CN112634457B - Point cloud simplification method based on local entropy of Hausdorff distance and average projection distance - Google Patents
Point cloud simplification method based on local entropy of Hausdorff distance and average projection distance Download PDFInfo
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Abstract
The invention discloses a point cloud simplification method based on local entropy of a Hausdorff distance and an average projection distance, which comprises the steps of performing down-sampling on original point cloud data, searching to a plurality of near-neighbor points, and calculating the average projection distance corresponding to each point cloud; dividing the original point cloud data into an edge point cloud set and a point cloud set to be simplified, and calculating a corresponding first Housdov distance average value and an information entropy value of the average projection; utilizing an octree to subdivide the point cloud set to be condensed, and calculating a corresponding second Housdov distance average value; comparing the ratio of the first Hausdorff distance average value to the second Hausdorff distance average value with a plurality of set judgment threshold values, and simplifying the point cloud set to be simplified according to the comparison result and the information entropy value; and merging and splicing the edge point cloud set and the simplified point cloud to obtain a corresponding three-dimensional model, and improving the effect of simplifying the point cloud data of the three-dimensional model.
Description
Technical Field
The invention relates to the technical field of computer data processing, in particular to a point cloud simplification method based on local entropy of a Hausdorff distance and an average projection distance.
Background
With the development of science and technology, laser scanning equipment is continuously updated and updated to be new, and the three-dimensional real object can store geometric information into storage equipment through the laser scanning equipment. With the continuous improvement of the precision of the three-dimensional laser scanner, the data volume of the point cloud model obtained by single scanning is multiplied, and meanwhile, the problem is brought about by a large amount of redundant data in dense point cloud data. The redundant data greatly increases the cost of task processing such as storage, transmission and calculation of the three-dimensional model point cloud data, and brings great challenges to the subsequent related work such as surface fitting and model reconstruction. Therefore, it is necessary to improve the effect of simplifying the point cloud data of the three-dimensional model.
Disclosure of Invention
The invention aims to provide a point cloud simplification method based on local entropy of a Hausdorff distance and an average projection distance, and the simplification effect of point cloud data of a three-dimensional model is improved.
In order to achieve the aim, the invention provides a point cloud simplification method based on local entropy of a Hausdorff distance and an average projection distance, which comprises the following steps:
performing down-sampling processing on the acquired original point cloud data, searching a plurality of adjacent points, and calculating the average projection distance corresponding to each point cloud by using a principal component analysis method;
dividing the original point cloud data into an edge point cloud set and a point cloud set to be reduced, and calculating a first Hausdorff distance average value corresponding to the point cloud set to be reduced and an information entropy value of the average projection;
based on a subdivision criterion, utilizing an octree to subdivide the point cloud set to be simplified, and calculating a second Hausdorff distance average value corresponding to each subcube;
comparing the ratio of the first Hausdorff distance average value to the second Hausdorff distance average value with a plurality of set judgment threshold values, and simplifying the point cloud set to be simplified according to the comparison result and the information entropy value;
and merging and splicing the edge point cloud set and the simplified point cloud to obtain a corresponding three-dimensional model.
Dividing the original point cloud data into an edge point cloud set and a point cloud set to be reduced, and calculating a first Hausdorff distance average value corresponding to the point cloud set to be reduced and an information entropy value of the average projection, wherein the method comprises the following steps:
constructing a least square plane according to the plurality of neighbor points, projecting the neighbor points onto the minimum quadratic plane, and comparing the obtained ratio corresponding to the plurality of projection points with a set first threshold value to obtain a first edge point;
dividing the point cloud density histogram by using a set second threshold value, and performing down-sampling processing on the extracted point cloud data to obtain a second edge point;
dividing the first edge point and the second edge point into edge point cloud sets, and dividing the point cloud of the original point cloud data except the edge point cloud set into point cloud sets to be condensed;
and calculating a first Housdov distance average value corresponding to the point cloud set to be reduced and an information entropy value of the average projection.
