CN116310244A - Ceramic fragment three-dimensional intelligent splicing method based on contour features - Google Patents

Ceramic fragment three-dimensional intelligent splicing method based on contour features Download PDF

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CN116310244A
CN116310244A CN202211100410.4A CN202211100410A CN116310244A CN 116310244 A CN116310244 A CN 116310244A CN 202211100410 A CN202211100410 A CN 202211100410A CN 116310244 A CN116310244 A CN 116310244A
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contour
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赵书良
孙婧涵
杨依涵
穆翔宇
丁雪怡
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Hebei Normal University
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Abstract

The invention discloses an intelligent splicing method for cultural relic fragments based on contour line features, which comprises the steps of obtaining three-dimensional point cloud data, carrying out noise reduction treatment, extracting contour points of non-abnormal point cloud data, calculating mathematical geometric features of a contour point set, rough contour line comparison, fine contour line similarity matching and virtual fragment splicing. According to the method, a path with the smallest difference accumulation is selected through a dynamic optimization method to carry out rough matching on the contour lines, so that the similar contour lines are prevented from being removed during rough matching; and the longest common subsequence length is used as a discrimination standard to perform further similarity comparison on fragment outlines, so that the matching accuracy is improved. The limitation of Euclidean distance is broken through in the process of calculating the characteristic point difference of the contour lines, the characteristic points of the contour lines subjected to comparison are not equal in length, and the contour line characteristic point difference calculation method has wide applicability to application objects.

Description

Ceramic fragment three-dimensional intelligent splicing method based on contour features
Technical Field
The invention designs a three-dimensional intelligent splicing method for cultural relic fragments, in particular relates to a three-dimensional intelligent splicing method for cultural relic fragments based on contour features, and belongs to the technical field of computer vision.
Background
After the fragments are collected on the archaeological site, technicians need to clean, classify and compare the fragments according to own experience so as to restore the original shape of the ancient ceramic, and extremely high technical and experience requirements are provided for manual restoration work. There are a number of problems with the manual methods of splicing and restoration of ancient ceramic chips, such as: due to the material characteristics, hidden danger of re-damage of the cultural relic fragments and the like can exist in the manual processing process. The artificial splicing work of the ceramic fragments is irreversible and can not be recovered, and can only be formed in one step, so that the artificial participation in the treatment of the ceramic fragments of the archaeological relics is reduced as much as possible. At present, computer-aided cultural relic intelligent restoration systems are gradually developed. Approximating the edge curve of the cultural relic fragment based on the B-spline curve, extracting data points from the contour line of the fragment object, parameterizing the arc length, calculating the characteristic of the aggregate curvature and the flexibility rate, sequencing the characteristic set, and finally realizing the object contour curve represented by the B-spline. The point cloud integration network method based on edge perception is based on combining point clouds of the edges of the cultural relics, and the detected sharp edges are processed in the combining process, so that three-dimensional reconstruction is realized more accurately.
Zhang et al disclose a method for digitally protecting and three-dimensionally virtually repairing cultural relic fragments in the paper of university of northwest industry in 2019, cultural relic fragment hole repair and splicing method research based on fracture surfaces. Wang Kegang et al in the paper of the university of northwest industry in 2009, ancient ceramic chip classification research based on digital image features, disclose a ceramic cultural relic chip classification method based on learning optimization and information fusion, and based on the texture features, the ceramic cultural relic chip classification is realized by fusing color emotion features, so that a system construction algorithm of ceramic cultural relic classification is realized. Dimitrios Skarlatos et al, journal Visual Computing for Cultural Heritage, publication Image-Based rendering 3D Reconstruction for Cultural Heritage, disclose a method for three-dimensional modeling of heritage Underwater cultural relics, using color restoration enhancement algorithm, and motion extraction structure (Structure From Motion, SFM) principles and multi-view stereo techniques (MVS) to generate an accurate and complete three-dimensional model. The three-dimensional intelligent splicing method has the limitation of depending on two-dimensional space data to a certain extent in the implementation process, meanwhile, the fracture surface is used for splicing, local features of the whole outline of the fragment and different parts of the outline are ignored, and the fact that how elements contained in the sequence to be compared generated by the fragment are compared when the number of the elements is inconsistent is not considered.
Disclosure of Invention
The invention aims to solve the technical problem of providing an intelligent splicing method for cultural relic fragments based on contour line characteristics.
The scheme adopted by the invention is as follows:
an intelligent splicing method for cultural relic fragments based on contour line features comprises the following steps:
step 1: acquiring three-dimensional point cloud data: collecting more than 1 piece of cultural relic fragments, and carrying out three-dimensional scanning on each collected cultural relic fragment to obtain corresponding cultural relic fragments
Figure BDA0003837932200000021
Figure BDA0003837932200000022
Wherein M is the total number of fragments, +.>
Figure BDA0003837932200000023
PC for cultural relic fragments m Points in the point cloud data;
step 2: the cultural relic fragments are processed one by using a statistical filtering method
Figure BDA0003837932200000024
Figure BDA0003837932200000025
The point cloud data of (2) is subjected to noise reduction treatment, and the noise reduction treatment method comprises the following specific steps of:
step 2-1: PC for fragments of cultural relics one by one m Current point p in point cloud data of (a) is With other points p js The distances of (2) are ordered from small to large,
Figure BDA0003837932200000031
and is not equal to js, taking the points p corresponding to the first k distances js Put into the current point p is K neighborhood set { PkNN } is In };
step 2-2: calculating the current point p one by one is K neighborhood point set { PkNN is Midpoint p is Neighbor distance average of (2)
Figure BDA0003837932200000032
Figure BDA0003837932200000033
Figure BDA0003837932200000034
wherein ,
Figure BDA0003837932200000035
(x is ，y is ，z is ) For the current point p is Is a three-dimensional coordinate of (2);
step 2-3: calculate cultural relic fragment PC m Neighbor distance average value of all points in point cloud data of (a)
Figure BDA0003837932200000036
