CN108564518A - Point cloud watermarking algorithm based on radial distance and characteristic point - Google Patents
Point cloud watermarking algorithm based on radial distance and characteristic point Download PDFInfo
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- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T1/00—General purpose image data processing
- G06T1/0021—Image watermarking
- G06T1/005—Robust watermarking, e.g. average attack or collusion attack resistant
- G06T1/0064—Geometric transfor invariant watermarking, e.g. affine transform invariant
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Abstract
The invention discloses a kind of point cloud watermarking algorithm based on radial distance and characteristic point, specifically follows the steps below：Step 1, the average curvature on each vertex in three-dimensional point cloud model is calculated, and model inner vertex is divided into two parts according to average curvature result of calculation；Step 2, all apex coordinates in model are indicated with the cartesian coordinate of the newly-established invariant space, and is spherical coordinate by the coordinate transformation on its all vertex；Step 3, according to embedded watermark bit position number, the three-dimensional point cloud model for having converted coordinate is subjected to equidistant annulus division operation according to vertex radial distance；By an embedded watermark bit position in each annulus, and counted according to the feature fallen into annulus to control the number of embedded same watermark bit position.Vertex of the present invention using average curvature less than 0 can increase the invisibility of watermark as watermark insertion characteristic point；The integrality of watermark can be improved according to the multiple embedded watermark bit of distribution of the characteristic point in annulus.
Description
Technical field
The invention belongs to three-dimensional point cloud digital watermark fields, and in particular to a kind of point cloud based on radial distance and characteristic point
Watermarking algorithm.
Background technology
Threedimensional model continuously emerges in people's lives in recent years, therefore the protection of threedimensional model copyright also obtains weight
Depending on.
Existing cloud watermarking algorithm is mainly the following：First method is the high correlation using vertex neighborhood
The three-dimensional point cloud scheme of embedded watermark, but it the shortcomings that be if archetype cannot extract complete water by attack
Print position, i.e. poor robustness；Second method is a kind of three-dimensional point cloud model watermarking algorithm extracted based on local feature region, is passed through
Change embedded vertex information to be embedded in watermark, but its invisibility is poor.The third method is a kind of based on range normalization adjustment
New insertion three-dimensional point cloud model watermarking algorithm, by adjusting each watermark bit normalize after distance mean value be embedded in water
Print, but this algorithm is bad to the attacked by noise of high intensity and the resistivity sheared on a large scale, so as to cause three-dimensional point cloud
Model digital watermark progress is slow.
Invention content
The object of the present invention is to provide a kind of point cloud watermarking algorithm based on radial distance and characteristic point, solves existing
The problems such as geometric attacks abilities such as the point poor, anti-rotation of cloud watermarking algorithm robustness are weaker, visual poor.
The technical solution adopted in the present invention is the point cloud watermarking algorithm based on radial distance and characteristic point, specifically according to
Following steps carry out：
Step 1, the average curvature on each vertex in three-dimensional point cloud model is calculated, and by model inner vertex according to average song
Rate result of calculation is divided into two parts：A part of vertex is used for establishing the invariant space, feature of a part of vertex as embedded watermark
Point；
Step 2, all apex coordinates in model are indicated with the cartesian coordinate of the newly-established invariant space, and by its institute
It is spherical coordinate to have the coordinate transformation on vertex；
Step 3, according to embedded watermark bit position number, will convert the three-dimensional point cloud model of coordinate according to vertex it is radial away from
From the equidistant annulus division operation of progress；In each annulus will an embedded watermark bit position, and according to falling into annulus
Feature count to control the number of embedded same watermark bit position；
Step 4, the radial distance of characteristic point is normalized into [0,1] range, is conveniently operated and calculates；
Step 5, the binary watermarking bit contents that are embedded according to this position according to histogram mapping function adjust characteristic point
Radial distance, complete each annulus watermark insertion；
Step 6, it is original radial distance range by the characteristic point renormalization of radial distance has been adjusted after embedded watermark, and
Convert spherical coordinate to cartesian coordinate；
Step 7, the vertex after embedded watermark is reconstructed to obtain complete embedded watermark with the vertex for being not embedded into watermark
Image afterwards.