Calculating a first Housdov distance average value corresponding to the point cloud set to be reduced and an information entropy value of the average projection, wherein the calculating comprises the following steps:
calculating a third Housdov distance corresponding to each point cloud in the point cloud set to be reduced, arranging the third Housdov distances in a descending order, taking the first third Housdov distance as a first Housdov distance, and calculating a corresponding first Housdov distance average value according to the first Housdov distance;
and calculating the information entropy value of the average projection distance based on an information entropy formula, and arranging the information entropy values according to a descending order.
The method comprises the following steps of subdividing the point cloud set to be simplified by using an octree based on subdivision criteria, and calculating a second Hausdorff distance average value corresponding to each subcube, and comprises the following steps:
based on a subdivision criterion, utilizing an octree method to subdivide the constructed cube until the number of point clouds in the obtained sub-cube is less than a subdivision threshold;
and calculating a second Housdov distance average value corresponding to each subcube.
Wherein, calculating the second Housdov distance average corresponding to each subcube comprises:
and calculating fourth Hausdorff distances corresponding to all point clouds in each subcube, arranging the fourth Hausdorff distances according to a descending order, taking the first fourth Hausdorff distance as a second Hausdorff distance, and calculating a corresponding second Hausdorff distance average value.
Comparing the ratio of the first Hausdorff distance average value to the second Hausdorff distance average value with a plurality of set judgment thresholds, and simplifying the point cloud set to be simplified according to the comparison result and the information entropy value, wherein the method comprises the following steps:
calculating a ratio of the first Hausdorff distance average value to the second Hausdorff distance average value, and comparing the ratio with a plurality of set judgment threshold values to obtain a point cloud simplification factor;
if the ratio is larger than the set multiple judgment thresholds, calculating the quantity of point clouds needing to be simplified in the subcubes according to the point cloud simplification factors, and simplifying according to the information entropy;
and if the ratio is smaller than all the judgment thresholds, replacing the point cloud set to be condensed in the cube by using a set number of point clouds.
If the ratio is greater than the set multiple judgment thresholds, the method of simplifying according to the size of the information entropy value includes:
if the ratio is larger than any judgment threshold, calculating the number of point clouds to be simplified in the subcube according to the point cloud simplification factors, and simplifying the point cloud set to be simplified according to the corresponding information entropy;
and if the ratio is greater than at least one judgment threshold value in the plurality of judgment threshold values, performing descending arrangement on the corresponding information entropy values, and simplifying the point cloud set to be simplified according to the arrangement order.
The invention discloses a point cloud simplification method based on local entropy of Hausdorff distance and average projection distance, which comprises the steps of carrying out down-sampling processing on obtained original point cloud data, searching a plurality of near-neighbor points, and calculating the average projection distance corresponding to each point cloud and the information entropy value of the average projection by using a principal component analysis method; dividing the original point cloud data into an edge point cloud set and a point cloud set to be simplified, and calculating a corresponding first Housdov distance average value; subdividing the point cloud set to be simplified by using an octree based on a subdivision criterion, and calculating a second Hausdorff distance average value corresponding to each subcube; comparing the ratio of the first Hausdorff distance average value to the second Hausdorff distance average value with a plurality of set judgment threshold values, and simplifying the point cloud set to be simplified according to a comparison result and the information entropy value; and merging and splicing the edge point cloud set and the simplified point cloud to obtain a corresponding three-dimensional model, thereby improving the effect of simplifying the point cloud data of the three-dimensional model.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without any creative effort.
FIG. 1 is a schematic diagram of a point cloud refinement method based on local entropy of Hausdorff distance and average projection distance according to the present invention.
FIG. 2 is a schematic flow chart diagram of a point cloud refining method based on local entropy of Hausdorff distance and average projection distance.
FIG. 3 is a schematic diagram of the present invention for calculating the projection distance.
Fig. 4 is a schematic diagram of the principle of proxel detection provided by the present invention.
Fig. 5 is a schematic diagram of the effect of performing the extraction and retention of the edge contour points of the oral cavity model provided by the invention.
Fig. 6 is a schematic diagram of the oral cavity model reduction result provided by the present invention.
FIG. 7 is a schematic diagram of the rabbit and dragon edge contour point extraction and retention effect provided by the present invention.
FIG. 8 is a diagram illustrating the point cloud reduction effect on a rabbit model according to the present invention.
