according to a histogram mapping formula, if the normalization parameter alpha is reduced, the radial distance is increased, the average value is increased, and namely, the watermark bit 1 is embedded; if α increases, the radial distance decreases, and the average value decreases, i.e., watermark bit 0 is embedded.
Four models were selected for this example. Fig. 6-9 show the original model images of rabbit, human face, leopard and ant as experimental objects. Wherein, the rabbit model consists of 5326 vertexes; the face model consists of 1884 vertexes; the leopard model consists of 7256 vertices; the ant model consists of 7823 vertices. Embedding by using 16-bit watermark, wherein the value range of the watermark embedding strength beta is more than 0 and less than 1/2. The watermark embedding process is as follows:
step 1, calculating the average curvature of each vertex in four three-dimensional point cloud models, and dividing all the vertices of the models into two parts: the C1 region represents the vertices with average curvature less than 0 for embedding the watermark; the C2 region is the remaining vertices and is used to create an invariant space whose centroid is determined by calculating the mean of all vertices in the C2 region.
Step 2, expressing all vertex coordinates in the model by newly established Cartesian coordinates of an invariant space, and converting all vertex coordinates into spherical coordinates;
and 3, performing equidistant ring division operation on the three-dimensional point cloud model with the transformed coordinates according to the maximum and minimum values of the vertex radial distance according to the number of the embedded watermark bits. And embedding a watermark bit in each ring, iteratively embedding the watermark bit, and controlling the embedding times of the same watermark bit according to the number of the characteristic points falling into the ring.
Step 4, normalizing the radial distance of the feature points to a range of [0, 1] by using a normalization formula, so that the operation and calculation are convenient;
step 5, adjusting the radial distance of the feature points according to the binary watermark bit content embedded at the position according to the histogram mapping function, wherein if the embedded watermark bit is 0, the radial distance of the feature points is reduced, and the average value of all the feature points in the same circle is reduced; if the embedded watermark bit is 1, the radial distance of the feature point becomes larger, and the mean value of all the feature points in the same circle becomes larger. The watermark embedding of each ring is completed by the method;
step 6, inverse normalization is carried out on the characteristic points embedded with the watermarks to be within the range of the original radial distance, and the vertex spherical coordinates are converted into Cartesian coordinates;
and 7, reconstructing the vertex with the embedded watermark and the vertex without the embedded watermark to obtain a complete image with the embedded watermark, wherein the images are model images of the rabbit, the human face, the leopard and the ant with the embedded watermark as shown in fig. 10-13.
Whether the watermarking method is feasible or not is shown from two aspects, on one hand, the invisibility of the watermarking algorithm is evaluated by adopting root mean square difference (RMSE) through the invisibility consideration before and after the original model is embedded with the watermark, and the calculation method is as the following formula (8):
wherein r isoriginal，iAnd rtest，iRespectively representing radial distance values of corresponding vertexes of the original model and the test model, wherein n is the number of watermark bits; on the other hand, the watermark extracted from the three-dimensional model suffering from the attack is verified by carrying out similarity value calculation with the original watermark, and the correlation coefficient value (Corr) is adopted in the invention to verify the similarity, as shown in formula (9): when the Corr value is closer to 1, the robustness of the three-dimensional point cloud model watermarking algorithm is better.
Wherein m isnAnd mn' respectively embedded watermark sequences wnAnd the extracted watermark sequence wn' average value.
1. Invisibility testing
After the watermark is embedded, the model is compared with the schematic diagram, so that the error between the model and the original model after the watermark is embedded by the algorithm is small, and the visual quality is not interfered. Experimental results show that the watermark algorithm has small influence on model vision, the three-dimensional point cloud model after the watermark is embedded is basically consistent with the original model, and human eyes cannot distinguish the difference between the three-dimensional point cloud model and the original model, so that the watermark is proved to have good invisibility. The invisibility of the watermark can be improved by reducing the embedding strength beta of the watermark, but the robustness of the watermark is reduced along with the improvement of the transparency, so that the balance between the transparency and the robustness of the watermark needs to be obtained according to the requirements of practical problems.
2. Robustness testing
Table 1 shows the comparison of the correlation coefficient values between the four three-dimensional point cloud models and the original model when the four three-dimensional point cloud models are subjected to various attacks.
1) Shear attack
In the shearing attack experiment, the watermark is only embedded in the characteristic points, and in the algorithm of the invention, the characteristic points are iteratively and discretely embedded in all positions of the model, the model is sheared, only the watermark bit embedded in the shearing part is lost, the watermark cannot be completely damaged, and the relatively complete watermark can still be extracted from the rest of the model, so that the algorithm provided by the invention is beneficial to resisting shearing attack. As can be seen from the data in Table 1, the smaller the cut portion, the better the effect.
2) Rotational attack
The vertex coordinates may change when the model is rotated, thereby affecting the integrity of watermark extraction. In the present invention, the defect is complemented by establishing an invariant space: an invariant space is created with non-feature points (points with an average curvature less than 0) to ensure that feature points can determine coordinate positions in the new coordinate space. In the experiment, the original model is rotated around the Y axis and the Z axis respectively, as shown in fig. 14, fig. 15, and fig. 16, the rabbit three-dimensional point cloud original model is not attacked, the rabbit three-dimensional point cloud original model is rotated around the Y axis by 90 ° in the embodiment, and the rabbit three-dimensional point cloud original model is rotated around the Z axis by 45 °. The experimental result shows that different rotation angles have different influences on the robustness of the watermark.