The features of the present invention also characterized in that
In step 1, it is divided into two parts according to all vertex of average curvature size model：The regions C1 indicate that average curvature is less than
0 vertex, for being embedded in watermark；The regions C2 indicate remaining vertex, for establishing the invariant space.
Coordinate transformation formula is as follows in step 2：
Wherein M (xc, yc, zc) indicate coordinate of the model center point in cartesian coordinate system, Ai(xi, yi, zi) indicate i-th
The cartesian coordinate on a vertex；riIndicate i-th of vertex in spherical coordinate apart from the radial distance of central point, θiIt is vertex Ai
Angle between the line segment and positive Z axis of model center point,For AiHorizontal plane subpoint to model center point line segment
With the angle of positive X-axis.
In step 3, it is as follows to calculate invariant space origin formula：
Wherein,For i-th in model non-characteristic point spherical coordinate,For model non-characteristic point
Number；
Calculating divides ring formula as follows：
Wherein GnIt is the number of vertices in n-th of ring, rn,jIt is j-th of vertex in n-th of ball.
In step 4, it is as follows that characteristic point normalizes formula：
WhereinRadial distance value after being normalized for j-th of characteristic point in n-th of ball,WithFor the radial distance value of minimum and maximum characteristic point in n-th of ball.
In step 5, Histogram Mapping formula is as follows：
WhereinFor the radial distance value after adjustment,For the radial distance value after normalization, α is parameter.
In step 6, it is respectively following formula (6) that characteristic point renormalization formula and spherical coordinate, which are converted into cartesian coordinate formula,
(7)：
For the radial distance value after j-th of characteristic point renormalization in n-th of ball；
It indicates by the cartesian coordinate on i-th of vertex of spherical coordinate inverse transformation；It indicates
Radial distance after i-th of vertex adjustment.
In step 3, divide ring number for embedded watermark bit position size, i.e., 16.
Radial distance is adjusted using Histogram Mapping formula in step 5, characteristic point radial distance becomes if parameter alpha reduces
Greatly, mean value becomes larger, that is, is embedded in watermark bit 1；On the contrary, characteristic point radial distance becomes smaller if α increases, mean value becomes smaller, i.e., embedded water
Print position 0.
Advantageous effect the present invention is based on radial distance and the point cloud watermarking algorithm of characteristic point is less than using average curvature
0 vertex can increase the invisibility of watermark as watermark insertion characteristic point；Using average curvature not less than 0 point establish it is constant
Space can increase watermark robustness for resisting the geometric attacks such as rotational shear；It is multiple according to distribution of the characteristic point in annulus
The integrality of watermark can be improved in embedded watermark bit.
Description of the drawings
Fig. 1 is that the present invention is based on radial distances and the point cloud watermarking algorithm embodiment rabbit model characteristic point of characteristic point to choose
Schematic diagram；
Fig. 2 is that the present invention is based on the selections of point cloud watermarking algorithm embodiment faceform's characteristic point of radial distance and characteristic point
Schematic diagram；
Fig. 3 is that the present invention is based on radial distances and the point cloud watermarking algorithm embodiment rabbit model projection of characteristic point in level
Face schematic diagram；
Fig. 4 is that the present invention is based on the insertion watermarking process signals of the point cloud watermarking algorithm embodiment of radial distance and characteristic point
Figure；
Fig. 5 is that the present invention is based on the extraction watermarking process signals of the point cloud watermarking algorithm embodiment of radial distance and characteristic point
Figure；
Fig. 6 is the original mould of point cloud watermarking algorithm embodiment rabbit three-dimensional point cloud the present invention is based on radial distance and characteristic point
Type；
Fig. 7 is the original mould of point cloud watermarking algorithm embodiment face three-dimensional point cloud the present invention is based on radial distance and characteristic point
Type；
Fig. 8 is the original mould of point cloud watermarking algorithm embodiment leopard three-dimensional point cloud the present invention is based on radial distance and characteristic point
Type；
Fig. 9 is the original mould of point cloud watermarking algorithm embodiment ant three-dimensional point cloud the present invention is based on radial distance and characteristic point
Type；
Figure 10 is that the present invention is based on radial distances and the point cloud watermarking algorithm embodiment rabbit three-dimensional point cloud of characteristic point to be embedded in
Model after watermark；
Figure 11 is that the present invention is based on radial distances and the point cloud watermarking algorithm embodiment face three-dimensional point cloud of characteristic point to be embedded in
Model after watermark；
Figure 12 is that the present invention is based on radial distances and the point cloud watermarking algorithm embodiment leopard three-dimensional point cloud of characteristic point to be embedded in
Model after watermark；
Figure 13 is that the present invention is based on radial distances and the point cloud watermarking algorithm embodiment ant three-dimensional point cloud of characteristic point to be embedded in
Model after watermark；
Figure 14 is that the present invention is based on the point cloud watermarking algorithm embodiment rabbit three-dimensional point cloud of radial distance and characteristic point is original
Model；
Figure 15 is that the present invention is based on radial distances and the point cloud watermarking algorithm embodiment rabbit model of characteristic point to be rotated along Y-axis
90 ° of schematic diagrames；
Figure 16 is that the present invention is based on radial distances and the point cloud watermarking algorithm embodiment rabbit model of characteristic point to be rotated along Z axis
45 ° of schematic diagrames.