FIG. 9 is a diagram illustrating the effect of point cloud reduction on the dragon model provided by the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are illustrative and are intended to be illustrative of the invention and should not be construed as limiting the invention.
In the description of the present invention, "a plurality" means two or more unless specifically defined otherwise.
Referring to fig. 1, the present invention provides a method for point cloud reduction based on local entropy of hausdorff distance and average projection distance, comprising the following steps:
s101, performing down-sampling processing on the acquired original point cloud data, searching a plurality of adjacent points, and calculating the average projection distance corresponding to each point cloud by using a principal component analysis method.
Specifically, the method comprises the steps of obtaining original point cloud data of a three-dimensional model, achieving initial simplification of the point cloud of the three-dimensional model through point cloud downsampling sample processing, establishing a k-d tree to search k neighbor points of each data point, calculating a normal vector of each point cloud by using a Principal Component Analysis (PCA), and calculating an average projection distance value of the normal vector.
The average projection distance can better reflect the concave-convex condition of the curved surface, and the local distribution density can better reflect the density condition of the point cloud in the space area. Let the sample point be p and its k neighbors be pi(i＝1,2,…,k)，NpIs a set of neighbor points for sample point p,
is NpThe center of gravity of the vehicle. The invention passes through the formula(1) Obtaining a fitting plane F, and calculating a covariance matrix C through a formula (2) to obtain a characteristic value lambdaj(j is 0,1,2), the minimum eigenvalue λ0Corresponding feature vector v0Is an estimated normal vector for the sample point. Average projected distance wpLocal distribution density ρpThe calculation formulas of the equal characteristic weighing factors are respectively shown in (3) to (4):
wherein, the sample point is p, and k neighboring points p thereofi(i＝1,2,…,k)，NpIs a set of neighboring points of the sample point p,
is NpThe distribution center of gravity of (1) (calculation method: three point cloud coordinates are (x1, y1, z1), (x2, y2, z2), (x3, y3, z3), then the distribution center of gravity of the point cloud set is
d is the spatial distance of the fitted plane to the origin of coordinates.
C is a semi-positive definite covariance matrix, and different eigenvalues can be obtained by solving the semi-positive definite covariance matrix C through a calculation formula (2): lambda1～λ3Wherein the minimum eigenvalue is set to λ1The maximum eigenvalue is set to λ3. T is the inversion operation of the matrix.
The symbols of formula (3) are specifically interpreted:
ni is the normal vector (i.e., the vector with the direction) of the ith neighbor of the sample point p, and is vector 1;
(p-pi) subtracting the three-dimensional coordinates of the sample point p and the two points of the neighboring point pi (x1-x2, y1-y2, y1-y2), and determining a vector as vector 2;
|ni(p-pi) L: multiplication of two vectors (vector 1: ni, vector 2 (p-pi)) can obtain the sample point p to any adjacent point pi(i ═ 1,2, …, k) fitting the projection distance of the least squares plane (the projection distance is the vertical distance, and the calculation formula is:
then, the projection distance from the sample point to the fitting plane where each neighboring point is located is calculated, and finally, the average is calculated.
The calculation formula is as follows: (molecular: all projection distances are added
) /(denominator: k neighbors).
Equation (4) explains:
a minimum bounding sphere is constructed that encloses the k neighbors. Wherein k is the number of the adjacent points, r is the radius of the surrounding sphere, and pi is the circumferential rate. Therefore, a density formula is calculated as equation (4), density ρpEqual to the number of neighbors k (numerator)/volume surrounding the sphere (denominator).
S102, dividing the original point cloud data into an edge point cloud set and a point cloud set to be reduced, and calculating a corresponding first Housdov distance average value and an information entropy value of the average projection.
Specifically, a least square plane is constructed according to the plurality of adjacent points, the adjacent points are projected onto the least square plane to obtain a plurality of corresponding projection points, and the ratio of the difference between the number of the projection points on the two sides of the least square plane and the number of the plurality of adjacent points is compared with a set first threshold value, so that whether the sample point is an edge point is judged. And if the ratio is larger than the first threshold value, obtaining a first edge point.