Mean. Mu.of (A) m And standard deviation sigma m ：
Figure BDA0003837932200000037
Figure BDA0003837932200000038
Step 2-4: judging the current point p is Neighbor distance average of (2)
Figure BDA0003837932200000039
Whether or not in the threshold range (mu) m -Qσ m ，μ m +Qσ m ) In which Q is a preset weight value, if not in the range, the current point p is Regarded as outliers, the current point p is From cultural relic fragment PC m Removing the point cloud data of the cultural relic fragments to obtain the cultural relic fragments PC m Is a non-abnormal point cloud data of +.>
Figure BDA00038379322000000310
Step 3: extracting each cultural relic fragment PC one by one m M=1,.. contour points of non-outlier cloud data of M, the method comprises the following specific steps:
step 3-1: fitting a plane: PC for cultural relic fragments m Current target point p in non-outlier point cloud data of (2) tar With other points p oth The distances of (2) are ordered from small to large,
Figure BDA00038379322000000311
oth is not equal to tar, and the first k' points p corresponding to the distances are taken js Put into the current target point p tar K ' neighborhood point set { Pk ' NN ' tar In { Pk 'NN' using the k 'neighborhood point set' tar Fitting the data in the current target point p tar Is a plane adjacent to the plane of the substrate;
step 3-2: will be the current target point p tar And its k ' neighborhood point set Pk ' NN ' * tar Each neighborhood point in the map is projected to the current target point p tar To obtain the current target point p tar Is (are) projected points of (a)
Figure BDA0003837932200000041
And the projection point set of each neighborhood point in the k' neighborhood point set +.>
Figure BDA0003837932200000042
Step 3-3: constructing an included angle sequence: to be used for
Figure BDA0003837932200000043
As a reference vector, a neighborhood vector is calculated>
Figure BDA0003837932200000044
Angle with reference vector->
Figure BDA0003837932200000045
Thereby generating the sequence of included angles->
Figure BDA0003837932200000046
Figure BDA0003837932200000047
Step 3-4: calculating adjacent included angle difference value sequence
Figure BDA0003837932200000048
Figure BDA0003837932200000049
Figure BDA00038379322000000410
Figure BDA00038379322000000411
Step 3-5: find the adjacent included angle difference value sequence theta tar Maximum value of (2)
Figure BDA00038379322000000412
Comparing with a preset included angle threshold value, if +.>
Figure BDA00038379322000000413
If the included angle is larger than the preset included angle threshold value, the current target point p is set tar Contour point set { P } added as contour point to relic fragment PCm edge } m ，edge＝1，...k m ，k m PC for cultural relic fragments m Is defined by the number of contour points;
step 4: calculating each contour point set { P }, one by one edge } m Is composed of the following steps:
step 4-1: at the contour point set { P edge } m Is selected randomly by K subL The points are used as initial values of the centers of the contour lines and are moved into corresponding contour line sets; adopting an iterative clustering method to collect the contour point set { P edge } m Divided into K subL Contour lines K subL Is an integer greater than 1; when the change value of the center of each contour line is smaller than a preset center change threshold value or reaches the preset iteration times, ending the iterative clustering;
the iterative clustering process is as follows: calculating the contour point set { P }, one by one edge } m The distance between the points in (a) and the center of each contour line is added into the contour line set closest to the points in (b) and (c); calculating the mean value of the coordinates of the middle points of the centers of the outlines, and updating the centers of the corresponding outlines by using the mean value;
step 4-2: sequencing contour points in each contour line to obtain an ordered contour line point set
Figure BDA0003837932200000051
Figure BDA0003837932200000052
Figure BDA0003837932200000053
Is the ith contour line subl i The number of contour points in (a);
step 4-3: for each ordered contour line point set one by one
Figure BDA0003837932200000054
Fitting the B-spline function parameter equation, and sequentially selecting w contour points to fit the B-spline function parameter equation
Figure BDA0003837932200000055
Step 4-4: calculating the curvature of each contour line at each contour point one by one to obtain a curvature sequence
Figure BDA0003837932200000056
Step 4-5: extracting each ordered contour line point set one by one
Figure BDA0003837932200000057
Is characterized by: for curvature sequence->
Figure BDA0003837932200000058
Equal length segmentation, K c For the segment length, the local curvature maximum value is determined segment by segment, and the contour point corresponding to the local curvature maximum value is used for +.>
Figure BDA0003837932200000059
Building contour lines subl for elements i Feature point set->
Figure BDA00038379322000000510
The corresponding feature point index set is +.>
Figure BDA00038379322000000511
Step 4-6: calculating the current contour line subl one by one i To be compared with characteristic points
Figure BDA00038379322000000512
Figure BDA00038379322000000513
Is a mathematical geometric feature of (a):
characteristic points to be compared
Figure BDA0003837932200000061
Curvature of->
Figure BDA0003837932200000062
Figure BDA0003837932200000063
From the curvature sequence->
Figure BDA0003837932200000064
Extracting;
characteristic points to be compared
Figure BDA0003837932200000065
Flexibility ratio of->
Figure BDA0003837932200000066
The method comprises the following steps:
Figure BDA0003837932200000067
wherein ,
Figure BDA0003837932200000068
Figure BDA0003837932200000069
characteristic points to be compared
Figure BDA00038379322000000610
Feature points adjacent to the left side->
Figure BDA00038379322000000611
Constituent left-neighbor vector
Figure BDA00038379322000000612
Is->
Figure BDA00038379322000000613
The method comprises the following steps:
Figure BDA00038379322000000614
wherein ,
Figure BDA00038379322000000615
for->
Figure BDA00038379322000000616
Three-dimensional space coordinates of>
Figure BDA00038379322000000617
Is taken as a point
Figure BDA00038379322000000618
Is a three-dimensional space coordinate of (2);
characteristic points to be compared
Figure BDA00038379322000000619
Feature points adjacent to the right side->
Figure BDA00038379322000000620
Right neighbor vector of the composition
Figure BDA00038379322000000621
Is->
Figure BDA00038379322000000622
The method comprises the following steps:
Figure BDA00038379322000000623
wherein ,
Figure BDA0003837932200000071
for->
Figure BDA0003837932200000072
Three-dimensional space coordinates of>
Figure BDA0003837932200000073
For->
Figure BDA0003837932200000074
Is a three-dimensional space coordinate of (2);
characteristic points to be compared
Figure BDA0003837932200000075
Included angle of vector formed by the adjacent characteristic points>
Figure BDA0003837932200000076
Is vector quantity
Figure BDA0003837932200000077
Vector->
Figure BDA0003837932200000078
Included angle of (2):
Figure BDA0003837932200000079
characteristic points to be compared
Figure BDA00038379322000000710
The feature vectors of (a) are:
Figure BDA00038379322000000711
building a contour line subl i Characteristic representation matrix of (a)
Figure BDA00038379322000000712
The r-th behavior in the matrix is to be compared with the feature point +.>
Figure BDA00038379322000000713
Feature vector +.>
Figure BDA00038379322000000714
Figure BDA00038379322000000715