Specific implementation mode
The following describes the present invention in detail with reference to the accompanying drawings and specific embodiments.
The present invention is based on the point cloud watermarking algorithms of radial distance and characteristic point, specifically follow the steps below：
Step 1, the average curvature on each vertex in three-dimensional point cloud model is calculated, and by model inner vertex according to average song
Rate result of calculation is divided into two parts：A part of vertex is used for establishing the invariant space, feature of a part of vertex as embedded watermark
Point is as shown in Figure 1 rabbit instance model progress characteristic point selection schematic diagram, and RED sector is selected feature in figure
Point；It is illustrated in figure 2 face instance model and carries out characteristic point and choose schematic diagram, RED sector is selected feature in figure
Point.Rabbit model shown in Fig. 3 horizontal plane perspective view, as seen from the figure, selected characteristic point from model dot compared with
Closely；
Step 2, all apex coordinates in model are indicated with the cartesian coordinate of the newly-established invariant space, and by its institute
It is spherical coordinate to have the coordinate transformation on vertex；
Step 3, according to embedded watermark bit position number, will convert the three-dimensional point cloud model of coordinate according to vertex it is radial away from
From the equidistant annulus division operation of progress；In each annulus will an embedded watermark bit position, and according to falling into annulus
Feature count to control the number of embedded same watermark bit position.If Fig. 4 is watermark telescopiny schematic diagram, it is shown that point cloud
The Embedded step of model；
Step 4, the radial distance of characteristic point is normalized into [0,1] range, is conveniently operated and calculates；
Step 5, the binary watermarking bit contents that are embedded according to this position according to histogram mapping function adjust characteristic point
Radial distance, complete each annulus watermark insertion；
Step 6, it is original radial distance range by the characteristic point renormalization of radial distance has been adjusted after embedded watermark, and
Convert spherical coordinate to cartesian coordinate；
Step 7, the vertex after embedded watermark is reconstructed to obtain complete embedded watermark with the vertex for being not embedded into watermark
Image afterwards；Fig. 5 is watermark extraction process schematic diagram.
In step 1, it is divided into two parts according to all vertex of average curvature size model：The regions C1 indicate that average curvature is less than
0 vertex, for being embedded in watermark；The regions C2 indicate remaining vertex, for establishing the invariant space.
Coordinate transformation formula is as follows in step 2：
Wherein M (xc, yc, zc) indicate coordinate of the model center point in cartesian coordinate system, Ai(xi, yi, zi) indicate i-th
The cartesian coordinate on a vertex；riIndicate i-th of vertex in spherical coordinate apart from the radial distance of central point, θiIt is vertex Ai
Angle between the line segment and positive Z axis of model center point,For AiHorizontal plane subpoint to model center point line segment
With the angle of positive X-axis.
In step 3, it is as follows to calculate invariant space origin formula：
Wherein,For i-th in model non-characteristic point spherical coordinate,For model non-characteristic point
Number；
Calculating divides ring formula as follows：
Wherein GnIt is the number of vertices in n-th of ring, rn,jIt is j-th of vertex in n-th of ball.