And based on the local distribution density condition of the point cloud, dividing the point cloud density histogram by using a set second threshold value, and performing down-sampling processing on the extracted point cloud data to obtain a second edge point, wherein the second edge point cloud is a tooth gap point cloud when used in the oral cavity model. The second edge point cloud extraction and corresponding downsampling processing steps are only specific to the specific model: in an oral cavity model.
And dividing the first edge point and the second edge point into edge point cloud sets, and dividing the point cloud of the original point cloud data except the edge point cloud set into point cloud sets to be condensed.
And determining the similarity between the point sets by using the Hausdorff (Hausdorff) distance of the main curvature of the point cloud, thereby determining the characteristic degree of the data points in the local area where the point cloud is located. And calculating a third Hausdorff distance corresponding to all point clouds in the point cloud set to be simplified, wherein the Hausdorff distance is calculated as follows:
let the principal curvature of the sample point p be ki, kj, and the principal curvature of any point near the sample point p be ki ', kj', then the hausdorff distance value obtained by calculation be H1, which is the hausdorff distance calculation process performed once.
After the third hausdorff distances are arranged in a descending order, the first third hausdorff distance is taken as the first hausdorff distance, that is, the maximum value of the third hausdorff distance is taken as the first hausdorff distance of the sample point, and the following calculation is performed:
Hp＝max(H1,H2,H3,...,Hk) (6)
since the sample point p has k neighboring points, the above hausdorff distance calculation process is repeated once for each neighboring point, that is, the symbolic representations of the numerical values of the hausdorff distance calculated by equation (5) are H2, H3. Then, the maximum value is taken as the value of the sample point p hausdorff distance, and the symbol is denoted by Hp.
S103, subdividing the point cloud set to be simplified by using an octree based on a subdivision criterion, and calculating a second Hausdorff distance average value corresponding to each subcube.
Specifically, based on a subdivision criterion, the constructed cube is subdivided by using an octree method until the number of point clouds in the obtained subcubes is less than a subdivision threshold, and the method specifically comprises the following steps: in order to obtain each small cube, a minimum cube V is first generated which can contain the remaining point cloud of the three-dimensional modelmThe side length of the cube is L. Setting the maximum value of the three-dimensional model point cloud in the X.Y.Z three axes as xmax，xmin，ymax，ymin，zmax，zminThen the side length L is calculated as follows:
L＝Max((Xmax-Xmin),(Ymax-Ymin),(Zmax-Zmin)) (7)
and carrying out space segmentation by using the octree, and incorporating the point cloud into different sub-cube spaces according to the spatial position coordinates of the point cloud. Setting the condition that the octree ends the subdivision to be that the point cloud number of the sub-cube is smaller than the subdivision threshold value u, and therefore when no point cloud exists in the sub-cube or the point cloud number is larger than the subdivision threshold value u, continuing to perform octree subdivision; otherwise, stopping the octree subdivision.
Calculating fourth hausdorff distances corresponding to all point clouds in each subcube, arranging the fourth hausdorff distances in a descending order, taking the first fourth hausdorff distance as a second hausdorff distance, and calculating a corresponding second hausdorff distance average value, wherein the fourth hausdorff distance may be the third hausdorff distance in step S102, and a calculation formula of the fourth hausdorff distance is as follows:
let the principal curvature of the sample point p be ki, kj, and the principal curvature of any point near the sample point p be ki ', kj', then the hausdorff distance value obtained by calculation be H1, which is the hausdorff distance calculation process performed once.
The second hausdorff distance is calculated as:
Hp＝max(H1,H2,H3,...,Hk) (9)
since the sample point p has k neighboring points, the above hausdorff distance calculation process is repeated once for each neighboring point, that is, the symbolic representations of the numerical values of the hausdorff distance calculated by equation (5) are H2, H3. Then, the maximum value is taken as the value of the sample point p hausdorff distance, and the symbol is denoted by Hp.
Combining the average projection distance with the information entropy theory, the information entropy value of a certain data point can be expressed as the degree of membership to a certain class of features. The entropy of information is expressed quantitatively as follows:
wherein K is a constant with a fixed positive value,
pi is the corresponding probability of occurrence of the event Xi,
and is
(i.e., the sum of all the probabilities of occurrence equals 1.)