Step 5: the contour line rough comparison comprises the following specific steps:
step 5-1: PC for breaking cultural relics m Sequentially with PC n Pairing, m=1,. -%, M; n=m+1,. -%, M; PC for calculating cultural relic fragments one by one m Is a contour line subl of (2) i And cultural relic fragment PC n Is a contour line subl of (2) j Differences between pairs of feature points:
calculating contour lines subl i And subl j Curvature variability of (c):
Figure BDA00038379322000000716
wherein i=1,.. subL ；j＝1，...，K subL ；
Figure BDA00038379322000000717
Figure BDA0003837932200000081
Figure BDA0003837932200000082
Respectively the contour lines subl i And subl j
The number of points involved; the D function is calculated by the following steps:
Figure BDA0003837932200000083
and->
Figure BDA0003837932200000084
Figure BDA0003837932200000085
Calculating contour lines subl i And subl j Flexibility ratio variability of (c):
Figure BDA0003837932200000086
the D function calculation mode is as follows:
Figure BDA0003837932200000087
and->
Figure BDA0003837932200000088
Figure BDA0003837932200000089
Calculating contour lines subl i And subl j Left neighbor vector mode difference of (c):
Figure BDA00038379322000000810
Figure BDA00038379322000000811
Figure BDA00038379322000000812
calculating contour lines subl i And subl j Right neighbor vector mode difference of (c):
Figure BDA0003837932200000091
Figure BDA0003837932200000092
Figure BDA0003837932200000093
calculating contour lines subl i And subl j Is different from the left and right adjacent vector included angles:
Figure BDA0003837932200000094
Figure BDA0003837932200000095
wherein ,
Figure BDA0003837932200000096
is a contour line subl i The included angle formed by the q-th feature point and the left and right adjacent vectors,
Figure BDA0003837932200000097
is a contour line subl j An included angle formed by the q-th feature point and left and right adjacent vectors;
step 5-2: calculating contour lines subl i And subl j Crude alignment variability of (c):
Figure BDA0003837932200000098
if the contour line subl i And subl j The rough alignment difference of (2) is smaller than the rough alignment difference threshold epsilon, and the contour line subl i And subl j Adding a rough matching result set as a matching contour pair;
step 6: contour line similarity fine matching:
step 6-1: one by one coarse alignmentMatching contour pair subl in fruit set i and sublj Segmentation is carried out: contour points contained between two adjacent feature points on each contour line
Figure BDA0003837932200000101
Respectively forming a section, calculating the chord diameter length in each section>
Figure BDA0003837932200000102
and />
Figure BDA0003837932200000103
Construction of subl i and sublj Is a set of chord and perpendicular diameter lengths of the contour section>
Figure BDA0003837932200000104
And (3) with
Figure BDA0003837932200000105
Figure BDA0003837932200000106
Figure BDA0003837932200000107
wherein ,
Figure BDA0003837932200000108
and->
Figure BDA0003837932200000109
Point +.>
Figure BDA00038379322000001010
And (4) point->
Figure BDA00038379322000001011
Corresponding to the length of the chord diameter, the +.>
Figure BDA00038379322000001012
Is a contour line subl i Contour points in the upper segi segment, zi=1, & e segi ；/>
Figure BDA00038379322000001013
Is a contour line subl j The contour points in the upper segj segment, zj=1 and, e segj ；e segi 、e segj Respectively the contour lines subl i Middle segi segment and contour line subl j The number of contour points contained in the segj section; />
Figure BDA00038379322000001014
Figure BDA00038379322000001015
Respectively represent contour lines subl i ，subl i The upper section number,/->
Figure BDA00038379322000001016
and />
Figure BDA00038379322000001017
Two contour lines subl respectively i ，subl j The number of segments in (a);
subl i and sublj Profile segment chord sag length
Figure BDA00038379322000001018
And->
Figure BDA00038379322000001019
Is calculated by the same method as that of the subl i Length of chord diameter of contour segment +.>
Figure BDA00038379322000001020
The calculation method of (1) is as follows:
Figure BDA00038379322000001021
wherein ,
Figure BDA00038379322000001022
for vectors in the segi segment with the 1 st feature point as the source point and the last feature point as the end point +.>
Figure BDA0003837932200000111
The 1 st feature point is taken as a source point in the segi segment, and the zi contour point contained in the segment is taken as a +.>
Figure BDA0003837932200000112
Is the vector of the endpoint, +.>
Figure BDA0003837932200000113
For vector->
Figure BDA0003837932200000114
Is (are) mould>
Figure BDA0003837932200000115
For vector->
Figure BDA0003837932200000116
Is a mold of (2);
step 6-2: calculating contour lines subl one by using a dynamic programming method i ，subl j Inner chord perpendicular diameter length set of middle corresponding section
Figure BDA0003837932200000117
And->
Figure BDA0003837932200000118
Length of the longest common subsequence of +.>
Figure BDA0003837932200000119
Figure BDA00038379322000001110
Figure BDA00038379322000001111
For matrix->
Figure BDA00038379322000001112
Zj column element, zi=1,.. segi ；zj＝1，...，e segj ；/>
Figure BDA00038379322000001113
If it is
Figure BDA00038379322000001114
v_lcs is a preset threshold value, contour line subl i ，subl j The corresponding segment in (a) is a common subsequence; />
Figure BDA00038379322000001115
Figure BDA00038379322000001116
Otherwise, let go of>
Figure BDA00038379322000001117
Figure BDA00038379322000001118
Step 6-3: segment similarity judgment: calculating a threshold ω for similarity discrimination sim ：
ω sim ＝|setl max -setl min | (22)
If it is
Figure BDA00038379322000001119
Judging that the segments are similar; setl min 、setl max Respectively is a chord diameter length set +.>
Figure BDA00038379322000001120
And->
Figure BDA00038379322000001121
Middle e segi And e segj Minimum and maximum of (2)A value;
step 6-4: if the contour line subl i And subl j All the sections are similar, the contour line subl i And subl j Is similarly matchable;
step 7: virtually splicing fragments, namely, matching similar contour lines subl i And subl j Virtual splicing is carried out, and the method comprises the following specific steps:
step 7-1: transform parameters using gaussian mixture distribution
Figure BDA00038379322000001122
Transformation relation
Figure BDA00038379322000001123
Transformation parameters->
Figure BDA00038379322000001124
From the rotation parameter->
Figure BDA00038379322000001125
Translation parameter->
Figure BDA00038379322000001126
Scaling parameter->
Figure BDA00038379322000001127
Composition;
building a contour line subl j Contour point set PL of (1) j Likelihood function of (2)
Figure BDA0003837932200000121
Figure BDA0003837932200000122
Figure BDA0003837932200000123
wherein ,
Figure BDA0003837932200000124
the weight value is preset; v 2 Is a preset model parameter;
solving maximized contour subl j Contour point set PL of (1) j Obtaining a gaussian mixture distribution transformation parameter from likelihood functions of (a)
Figure BDA0003837932200000125
Transformation relation->
Figure BDA0003837932200000126
Step 7-2: virtual splicing:
Figure BDA0003837932200000127
wherein ,PLi ' PL i Iterating the transformed result;
the deviation is:
Figure BDA0003837932200000128
step 7-3: if the number of iterative transformations reaches the preset maximum value iter max Or |delta' 2 -δ 2 Whether or not is smaller than the deviation tolerance t e ，|δ′ 2 -δ 2 |＜t e Stopping the iteration; otherwise, update value v 2 and PLj ：
v 2 ＝v′ 2
PL i ＝PL i ′ (27)
Figure BDA0003837932200000129
Figure BDA00038379322000001210
For PL i Points in'; steering stepStep 7-1.