In step 4, it is as follows that characteristic point normalizes formula：
WhereinRadial distance value after being normalized for j-th of characteristic point in n-th of ball,WithFor the radial distance value of minimum and maximum characteristic point in n-th of ball.
In step 5, Histogram Mapping formula is as follows：
WhereinFor the radial distance value after adjustment,For the radial distance value after normalization, α is parameter.
In step 6, it is respectively following formula (6) that characteristic point renormalization formula and spherical coordinate, which are converted into cartesian coordinate formula,
(7)：
For the radial distance value after j-th of characteristic point renormalization in n-th of ball.
It indicates by the cartesian coordinate on i-th of vertex of spherical coordinate inverse transformation；It indicates
Radial distance after i-th of vertex adjustment.
In step 3, divide ring number for embedded watermark bit position size, i.e., 16.
Radial distance is adjusted using Histogram Mapping formula in step 5, characteristic point radial distance becomes if parameter alpha reduces
Greatly, mean value becomes larger, that is, is embedded in watermark bit 1；On the contrary, characteristic point radial distance becomes smaller if α increases, mean value becomes smaller, i.e., embedded water
Print position 0.
The present invention is based on the point cloud watermarking algorithms of radial distance and characteristic point, and index drawing process is utilized and realizes watermark letter
The insertion of breath classifies to all vertex of point cloud model by calculating average curvature values, so in selected characteristic point process
Point of the value less than 0 is selected afterwards as watermark is embedded in point；When adjusting radial distance position according to Histogram Mapping formula, if normalization
Parameter alpha reduces then radial distance and becomes larger, and mean value becomes larger, that is, is embedded in watermark bit 1；Radial distance becomes smaller if α increases, and mean value becomes
It is small, that is, it is embedded in watermark bit 0.
Embodiment the present embodiment selects four models.As Fig. 6-9 respectively embodiment rabbit, face, leopard, ant are original
Illustraton of model is as experimental subjects.Wherein, rabbit model is made of 5326 vertex；Faceform is made of 1884 vertex；Leopard
Submodel is made of 7256 vertex；Ant model is made of 7823 vertex.It is embedded in using 16 watermarks, watermark insertion
Intensity β value ranges are 0<β<1/2.Embedded watermarking process is as follows：
Step 1, the average curvature on each vertex in four three-dimensional point cloud models is calculated, and all vertex of model are divided
For two parts：The regions C1 indicate the vertex that average curvature is less than 0, for being embedded in watermark；The regions C2 are remaining vertex, for establishing
The barycenter of the invariant space, the invariant space is determined by calculating the mean value on all vertex in the regions C2.
Step 2, all apex coordinates in model are indicated with the cartesian coordinate of the newly-established invariant space, and by its institute
It is spherical coordinate to have the coordinate transformation on vertex；
Step 3, according to embedded watermark bit position number, will convert the three-dimensional point cloud model of coordinate according to vertex it is radial away from
From maximin carry out equidistant annulus division operation.By an embedded watermark bit position in each annulus, iteration is embedding
Enter watermark bit, and is counted according to the feature fallen into annulus to control the number of embedded same watermark bit position.
Step 4, the radial distance of characteristic point is normalized into [0,1] range using normalization formula, is conveniently operated and counts
It calculates；
Step 5, the binary watermarking bit contents that are embedded according to this position according to histogram mapping function adjust characteristic point
Radial distance, if embedded watermark bit is 0, characteristic point radial distance becomes smaller, all characteristic point mean values in same annulus
Become smaller；If embedded watermark bit is 1, characteristic point radial distance becomes larger, and all characteristic point mean values in same annulus become larger.With
The method completes the watermark insertion of each annulus；
Step 6, it is original radial distance range by the characteristic point renormalization after embedded watermark, and by vertex spherical coordinate
It is converted into cartesian coordinate；
Step 7, the vertex after embedded watermark is reconstructed to obtain complete embedded watermark with the vertex for being not embedded into watermark
Image afterwards, if Figure 10-13 is respectively the illustraton of model after embodiment rabbit, face, leopard, ant insertion watermark.