If the data point p is a sample point, the information entropy value corresponding to the average projection distance at the point is calculated as follows:
wherein w and wiMean projection distances of point P and neighboring points i, PwAnd
is the probability of the point P and the neighboring point i corresponding to the average projection distance, w and wiRespectively, the average projection distances of the sample point P and its i-th neighboring point, and PwAnd
respectively, the probability values (weight product) of the average projection distances corresponding to the sample point P and the ith neighbor point.
To a certain extent, the entropy value of the average projection distance information can reflect the situation of the geometric characteristics of the surface of the three-dimensional model. The larger the entropy value is, the closer the area of the point cloud is to the plane characteristic; otherwise, it means that the area where the point cloud is located is closer to the curved surface feature, and if the point cloud is reduced, the geometric feature information of the model surface area will be lost. Therefore, after the average projection distance local entropy of the point clouds is calculated and sorted according to the size of the entropy values, the point clouds with larger entropy values are preferentially simplified, and the point clouds with smaller local entropy values are reserved as the feature points.
S104, comparing the ratio of the first Hausdorff distance average value to the second Hausdorff distance average value with a plurality of set judgment threshold values, and simplifying the point cloud set to be simplified according to the comparison result and the information entropy value.
Specifically, the cubes may be considered to have different degrees of features because the cubes include different numbers of feature point clouds. The invention sets a multilevel point cloud simplification criterion, and the content comprises a plurality of judgment threshold values lambdaj(j ═ 1,2,3) and the corresponding point cloud simplification factors.
Calculating a ratio λ of the first Hausdorff distance average to the second Hausdorff distance average within each of the sub-cubes, and applying the ratio λ to the sub-cubesMultiple judgment threshold values lambda set by ratiojAnd (j ═ 1,2,3,. times.n) to evaluate the degree of the cube feature. And determining the degree of point cloud simplification in the cube according to the point cloud simplification factors corresponding to the multilevel simplification criteria. When the ratio lambda is larger than a certain judgment threshold lambdajAnd (3) in the process, jumping to the step 1, simplifying the corresponding number of model point clouds with larger entropy values in the cube according to the idea of simplifying the model point clouds with larger entropy values, and otherwise, jumping to the step 2.
Step 1, if the ratio lambda is larger than any one judgment threshold lambdajDetermining the characteristic degree of the cube, determining corresponding point cloud simplification factors corresponding to the multilevel simplification criteria, and simplifying the corresponding number of non-characteristic points in the cube according to the corresponding information entropy. If the ratio lambda is larger than at least one judgment threshold lambda in the plurality of judgment thresholdsj(j ═ 1,2, 3.. n), where at least one judgment threshold means that one judgment threshold is not included, the characteristic degree of the cube can be determined, the corresponding point cloud simplification factor can be determined corresponding to the multi-level simplification criterion, then the corresponding information entropy values are arranged in a descending order, and the point cloud set to be simplified is simplified according to the arrangement order, that is, the point cloud with larger entropy value is preferentially simplified.
Step 2, if the ratio lambda is less than all the judgment threshold values lambdajAnd if the ratio is less than all judgment thresholds (namely the ratio is less than the minimum judgment threshold certainly), calculating the spatial distance value from each point cloud in the cube to the distribution gravity centers of all point clouds (point cloud sets) in the cube, only storing a few point clouds closest to the distribution gravity centers of the point cloud sets according to the principle that the smaller the spatial distance value is, the better the spatial distance value is, and replacing the to-be-reduced point cloud set in the cube. Wherein the set numberThe measured point clouds are a set smaller number of point clouds for reasons: when the ratio lambda is less than all the judgment threshold lambdajIn this case, it is indicated that the cube has a large number of non-characteristic point clouds, and thus the large number of non-characteristic point clouds needs to be simplified, and the number of retained point clouds is small.