Further, a contour line subl i And subl j Is set of contour points of (a)
Figure BDA00038379322000001211
Figure BDA0003837932200000131
And (3) with
Figure BDA0003837932200000132
Is equal to->
Figure BDA0003837932200000133
The step 7 can be simplified as the following steps:
step 7-1: calculating contour lines subl i And contour line subl j Transform relation PL of (2) j ＝R ij PL i +T ij Rotation parameter R in (a) ij And a displacement parameter T ij ：
R ij ＝VU T (28)
Figure BDA0003837932200000134
Figure BDA0003837932200000135
And->
Figure BDA0003837932200000136
Outline subl respectively i And subl j The centroid of the contour point set of (2) is calculated by:
Figure BDA0003837932200000137
Figure BDA0003837932200000138
wherein ,
Figure BDA0003837932200000139
respectively contour point sets PL i With PL j Point in->
Figure BDA00038379322000001310
The matrices V and U are defined by the matrix->
Figure BDA00038379322000001311
Performing SVD decomposition h=u Σv T The sigma is obtained as a diagonal matrix; />
Figure BDA00038379322000001312
and />
Figure BDA00038379322000001313
The method comprises the following steps of:
Figure BDA00038379322000001314
Figure BDA00038379322000001315
step 7-2: virtual splicing: contour line subl j Using transformation relation PL j Transformed and contour line subl i And (5) splicing.
Further, step 2-1 is directed to point p is ＝(x is ，y is ，z is ) The distance is Euclidean distance when k neighbor sampling is carried out, and the point p js And the current point p is The Euclidean distance of (2) is:
Figure BDA00038379322000001316
further, the threshold value range (. Mu.) in step 2-4 m -Qσ m ，μ m +Qσ m ) The value range of the weight value Q of (1, 5)]。
Further, the threshold value range (. Mu.) in step 2-4 m -Qσ m ，μ m +Qσ m ) The weight value Q of the (B) is in the range of [1,10 ]]。
Further, step 3-1 is performed for each point p tar ＝(x tar ，y tar ，z tar )，
Figure BDA0003837932200000141
Performing k 'neighbor sampling to construct a k' neighborhood point set { Pk 'NN' tar When the value of k' is [10,60 ]]And selecting positive integers in the same.
Further, the initial value number K of the contour line center in step 4-1 subL In [2,10]And selecting positive integers in the same.
Further, step 4-2 sorts the contour points in each contour line to obtain an ordered contour line point set
Figure BDA0003837932200000142
Through the visual window interface, according to the contour point selected by the user +.>
Figure BDA0003837932200000143
And (3) taking the outline points as starting points, and sequencing from the near to the far according to the Euclidean space distance between other residual outline points and the starting points.
Further, step 6-2 compares the contour lines subl one by one using a dynamic programming method i ，subl j The chord diameter length set of the corresponding section in the middle is calculated, and the chord diameter length set in the corresponding section is calculated
Figure BDA0003837932200000144
And->
Figure BDA0003837932200000145
Length of the longest common subsequence of +.>
Figure BDA0003837932200000146
When in use, will->
Figure BDA0003837932200000147
In the lower segment, the value of the threshold v_lcs in the segment is equal to the average value of the corresponding two-segment chord diameter length sets ∈>
Figure BDA0003837932200000148
And->
Figure BDA0003837932200000149
{ e segi ，e segj The larger value in }:
Figure BDA00038379322000001410
wherein ,esegj Is a contour line subl j The number of contour points contained in the second segi segment;
Figure BDA00038379322000001411
Figure BDA0003837932200000151
respectively represent contour lines subl i ，subl i The upper segment number.
Further, in step 7-3, it is determined whether the number of iterative transformations reaches a preset maximum value iter max The value is [20,50]A positive integer therebetween.
The method has the following beneficial effects:
1) The method breaks through the general limitation of Euclidean distance in the process of calculating the characteristic point difference of the contour lines, the characteristic points of the contour lines to be compared can not be equal in length, and the method has wide applicability to application objects;
2) According to the invention, a target path is selected by a dynamic optimization method to carry out rough matching on the contour lines, and the difference accumulation minimum value of all points on the path is avoided, so that similar contour lines are eliminated during rough matching;
3) According to the invention, the three-dimensional point cloud fragment data is represented by the contour points, the contour lines are represented by the feature points, the data is reduced to the minimum, the calculation efficiency of an algorithm is improved, the matching speed and the matching flow are simplified, and the complex redundancy process is replaced by simple workload;
4) The invention uses the improved longest public subsequence length as a discrimination standard to further carry out similarity comparison on the fragment profile, thereby improving the matching accuracy.
Drawings
FIG. 1 is a flow chart of the present invention.
Fig. 2 is a schematic vector diagram of projection generation when contour points are found.
Fig. 3 is a schematic drawing of chord diameter length.
Fig. 4 is a contour point extraction effect diagram.
Fig. 5 is a feature point extraction effect diagram of the contour line 1 obtained by the segmentation.
Detailed Description
Example 1
The three-dimensional intelligent ceramic fragment splicing method based on the contour features comprises the following implementation steps:
step 1: acquiring three-dimensional point cloud data: collecting more than 1 piece of cultural relic fragments, and carrying out three-dimensional scanning on each collected cultural relic fragment to obtain corresponding cultural relic fragments
Figure BDA0003837932200000161
Figure BDA0003837932200000162
Wherein M is the total number of fragments, +.>
Figure BDA0003837932200000163
PC for cultural relic fragments m Points in the point cloud data;
step 2: the cultural relic fragments are processed one by using a statistical filtering method
Figure BDA0003837932200000164
Figure BDA0003837932200000165
The point cloud data of (2) is subjected to noise reduction treatment, and the noise reduction treatment method comprises the following specific steps of:
step 2-1: PC for fragments of cultural relics one by one m Current point p in point cloud data of (a) is With other points p js The distances of (2) are ordered from small to large,
Figure BDA0003837932200000166
and is not equal to js, taking the points p corresponding to the first k distances js Put into the current point p is K neighborhood set { PkNN } is In }:
current document fragment PC m Points in the point cloud data of (a) are
Figure BDA0003837932200000167
Calculating the current point p is ＝(x is ，y is ，z is )，/>
Figure BDA0003837932200000168
With current cultural relic fragment PC m Other points p in the point cloud data of (a) js ＝(x js ，y js ，z js )，
Figure BDA0003837932200000169
And is not equal to js distance is，js ：
Figure BDA00038379322000001610
Ordering distance from small to large is，js Taking the points p corresponding to the first k distances js Put into the current point p is K neighborhood set { PkNN } is In }; in this embodiment k is 60.