Whether water mark method of the present invention is feasible, illustrates in terms of two, is on the one hand embedded in before and after watermark by archetype
Invisibility considers, the invisibility of watermarking algorithm, computational methods such as following formula (8) are evaluated using the equal value difference in root side (RMSE)：
Wherein, roriginal,iAnd rtest,iThe respectively radial distance value of archetype, test model corresponding vertex, n are water
Print position number；On the other hand, by the watermark extracted from the threedimensional model attacked, similar value meter is carried out with original watermark
It calculates to verify, its similitude is verified using correlation coefficient value (Corr) in the present invention, such as formula (9)：When Corr values are closer
1, illustrate that three-dimensional point cloud model watermarking algorithm robustness is better.
Wherein, mnAnd mn' it is respectively embedded watermark sequence wnWith the watermark sequence w extractedn' mean value.
1. invisibility is tested
After watermark insertion, model and archetype error after algorithm insertion watermark it can be seen from model contrast schematic diagram
Smaller, visual quality is interference-free.The experimental results showed that the watermarking algorithm is smaller on model-based vision influence, after embedded watermark
Three-dimensional point cloud model is almost the same with archetype, human eye can not differentiate difference between the two, hence it is demonstrated that watermark have compared with
Good invisibility.The invisibility of watermark can be promoted by reducing watermark embedment strength β, but carrying with the transparency
The robustness of high watermark can reduce, it is therefore desirable to be obtained between the transparency and robustness of watermark according to the requirement of practical problem
Balance.
2. robustness is tested
Table 1 be four three-dimensional point cloud models by when various attacks compared with the correlation coefficient value between archetype feelings
Condition.
1) shearing attack
In shearing attack experiment, since watermark is only embedded in watermark at characteristic point, and characteristic point changes in inventive algorithm
Everywhere for discrete incorporation model, shear only the watermark bit that can be lost embedded by shearing part to model, can not break completely
Bad watermark still can extract relatively complete watermark from remaining model, therefore algorithm proposed by the invention is conducive to
Resist shearing attack.By data in table 1 it is found that shearing part is smaller, effect is better.
2) rotation attack
Apex coordinate is likely to occur variation when model is rotated, thus influences the integrality of watermark extracting.And this hair
This defect is supplied by establishing the invariant space in bright：It is established using non-characteristic point (average curvature is less than 0 point) constant
Space is to ensure that characteristic point can determine coordinate position in new coordinate space.Archetype is surrounded into Y-axis and Z respectively in experiment
Axis rotates, and if Figure 14 is schematic diagram when embodiment rabbit three-dimensional point cloud archetype is not affected by attack, Figure 15 is embodiment rabbit
Sub- three-dimensional point cloud model surrounds the schematic diagram that Y-axis is rotated by 90 °, and Figure 16 is that embodiment rabbit three-dimensional point cloud model is rotated around Z axis
45 ° of schematic diagram.The experimental results showed that different rotation angles influences difference to the robustness of watermark.
3) attacked by noise
Inventive algorithm attacks each three-dimensional point cloud model, used noise amplitude using the random noise that variance is σ
Size is respectively 0.001,0.003 and 0.005.The noise amplitude known to data in table 1 is bigger, and correlation coefficient value is smaller, model
More it is distorted.
Finally in order to examine the performance of watermark of the present invention, four threedimensional models are tested.It is attacked by calculating
Bit error rate (BER) between the rear watermark extracted and original watermark weighs the robustness of watermark.It is calculated using the present invention
Emulation is compared with Zhang algorithms and Qi algorithms in method, experimental result data such as the following table 2 after various attacks.
Algorithm proposed by the invention has very strong robustness to shearing attack, rotation attack, attacked by noise, is especially revolving
Turn, shearing attack experimental section effect it is best.Since archetype is counted and shears the difference of part in shearing experiment, made
At experimental result also differ, model more multi-model experimental result of counting is better, and shearing attack result is more below 30%
Good, robustness is stronger.