Setting the total number of point clouds of all non-characteristic cubes to num0The total number of the point clouds of all the non-characteristic cubes after simplification is num1Then, the point cloud simplification factor α is calculated as follows:
taking any sub-cube of the octree as an example, if the cube is a non-characteristic cube and the number of point clouds contained in the cube is n, the number of point clouds in the cube is niThe calculation is as follows:
wherein,
the representation value is upward; alpha is a simplification factor.
Example (c): when lambda is larger than lambda1The simplification factor is a; when lambda is larger than lambda2When, the simplification factor is b; when lambda is larger than lambda3When, the simplification factor is c; when lambda is less than lambda3Then, a smaller number of point clouds (λ) closest to the center of gravity of the point cloud distribution is selected1＞λ2＞λ3,0＜a,b,c＜1)。
The method for calculating the position coordinates of the point cloud distribution center of gravity of the point cloud set comprises the following steps: assuming three point cloud coordinates of (x1, y1, z1), (x2, y2, z2), (x3, y3, z3), the spatial coordinates of the centroid of the point cloud distribution are:
s105, merging and splicing the edge point cloud set and the simplified point cloud to obtain a corresponding three-dimensional model.
Specifically, the simplified point cloud and the edge point cloud set are merged, spliced and output, and then the point cloud of the three-dimensional model after final simplification is obtained.
The above procedure and results are described below by experiments.
Table 1 shows the simplification rates and the running times of different algorithms, and fig. 6 shows the corresponding oral cavity model simplification results, where in fig. 6, (a) is the point cloud after non-uniform downsampling, (b) is the algorithm of the present invention, (c) is the simplification method based on the octree, (d) is the simplification method based on the Hausdorff distance, and (e) is the simplification method based on the weight product local entropy. Fig. 7 shows the corresponding mouth model reconstruction result, wherein (a) in fig. 7 is the point cloud after non-uniform sample reduction, (b) is the algorithm of the present invention, (c) is the simplification method based on octree, (d) is the simplification method based on Hausdorff distance, and (e) is the simplification method based on the weight product local entropy.
TABLE 1 reduction ratio and runtime of different algorithms
As can be seen from table 1 and fig. 6: under the condition of similar point cloud simplification, compared with fig. 6(c) and 6(d), fig. 6(b) shows that the algorithm of the invention reserves fewer point clouds (second edge point clouds) in the tooth clearance, reserves more points in the characteristic areas such as tooth contour and tooth structure, and reasonably simplifies the point cloud in the flat area. The algorithm of the invention in fig. 6(b) is more reasonable for feature point extraction and non-feature point simplification.
Under the condition of close point cloud simplification, the algorithm can accurately extract regional points such as tooth outlines, tooth structures and the like, and well reserve the detailed characteristics of the oral cavity model. Meanwhile, the non-uniform descending sampling sample of the tooth gap point cloud and the reasonable simplification of the flat area point cloud can effectively avoid the occurrence of holes.
However, other comparison algorithms are not well suitable for the oral cavity model to a certain extent, and the main reason is that the algorithm does not consider the point cloud characteristics of the experimental object, so that the step design is unreasonable or there is error. For example, in the simplification method based on the weight product local entropy shown in fig. 6(e), the geometric feature attribute of the point cloud in the model region cannot be well reflected by the weight product local entropy, and the extracted feature point cloud is determined and retained by comparing the weight product local entropy of a single point cloud with the average value of the local entropies of the point clouds in the cluster, which easily causes excessive simplification of the point cloud in the strong feature region. For a three-dimensional model with a large number of complex features, the surface geometric features of the model are easily lost seriously. The algorithm of the invention reasonably sets a multi-level simplification criterion according to the point cloud characteristic analysis of the oral cavity model, and evaluates the characteristic degree of the cube to determine the simplification factor of the corresponding point cloud, thereby realizing reasonable simplification of non-characteristic point clouds and effective extraction of characteristic points. On the basis of point cloud characteristic analysis of the oral cavity model, algorithm step design of the algorithm is completed, so that the algorithm can be well suitable for the oral cavity model with a complex curved surface, huge point cloud data volume and uneven sampling, and has good performance on point cloud simplification results and reconstruction results.