Step 2-2: calculating the current point p one by one is K neighborhood point set { PkNN is Midpoint p is Neighbor distance average of (2)
Figure BDA00038379322000001611
Figure BDA00038379322000001612
Figure BDA0003837932200000171
wherein ,
Figure BDA0003837932200000172
(x is ，y is ，z is ) For the current point p is Is a three-dimensional coordinate of (2);
step 2-3: calculate cultural relic fragment PC m Neighbor distance average value of all points in point cloud data of (a)
Figure BDA0003837932200000173
Mean. Mu.of (A) m And standard deviation sigma m ：
Figure BDA0003837932200000174
Figure BDA0003837932200000175
Step 2-4: judging the current point p is Neighbor distance average of (2)
Figure BDA0003837932200000176
Whether or not in the threshold range (mu) m -Qσ m ，μ m +Qσ m ) In which Q is a preset weight value, if not in the range, the current point p is Regarded as outliers, the current point p is From cultural relic fragment PC m Removing the point cloud data of the cultural relic fragments to obtain the cultural relic fragments PC m Is a non-abnormal point cloud data of +.>
Figure BDA0003837932200000177
In this embodiment, the weight Q has a value range of [1,5].
Outlier points are points with smaller distribution density in the point cloud, the points in the point cloud can be regarded as points with attribute information, the density of the points in a certain range represents the importance of the part of the point cloud, so the information quantity represented by the point cloud with smaller point density is smaller, and the points can be regarded as insignificant outlier points to be removed. This step first assumes a precondition: the current point cloud contains
Figure BDA0003837932200000178
The distance between the points conforms to a Gaussian distribution, which distribution will be represented by the mean μ m And standard deviation sigma m Determining, calculating the average mu of the average distances between all the point pairs of the current point cloud m And standard deviation sigma m The space distance between any two points in the point cloud is calculated by using a Euclidean distance formula. In the current point neighborhood, the average value of the distances between the point pairs formed by other points without the current point represents the point set density distribution of the area;
step 3: extracting each cultural relic fragment PC one by one m M=1,.. contour points of non-outlier cloud data of M, the method comprises the following specific steps:
step 3-1: fitting a plane: PC for cultural relic fragments m Current target point p in non-outlier point cloud data of (2) tar With other points p oth The distances of (2) are ordered from small to large,
Figure BDA0003837932200000181
oth is not equal to tar, and the first k' points p corresponding to the distances are taken js Put into the current target point p tar K ' neighborhood point set { Pk ' NN ' tar In { Pk 'NN' using the k 'neighborhood point set' tar Fitting the data in the current target point p tar Is described as follows:
current document fragment PC m Points in non-outlier point cloud data of (a)
Figure BDA0003837932200000182
Calculating the current point p tar ＝(x tar ，y tar ，z tar )，/>
Figure BDA0003837932200000183
With current cultural relic fragment PC m Other points p in non-outlier cloud data oth ＝(x otj ，y oth ，z oth ) Distance of (2) tar，oth ，/>
Figure BDA0003837932200000184
Figure BDA0003837932200000185
And tar+. oth:
Figure BDA0003837932200000186
ordering distance from small to large tar，oth Taking the points p corresponding to the previous k' distances oth Put into the current point p tar K neighborhood set { Pk 'NN' tar In }; using k ' neighborhood point set { Pk ' NN ' tar Fitting the data in the current target point P tar Is defined by the adjacent planes of:
in this embodiment, the value of k' is selected from positive integers between [10,60 ].
The solving process comprises the following steps:
let the plane equation be: ρ 1 X+ρ 2 Y+ρ 3 Z+ρ 4 =0, the deformation can be:
Figure BDA0003837932200000187
the method comprises the following steps of: z=o 1 X+o 2 Y+o 3, wherein ,
Figure BDA0003837932200000188
after matrixing, solving for X' to obtain (o 1 ，o 2 ，o 3 )：
AX′＝b
wherein ,
Figure BDA0003837932200000191
And (x) 1 ，y 1 ，z 1 )，...，(x k ′，y k ′，z k ') is the point p tar Coordinates of k' neighborhood points;
step 3-2: will be the current target point p tar And its k ' neighborhood point set Pk ' NN ' * tar Each neighborhood point in the map is projected to the current target point p tar To obtain the current target point p tar Is (are) projected points of (a)
Figure BDA0003837932200000192
And the projection point set of each neighborhood point in the k' neighborhood point set +.>
Figure BDA0003837932200000193
Step 3-3: constructing an included angle sequence: to be used for
Figure BDA0003837932200000194
As a reference vector, a neighborhood vector is calculated>
Figure BDA0003837932200000195
Angle with reference vector->
Figure BDA0003837932200000196
Thereby generating the sequence of included angles->
Figure BDA0003837932200000197
Figure BDA0003837932200000198
Figure BDA0003837932200000199
Figure BDA00038379322000001910
Figure BDA00038379322000001911
Figure BDA00038379322000001912
Figure BDA00038379322000001913
wherein ,
Figure BDA00038379322000001914
step 3-4: calculating adjacent included angle difference value sequence
Figure BDA00038379322000001915
Figure BDA00038379322000001916
Figure BDA00038379322000001917
Figure BDA00038379322000001918
Step 3-5: find the adjacent included angle difference value sequence theta tar Maximum value of (2)
Figure BDA00038379322000001919
Comparing with a preset included angle threshold value, if +.>
Figure BDA0003837932200000201
If the included angle is larger than the preset included angle threshold value, the current state is setTarget point p tar Adding cultural relic fragments PC as contour points m Is set of contour points { P ] edge } m ，edge＝1，...k m ，k m PC for cultural relic fragments m Is defined by the number of contour points;
step 4: calculating each contour point set { P }, one by one edge } m Is composed of the following steps:
step 4-1: at the contour point set { P edge } m Is selected randomly by K subL The points are used as initial values of the centers of the contour lines and are moved into corresponding contour line sets; adopting an iterative clustering method to collect the contour point set { P edge } m Divided into K subL Contour lines K subL Is an integer greater than 1; when the change value of the center of each contour line is smaller than a preset center change threshold value or reaches the preset iteration times, ending the iterative clustering; in this embodiment, 5 points are randomly selected as initial values of the centers of the contour lines, and the number of the final contour line division results is 5.