3) Noise attack
The algorithm of the invention uses random noise with variance sigma to attack each three-dimensional point cloud model, and the amplitude of the noise is respectively 0.001, 0.003 and 0.005. From the data in table 1, it can be seen that the larger the noise amplitude, the smaller the correlation coefficient value, and the more distorted the model.
And finally, in order to test the performance of the watermark, the four three-dimensional models are tested. The robustness of a watermark is measured by calculating the Bit Error Rate (BER) between the extracted watermark and the original watermark after an attack. The algorithm of the invention is compared and simulated with the Zhang algorithm and the Qi algorithm, and the experimental result data after various attacks are shown in the following table 2.
The algorithm provided by the invention has strong robustness to shearing attack, rotation attack and noise attack, and particularly has the best effect in the experimental part of the rotation and shearing attack. In a shearing experiment, because the number of original model points is different from that of a shearing part, the caused experiment result is different, the more the number of model points is, the better the model experiment result is, and the shearing attack result below 30% is better, and the robustness is stronger.
TABLE 1 various attack Corr coefficients
TABLE 2 BER values of the algorithm of the present invention compared to two other algorithms
Claims (6)
1. The method for determining the cloud watermark based on the radial distance and the characteristic points is characterized by comprising the following steps:
step 1, calculating the average curvature of each vertex in a three-dimensional point cloud model, and dividing the vertices in the model into two parts according to the calculation result of the average curvature: a part of vertexes are used for establishing an invariant space, and a part of vertexes are used as characteristic points of the embedded watermark;
in the step 1, all vertexes are divided into two parts according to the average curvature size model: the C1 region represents the vertices with average curvature less than 0 for embedding the watermark; the C2 area represents the remaining vertices for building invariant space;
step 2, expressing all vertex coordinates in the model by newly established Cartesian coordinates of an invariant space, and converting all vertex coordinates into spherical coordinates;
in the step 2, the equation for calculating the coordinate of the invariant space origin is as follows:
wherein,
is the spherical coordinate of the ith non-characteristic point in the model,
the number of the model non-feature points is counted;
the calculation split ring formula is as follows:
for 1≤n≤N；0≤j≤Gn (3)
wherein G isnIs the number of vertices in the nth ring, rn,jIs the jth vertex in the nth torus; step 3, according to the number of the watermark embedding bits, performing equidistant ring division operation on the three-dimensional point cloud model with the transformed coordinates according to the vertex radial distance; embedding a watermark bit in each ring, and controlling the times of embedding the same watermark bit according to the number of characteristic points falling into the ring;
step 4, normalizing the radial distance of the feature points to a range of [0, 1], so that the operation and the calculation are convenient;
step 5, adjusting the radial distance of the characteristic points according to the binary watermark bit content embedded at the position according to the histogram mapping function, and completing the watermark embedding of each ring;
in step 5, the histogram mapping formula is as follows:
wherein
For the adjusted value of the radial distance,
the normalized radial distance value is, alpha is a parameter;
step 6, the feature points with the adjusted radial distance after the watermark is embedded are inversely normalized to be an original radial distance range, and the spherical coordinates are converted into Cartesian coordinates;
and 7, reconstructing the vertex after the watermark is embedded and the vertex without the watermark to obtain a complete image after the watermark is embedded.
2. The method for determining the cloud watermark based on the radial distance and the feature points according to claim 1, wherein the coordinate transformation formula in the step 2 is as follows:
wherein M (x)c，yc，zc) Representing the coordinates of the centre point of the model in a Cartesian coordinate system, Ai(xi，yi，zi) Cartesian coordinates representing the ith vertex; r isiDenotes the radial distance, θ, of the ith vertex from the center point in spherical coordinatesiIs vertex AiThe line segment from the center point of the model forms an angle with the positive Z axis,
is AiAnd the line segment from the projection point on the horizontal plane to the center point of the model forms an included angle with the positive X axis.
3. The method for determining point cloud watermark according to claim 1, wherein in the step 4, the normalization formula of the feature points is as follows:
wherein
The normalized radial distance value of the jth characteristic point in the nth spherical ring is obtained,
and
the radial distance value of the maximum characteristic point and the minimum characteristic point in the nth spherical ring.
4. The method for determining a point cloud watermark according to claim 1, wherein in the step 6, the inverse normalization formula of the feature points and the conversion of the spherical coordinates into cartesian coordinates are respectively given by the following formulas (6) and (7):
5. The method for determining point cloud watermark according to claim 4, wherein in the step 3, the number of the sub-rings is the bit size of the embedded watermark, i.e. 16 bits.
6. The method according to claim 1, wherein in step 5, the radial distance is adjusted by using a histogram mapping formula, and if the parameter α decreases, the radial distance of the feature point increases, and the mean value increases, that is, the watermark bit 1 is embedded; conversely, if α increases, the feature point radial distance decreases, and the average value decreases, i.e., watermark bit 0 is embedded.
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