The algorithm can better reserve characteristic area point clouds such as tooth outlines, tooth structures and the like in the oral cavity model, reasonably simplifies the flat area point clouds, and carries out non-uniform downsampling sample processing on the tooth gap point clouds. The detailed features of the oral cavity model have good retention, no holes are generated in the flat area and only a few holes with small area exist in the gaps between the teeth. The point cloud simplified by the algorithm of the invention still has a better reconstruction result in the subsequent three-dimensional reconstruction task.
In conclusion, the algorithm of the invention provides a point cloud reduction algorithm based on the local entropy of the Hausdorff distance and the average projection distance. Experiments prove that under the condition of certain simplification degree, the algorithm can better keep the detail characteristics of the oral cavity model, and the point cloud simplification result and the reconstruction result of the oral cavity model are superior to those of other comparison algorithms. Therefore, the algorithm has certain effectiveness and superiority.
In order to verify the effectiveness of the algorithm, other key steps except the second edge point cloud extraction and sample reduction processing are applied to the rabbit model and the dragon model, and a simplification experiment is carried out to obtain the following point cloud simplification condition result table and a point cloud processing effect graph respectively.
Table 2 is a point cloud simplified condition result table of the algorithm, fig. 7 is an edge contour point extraction effect diagram of the rabbit model and the dragon model, and fig. 8 and 9 are simplified results of the rabbit model and the dragon model, respectively. Fig. 8(a) is an original point cloud of the rabbit model, and fig. 8(b) to (d) are point cloud simplification results of the rabbit model at different simplification rates respectively; fig. 9(a) and 9(b) are the original point cloud of the dragon model and the point cloud after sample reduction, respectively, and fig. 9(c) to (e) are the point cloud simplification results at different simplification rates, respectively. The simplification rate is the ratio of the number of simplified point clouds to the number of point clouds after the sampling is reduced.
Table 2 algorithm point cloud simplification here
As can be seen from table 2 and fig. 8: the algorithm can reserve more points in detail characteristic parts of the rabbit model, such as ears, necks and the like, and reserve fewer points in flat areas of the rabbit legs, backs and the like.
As can be seen from table 2 and fig. 9: the algorithm can reserve more points in the detailed characteristic parts of the dragon model, such as the antennal, the tail, the feet, the body boundary and the like of the dragon, and reserve less points in a relatively smooth area such as the body of the dragon.
Through the above experiments, we can find that: under the condition of higher simplification rate, the algorithm can better keep a plurality of detailed characteristics of the three-dimensional model, can effectively simplify the point cloud of a flat area of the model, does not generate a hole phenomenon, and has certain advantages in precision.
In practical application, the algorithm can flexibly adjust a plurality of thresholds and point cloud simplification factors of a multilevel point cloud simplification criterion according to practical simplification and precision requirements, so that the algorithm can be better applied to different types of three-dimensional models.
The invention discloses a point cloud simplification method based on local entropy of a Hausdorff distance and an average projection distance, which comprises the steps of carrying out down-sampling processing on acquired original point cloud data, searching a plurality of near-neighbor points, and calculating the average projection distance corresponding to each point cloud by using a principal component analysis method; dividing the original point cloud data into an edge point cloud set and a point cloud set to be simplified, and calculating a corresponding first Housdov distance average value; subdividing the point cloud set to be simplified by using an octree based on a subdivision criterion, and calculating a second Hausdorff distance average value corresponding to each subcube and an information entropy value of the average projection; comparing the ratio of the first Hausdorff distance average value to the second Hausdorff distance average value with a plurality of set judgment threshold values, and simplifying the point cloud set to be simplified according to a comparison result and the information entropy value; and merging and splicing the edge point cloud set and the simplified point cloud to obtain a corresponding three-dimensional model, thereby improving the effect of simplifying the point cloud data of the three-dimensional model.
While the invention has been described with reference to a preferred embodiment, it will be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the invention.