The iterative clustering process is as follows: calculating the contour point set { P }, one by one edge } m The distance between the points in (a) and the center of each contour line is added into the contour line set closest to the points in (b) and (c); calculating the mean value of the coordinates of the middle points of the centers of the outlines, and updating the centers of the corresponding outlines by using the mean value;
Figure BDA0003837932200000202
/>
Figure BDA0003837932200000203
Figure BDA0003837932200000204
Figure BDA0003837932200000205
wherein ,
Figure BDA0003837932200000206
for any point in the cen-th contour cluster, cl=1 and the number of the cells to be processed, n cen ；n cen For the number of points in cluster cen, cen=1 subL ；
Calculating the distance between the points except the category center point in the contour point set and the center point of each category in each iteration, and gathering the current point and the category center closest to the current point into one category; after each clustering, calculating clustered class centers, taking the sample mean value in each class as a new class center, and updating each class center;
initial value number K of contour line center in this embodiment subL In [2,10]And selecting positive integers in the same.
Step 4-2: sequencing contour points in each contour line to obtain an ordered contour line point set
Figure BDA0003837932200000211
Figure BDA0003837932200000212
Figure BDA0003837932200000213
Is the ith contour line subl i The process is described as follows;
because the points in the point cloud data are unordered and are unfavorable for subsequent mathematical calculation, the points in the point cloud data of each contour line are ordered and added with ordered indexes, so that the conversion from unordered to ordered is realized, and the ordering is performed based on the distance between two points in the embodiment:
by end points
Figure BDA0003837932200000214
As the source point, with the current contour line subl i Middle unordered point +.>
Figure BDA0003837932200000215
Figure BDA0003837932200000216
And (2) the source point->
Figure BDA0003837932200000217
Distance of (2) start，nos Sequencing from small to large to obtain ordered contour line point set +.>
Figure BDA0003837932200000218
Figure BDA0003837932200000219
Is the ith contour line subl i Profile points in (a):
Figure BDA00038379322000002110
wherein ,(xstart ，y start ，z start ) Is taken as a point
Figure BDA00038379322000002111
Coordinates of (x) nos ，y nos ，z nos ) For->
Figure BDA00038379322000002112
Is used for the purpose of determining the coordinates of (a),
Figure BDA00038379322000002113
storing the ordered contour line point set;
step 4-3: for each ordered contour line point set one by one
Figure BDA00038379322000002114
Fitting the B-spline function parameter equation, and sequentially selecting w contour points to fit the B-spline function parameter equation
Figure BDA0003837932200000221
The present embodiment uses the current wheelPart point of the profile
Figure BDA0003837932200000222
Figure BDA0003837932200000223
For the target fitting point, since the contour line point set is stored, each point can adopt 4 points adjacent to the left and right, and 5 points including the current target point are used for carrying out B-spline function fitting, namely w=5, and a parameter equation of a B-spline line segment function is constructed for the target point:
Figure BDA0003837932200000224
step 4-4: calculating the curvature of each contour line at each contour point one by one to obtain a curvature sequence
Figure BDA0003837932200000225
The solving process comprises the following steps:
Figure BDA0003837932200000226
Figure BDA0003837932200000227
Figure BDA0003837932200000228
Figure BDA0003837932200000229
wherein x (l), y (l), z (l) are defined by
Figure BDA00038379322000002210
Produce->
Figure BDA00038379322000002213
Figure BDA00038379322000002212
In this example, take l=0;
step 4-5: extracting each ordered contour line point set one by one
Figure BDA0003837932200000231
Is characterized by: for curvature sequence->
Figure BDA0003837932200000232
Equal length segmentation, K c For the segment length, the local curvature maximum value is determined segment by segment, and the contour point corresponding to the local curvature maximum value is used for +.>
Figure BDA0003837932200000233
Building contour lines subl for elements i Feature point set->
Figure BDA0003837932200000234
The corresponding feature point index set is +.>
Figure BDA0003837932200000235
The embodiment takes 6 as a range standard, namely K c =6, finding the maximum value of every 6 values in the curvature sequence of the contour line, and taking the corresponding contour point as the feature point;
the feature points represent the contour lines, so that data are reduced to the minimum, the calculation efficiency of an algorithm is improved, and the matching speed and flow are simplified;
step 4-6: calculating the current contour line subl one by one i To be compared with characteristic points
Figure BDA0003837932200000236
Figure BDA0003837932200000237
Is a mathematical geometric feature of (a):
wait for the bitSign points
Figure BDA0003837932200000238
Flexibility ratio of->
Figure BDA0003837932200000239
The method comprises the following steps:
Figure BDA00038379322000002310
wherein ,
Figure BDA00038379322000002311
Figure BDA00038379322000002312
characteristic points to be compared
Figure BDA00038379322000002313
Feature points adjacent to the left side->
Figure BDA00038379322000002314
Constituent left-neighbor vector
Figure BDA00038379322000002315
Is->
Figure BDA00038379322000002316
The method comprises the following steps:
Figure BDA00038379322000002317
Figure BDA0003837932200000241
wherein ,
Figure BDA0003837932200000242
for->
Figure BDA0003837932200000243
Three-dimensional space coordinates of>
Figure BDA0003837932200000244
Is taken as a point
Figure BDA0003837932200000245
Is a three-dimensional space coordinate of (2);
characteristic points to be compared
Figure BDA0003837932200000246
Feature points adjacent to the right side->
Figure BDA0003837932200000247
Right neighbor vector of the composition
Figure BDA0003837932200000248
Is->
Figure BDA0003837932200000249
The method comprises the following steps:
Figure BDA00038379322000002410
wherein ,
Figure BDA00038379322000002411
for->
Figure BDA00038379322000002412
Three-dimensional space coordinates of>
Figure BDA00038379322000002413
Is taken as a point
Figure BDA00038379322000002414
Is a three-dimensional space coordinate of (2);
characteristic points to be compared
Figure BDA00038379322000002415
Included angle of vector formed by the adjacent characteristic points>
Figure BDA00038379322000002416
For vector->
Figure BDA00038379322000002417
Vector->
Figure BDA00038379322000002418
Included angle of (2):
Figure BDA00038379322000002419
characteristic points to be compared
Figure BDA00038379322000002420
The feature vectors of (a) are:
Figure BDA00038379322000002421
building a contour line subl i Characteristic representation matrix of (a)
Figure BDA00038379322000002422
The r-th behavior in the matrix is to be compared with the feature point +.>
Figure BDA00038379322000002423
Feature vector +.>
Figure BDA00038379322000002424
Figure BDA00038379322000002425
Figure BDA0003837932200000251
And->
Figure BDA0003837932200000252
Respectively the contour lines subl i And contour line subl j Each row contains the feature vector of part of effective feature points in the contour line, each column represents the sequence of a certain feature of the feature point set in the current contour line, and for 5 different features, we adopt the mode of calculating the difference firstly and then carrying out weighted combination to represent the difference of the two contour lines;
step 5: the contour line rough comparison comprises the following specific steps:
step 5-1: PC for breaking cultural relics m Sequentially with PC n Pairing, m=1,. -%, M; n=m+1,. -%, M; PC for calculating cultural relic fragments one by one m Is a contour line subl of (2) i And cultural relic fragment PC n Is a contour line subl of (2) j Differences between pairs of feature points:
calculating contour lines subl i And subl j Curvature variability of (c):
Figure BDA0003837932200000253
wherein i=1,.. subL ；j＝1，...，K subL ；
Figure BDA0003837932200000254
Figure BDA0003837932200000255
Figure BDA0003837932200000256
Respectively the contour lines subl i And subl j The number of points involved; the D function is calculated by the following steps:
Figure BDA0003837932200000257
and->
Figure BDA0003837932200000258
Figure BDA0003837932200000259
Calculating contour lines subl i And subl j Flexibility ratio variability of (c):
Figure BDA00038379322000002510
the D function calculation mode is as follows:
Figure BDA00038379322000002511
and->
Figure BDA00038379322000002512
Figure BDA0003837932200000261
Calculating contour lines subl i And subl j Left neighbor vector mode difference of (c):
Figure BDA0003837932200000262
Figure BDA0003837932200000263
Figure BDA0003837932200000264
calculating contour lines subl i And subl j Right neighbor vector mode difference of (c):
Figure BDA0003837932200000265
Figure BDA0003837932200000266
Figure BDA0003837932200000267
calculating contour lines subl i And subl j Is different from the left and right adjacent vector included angles:
Figure BDA0003837932200000268
/>
Figure BDA0003837932200000269
wherein ,
Figure BDA0003837932200000271
is a contour line subl i The included angle formed by the q-th feature point and the left and right adjacent vectors,
Figure BDA0003837932200000272
is a contour line subl j An included angle formed by the q-th feature point and left and right adjacent vectors;
calculating the variability using the D function has the following advantages: the Euclidean distance used for general differential calculation can be replaced, and the general limitations of Euclidean distance are broken through, such as: the two sequences compared must be of equal length; in the scheme, the D function does not have requirements and restrictions on the lengths of two feature sequences to be compared, and when the D function is used for calculating the difference, the accumulation of the difference is considered, and meanwhile, the current difference value is defined by selecting the minimum value from multiple differences, so that similar contour lines are prevented from being removed during rough matching;
step 5-2: calculating contour lines subl i And subl j Crude alignment variability of (c):
Figure BDA0003837932200000273
if the contour line subl i And subl j The rough alignment difference of (2) is smaller than the rough alignment difference threshold epsilon, and the contour line subl i And subl j Adding a rough matching result set as a matching contour pair;
step 6: contour line similarity fine matching:
step 6-1: match contour line pairs subl in a coarse comparison result set one by one i and sublj Segmentation is carried out: contour points contained between two adjacent feature points on each contour line
Figure BDA0003837932200000274
Respectively forming a section, calculating the chord diameter length in each section>
Figure BDA0003837932200000275
and />
Figure BDA0003837932200000276
Construction of subl i and sublj Is a set of chord and perpendicular diameter lengths of the contour section>
Figure BDA0003837932200000277
And (3) with
Figure BDA0003837932200000278
Figure BDA0003837932200000279
Figure BDA00038379322000002710
wherein ,
Figure BDA0003837932200000281
and->
Figure BDA0003837932200000282
Point +.>
Figure BDA0003837932200000283
And (4) point->
Figure BDA0003837932200000284
Corresponding to the length of the chord diameter, the +.>
Figure BDA0003837932200000285
Is a contour line subl i Contour points in the upper segi segment, zi=1, & e segi ；/>
Figure BDA0003837932200000286
Is a contour line subl j The contour points in the upper segj segment, zj=1 and, e segj ；e segi 、e segj Respectively the contour lines subl i Middle segi segment and contour line subl j The number of contour points contained in the segj section; />
Figure BDA0003837932200000287
Figure BDA0003837932200000288
Respectively represent contour lines subl i ，subl i The upper section number,/->
Figure BDA0003837932200000289
and />
Figure BDA00038379322000002810
Two contour lines subl respectively i ，subl j The number of segments in (a);
subl i and sublj Profile segment chord sag length
Figure BDA00038379322000002811
And->
Figure BDA00038379322000002812
Is calculated by the same method as that of the subl i Length of chord diameter of contour segment +.>
Figure BDA00038379322000002813
The calculation method of (1) is as follows:
Figure BDA00038379322000002814
wherein ,
Figure BDA00038379322000002815
for vectors in the segi segment with the 1 st feature point as the source point and the last feature point as the end point +.>
Figure BDA00038379322000002816
The 1 st feature point is taken as a source point in the segi segment, and the zi contour point contained in the segment is taken as a +.>
Figure BDA00038379322000002817
Is the vector of the endpoint, +.>
Figure BDA00038379322000002818
For vector->
Figure BDA00038379322000002819
Is (are) mould>
Figure BDA00038379322000002820
For vector->
Figure BDA00038379322000002821
Is a mold of (2);
step 6-2: calculating contour lines subl one by using a dynamic programming method i ，subl j Inner chord perpendicular diameter length set of middle corresponding section
Figure BDA00038379322000002822
And->
Figure BDA00038379322000002823
Length of the longest common subsequence of +.>
Figure BDA00038379322000002824
Figure BDA00038379322000002825
Figure BDA00038379322000002826
For matrix->
Figure BDA00038379322000002827
Zj column element, zi=1,.. segi ；zj＝1，...，e segj ；/>
Figure BDA00038379322000002828
If->
Figure BDA00038379322000002829
Delta_lcs preset threshold value and contour line subl i ，subl j The corresponding segment in (a) is a common subsequence; in this embodiment, the preset threshold is 6.85 +.>
Figure BDA0003837932200000291
Otherwise, let go of>
Figure BDA0003837932200000292
The method has the following advantages: the length of the longest public subsequence is taken as a criterion, meanwhile, a comparison rule is modified according to the characteristics of the scanned fragment point cloud data, the equal judgment rule of the original longest public subsequence is changed into a difference comparison rule, and meanwhile, the fragment profile is subjected to further similarity comparison, so that the matching accuracy is improved;
step 6-3: segment similarity judgment: calculating a threshold ω for similarity discrimination sim
ω sim ＝|setl max -setl min | (22)
If it is
Figure BDA0003837932200000293
Judging that the segments are similar; setl min 、setl max Respectively is a chord diameter length set +.>
Figure BDA0003837932200000294
And->
Figure BDA0003837932200000295
Middle e segi And e segj Minimum and maximum values of (a);
step 6-4: if the contour line subl i And subl j All the sections are similar, the contour line subl i And subl j Is similarly matchable;
step 7: virtually splicing fragments, namely, matching similar contour lines subl i And subl j Virtual splicing is carried out, and the method comprises the following specific steps:
step 7-1: transform parameters using gaussian mixture distribution
Figure BDA0003837932200000296
Transformation relation->
Figure BDA0003837932200000297
Transformation parameters->
Figure BDA0003837932200000298
From the rotation parameter->
Figure BDA0003837932200000299
Translation parameter->
Figure BDA00038379322000002910
Scaling parameter->
Figure BDA00038379322000002911
Composition;
building a contour line subl j Contour point set PL of (1) j Likelihood function of (2)
Figure BDA00038379322000002912
Figure BDA00038379322000002913
Figure BDA00038379322000002914
wherein ,
Figure BDA0003837932200000301
the weight value is preset; delta 2 Is a preset model parameter; />
Figure BDA0003837932200000302
The method is obtained by the following steps: from the following components
Figure BDA0003837932200000303
Figure BDA0003837932200000304
And is also provided with
Figure BDA0003837932200000305
The method can obtain:
Figure BDA0003837932200000306
Figure BDA0003837932200000307
solving maximized contour subl j Contour point set PL of (1) j Obtaining a gaussian mixture distribution transformation parameter from likelihood functions of (a)
Figure BDA0003837932200000308
Transformation relation->
Figure BDA0003837932200000309
Step 7-2: virtual splicing:
Figure BDA00038379322000003010
wherein ,PLi ' PL i Iterating the transformed result;
the deviation is:
Figure BDA00038379322000003011
step 7-3: if the number of iterative transformations reaches the preset maximum value iter max Or |delta' 2 -v 2 Whether or not is smaller than the deviation tolerance t e ，|δ′ 2 -v 2 |＜t e Stopping the iteration; otherwise, update value v 2 and PLj ：
δ 2 ＝δ′ 2
PL i ＝PL i ′ (27)
Figure BDA0003837932200000311
Figure BDA0003837932200000312
For PL i Points in'; turning to step 7-1.