1 various attack Corr coefficients of table
The BER values of 2 inventive algorithm of table and other two kinds of algorithm comparisons
Claims (9)
1. the point cloud watermarking algorithm based on radial distance and characteristic point, which is characterized in that specifically follow the steps below：
Step 1, the average curvature on each vertex in three-dimensional point cloud model is calculated, and by model inner vertex according to average curvature meter
It calculates result and is divided into two parts：A part of vertex is used for establishing the invariant space, characteristic point of a part of vertex as embedded watermark；
Step 2, all apex coordinates in model are indicated with the cartesian coordinate of the newly-established invariant space, and by its all top
The coordinate transformation of point is spherical coordinate；
Step 3, according to embedded watermark bit position number, will convert the three-dimensional point cloud model of coordinate according to vertex radial distance into
The equidistant annulus division operation of row；By an embedded watermark bit position in each annulus, and according to the spy fallen into annulus
Sign counts to control the number of embedded same watermark bit position；
Step 4, the radial distance of characteristic point is normalized into [0,1] range, is conveniently operated and calculates；
Step 5, the binary watermarking bit contents that are embedded according to this position according to histogram mapping function adjust the diameter of characteristic point
To distance, the watermark insertion of each annulus is completed；
Step 6, it is original radial distance range that will adjust the characteristic point renormalization of radial distance after embedded watermark, and by ball
Areal coordinate is converted into cartesian coordinate；
Step 7, the vertex after embedded watermark is reconstructed to scheme after obtaining complete embedded watermark with the vertex for being not embedded into watermark
Picture.
2. the point cloud watermarking algorithm according to claim 1 based on radial distance and characteristic point, which is characterized in that the step
In rapid 1, it is divided into two parts according to all vertex of average curvature size model：The regions C1 indicate the vertex that average curvature is less than 0, use
In embedded watermark；The regions C2 indicate remaining vertex, for establishing the invariant space.
3. the point cloud watermarking algorithm according to claim 1 based on radial distance and characteristic point, which is characterized in that the step
Coordinate transformation formula is as follows in rapid 2：
Wherein M (xc, yc, zc) indicate coordinate of the model center point in cartesian coordinate system, Ai(xi, yi, zi) indicate i-th of top
The cartesian coordinate of point；riIndicate i-th of vertex in spherical coordinate apart from the radial distance of central point, θiIt is vertex AiTo mould
Angle between the line segment of type central point and positive Z axis,For AiHorizontal plane subpoint to model center point line segment and positive X
The angle of axis.
4. the point cloud watermarking algorithm according to claim 1 based on radial distance and characteristic point, which is characterized in that the step
In rapid 3, it is as follows to calculate invariant space origin formula：
Wherein,For i-th in model non-characteristic point spherical coordinate,For the non-feature point number of model；
Calculating divides ring formula as follows：
for 1≤n≤N；0≤j≤Gn (3)
Wherein GnIt is the number of vertices in n-th of ring, rn,jIt is j-th of vertex in n-th of ball.
5. the point cloud watermarking algorithm according to claim 1 based on radial distance and characteristic point, which is characterized in that the step
In rapid 4, it is as follows that characteristic point normalizes formula：
WhereinFor the radial distance value after j-th of characteristic point normalization in n-th of ballWithFor the radial distance value of minimum and maximum characteristic point in n-th of ball.
6. the point cloud watermarking algorithm according to claim 1 based on radial distance and characteristic point, which is characterized in that the step
In rapid 5, Histogram Mapping formula is as follows：
WhereinFor the radial distance value after adjustment,For the radial distance value after normalization, α is parameter.
7. the point cloud watermarking algorithm according to claim 1 based on radial distance and characteristic point, which is characterized in that the step
In rapid 6, it is respectively following formula (6) and (7) that characteristic point renormalization formula and spherical coordinate, which are converted into cartesian coordinate formula,：
For the radial distance value after j-th of characteristic point renormalization in n-th of ball,
It indicates by the cartesian coordinate on i-th of vertex of spherical coordinate inverse transformation；It indicates i-th
Radial distance after the adjustment of vertex.
8. the point cloud watermarking algorithm according to claim 4 based on radial distance and characteristic point, which is characterized in that the step
In rapid 3, divide ring number for embedded watermark bit position size, i.e., 16.
9. the point cloud watermarking algorithm according to claim 6 based on radial distance and characteristic point, which is characterized in that the step
Radial distance is adjusted using Histogram Mapping formula in rapid 5, characteristic point radial distance becomes larger if parameter alpha reduces, and mean value becomes larger,
It is embedded in watermark bit 1；On the contrary, characteristic point radial distance becomes smaller if α increases, mean value becomes smaller, that is, is embedded in watermark bit 0.
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