Claims (3)
1. A point cloud simplification method based on a Housdov distance and an average projection distance local entropy is characterized by comprising the following steps:
performing down-sampling processing on the acquired original point cloud data, searching a plurality of adjacent points, and calculating the average projection distance corresponding to each point cloud by using a principal component analysis method;
dividing the original point cloud data into an edge point cloud set and a point cloud set to be reduced, and calculating a first Hausdorff distance average value corresponding to the point cloud set to be reduced and an information entropy value of the average projection;
subdividing the point cloud set to be simplified by using an octree based on a subdivision criterion, and calculating a second Hausdorff distance average value corresponding to each subcube;
comparing the ratio of the first Hausdorff distance average value to the second Hausdorff distance average value with a plurality of set judgment threshold values, and simplifying the point cloud set to be simplified according to the comparison result and the information entropy value;
merging and splicing the edge point cloud set and the simplified point cloud to obtain a corresponding three-dimensional model;
dividing the original point cloud data into an edge point cloud set and a point cloud set to be reduced, and calculating a first Hausdorff distance average value corresponding to the point cloud set to be reduced and an information entropy value of the average projection, wherein the method comprises the following steps:
constructing a least square plane according to the plurality of adjacent points, projecting the adjacent points onto the least square plane, and comparing the obtained ratio corresponding to the plurality of projection points with a set first threshold value to obtain a first edge point;
dividing the point cloud density histogram by using a set second threshold value, and performing down-sampling processing on the extracted point cloud data to obtain a second edge point;
dividing the first edge point and the second edge point into edge point cloud sets, and dividing the point cloud of the original point cloud data except the edge point cloud set into point cloud sets to be condensed;
calculating a first Housdov distance average value corresponding to the point cloud set to be reduced and an information entropy value of the average projection;
calculating a first Housdov distance average value corresponding to the point cloud set to be reduced and an information entropy value of the average projection, wherein the calculation comprises the following steps:
calculating a third Housdov distance corresponding to each point cloud in the point cloud set to be reduced, arranging the third Housdov distances in a descending order, taking the first third Housdov distance as a first Housdov distance, and calculating a corresponding first Housdov distance average value according to the first Housdov distance;
calculating the information entropy value of the average projection distance based on an information entropy formula, and arranging the information entropy values in a descending order;
comparing the ratio of the first Hausdorff distance average value to the second Hausdorff distance average value with a plurality of set judgment thresholds, and simplifying the point cloud set to be simplified according to the comparison result and the information entropy, wherein the method comprises the following steps:
calculating the ratio of the first Hausdorff distance average value to the second Hausdorff distance average value, and comparing the ratio with a plurality of set judgment threshold values to obtain a point cloud simplification factor;
if the ratio is larger than the set judgment thresholds, calculating the number of point clouds needing to be simplified in the subcubes according to the point cloud simplification factors, and simplifying the point clouds according to the information entropy;
if the ratio is smaller than all the judgment thresholds, replacing the point cloud set to be condensed in the cube by using a set number of point clouds;
if the ratio is greater than the set multiple judgment thresholds, the simplification is performed according to the size of the information entropy, and the method comprises the following steps:
if the ratio is larger than any judgment threshold, calculating the number of point clouds to be simplified in the subcube according to the point cloud simplification factors, and simplifying the point cloud set to be simplified according to the corresponding information entropy;
and if the ratio is greater than at least one judgment threshold value in the plurality of judgment threshold values, performing descending arrangement on the corresponding information entropy values, and simplifying the point cloud set to be simplified according to the arrangement order.
2. The point cloud reduction method based on the hounsfield distance and the average projection distance local entropy of claim 1, wherein subdividing the point cloud set to be reduced by using an octree based on a subdivision criterion and calculating a second hounsfield distance average value corresponding to each subcube comprises:
based on a subdivision criterion, utilizing an octree method to subdivide the constructed cube until the number of point clouds in the obtained subcubes is smaller than a subdivision threshold value;
and calculating a second Housdov distance average value corresponding to each subcube.
3. The point cloud reduction method based on the local entropy of the hausdorff distance and the average projection distance as claimed in claim 2, wherein calculating the second hausdorff distance average value corresponding to each of the subcubes comprises:
and calculating fourth Hausdorff distances corresponding to all point clouds in each subcube, arranging the fourth Hausdorff distances according to a descending order, taking the first fourth Hausdorff distance as a second Hausdorff distance, and calculating a corresponding second Hausdorff distance average value.
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