In this embodiment, the maximum value iter is preset max The value is [20,50]A positive integer therebetween.
Example 2
The difference from embodiment 1 is that the contour line subl i And subl j Is set of contour points of (a)
Figure BDA0003837932200000313
Figure BDA0003837932200000314
And->
Figure BDA0003837932200000315
Are equal to each other in the number of points
Figure BDA0003837932200000316
The step 7 can be simplified as the following steps:
step 7-1: calculating contour lines subl i And contour line subl j Transform relation PL of (2) j ＝R ij PL i +T ij Rotation parameter R in (a) ij And a displacement parameter T ij ：
R ij ＝VU T (28)
Figure BDA0003837932200000317
Figure BDA0003837932200000318
And->
Figure BDA0003837932200000319
Outline subl respectively i And subl j The centroid of the contour point set of (2) is calculated by:
Figure BDA00038379322000003110
Figure BDA00038379322000003111
wherein ,
Figure BDA00038379322000003112
respectively contour point sets PL i With PL j Point in->
Figure BDA00038379322000003113
The matrices V and U are defined by the matrix->
Figure BDA00038379322000003114
Performing SVD decomposition h=u Σv T The sigma is obtained as a diagonal matrix; />
Figure BDA00038379322000003115
and />
Figure BDA00038379322000003116
The method comprises the following steps of:
Figure BDA00038379322000003117
Figure BDA00038379322000003118
step 7-2: virtual splicing: contour line subl j Using transformation relation PL j Transformed and contour line subl i And (5) splicing.
Example 3
The difference from example 1 is that: threshold Range (μ) in Steps 2-4 m -Qσ m ，μ m +Qσ m ) The weight value Q of the (B) is in the range of [1,10 ]]。
Example 4
The difference from example 1 is that: step 6-2 comparing contour lines subl one by one using a dynamic programming method i ，subl j The chord diameter length set of the corresponding section in the middle is calculated, and the chord diameter length set in the corresponding section is calculated
Figure BDA0003837932200000321
And->
Figure BDA0003837932200000322
Length of the longest common subsequence of +.>
Figure BDA0003837932200000323
When in use, will->
Figure BDA0003837932200000324
Comparing with the threshold delta_lcs in the section, wherein in the current section, the threshold delta_lcs in the section takes the value of the average value of the corresponding two sections of chord diameter length sets +.>
Figure BDA0003837932200000325
And->
Figure BDA0003837932200000326
{ e segi ，e segj The larger value in }:
Figure BDA0003837932200000327
wherein ,esegj Is a contour line subl j The number of contour points contained in the second segi segment;
Figure BDA0003837932200000328
Figure BDA0003837932200000329
respectively represent contour lines subl i ，subl i The upper segment number.
Example 5
The difference from example 1 is that: step 4-2, sequencing contour points in each contour line to obtain an ordered contour line point set
Figure BDA00038379322000003210
Through the visual window interface, according to the contour point selected by the user +.>
Figure BDA00038379322000003211
As a starting point, according to the Euclidean space distance between other rest contour points and the starting pointAnd (5) sequencing.
It is necessary to explain that: at present, the technical scheme of the invention has performed small-scale pilot scale test, and the use investigation of the user is performed in a small range, and the investigation result shows that the user satisfaction is higher. Now, the technology conversion application is prepared, and the intellectual property risk early warning investigation is performed.

Claims (10)

1. The intelligent splicing method for the cultural relic fragments based on the contour line features is characterized by comprising the following steps of:
step 1: acquiring three-dimensional point cloud data: collecting more than 1 piece of cultural relic fragments, and carrying out three-dimensional scanning on each collected cultural relic fragment to obtain corresponding cultural relic fragments
Figure FDA0003837932190000011
Figure FDA0003837932190000012
Wherein M is the total number of fragments, +.>
Figure FDA0003837932190000013
PC for cultural relic fragments m Points in the point cloud data;
step 2: the cultural relic fragments are processed one by using a statistical filtering method
Figure FDA0003837932190000014
Figure FDA0003837932190000015
The point cloud data of (2) is subjected to noise reduction treatment, and the noise reduction treatment method comprises the following specific steps of:
step 2-1: PC for fragments of cultural relics one by one m Current point p in point cloud data of (a) is With other points p js The distances of (2) are ordered from small to large,
Figure FDA0003837932190000016
and is not equal to js, take the first k distancesCorresponding point p js Put into the current point p is K neighborhood set { PkNN } is In };
step 2-2: calculating the current point p one by one is K neighborhood point set { PkNN is Midpoint p is Neighbor distance average of (2)
Figure FDA0003837932190000017
Figure FDA0003837932190000018
Figure FDA0003837932190000019
wherein ,
Figure FDA00038379321900000110
(x is ,y is ,z is ) For the current point p is Is a three-dimensional coordinate of (2);
step 2-3: calculate cultural relic fragment PC m Neighbor distance average value of all points in point cloud data of (a)
Figure FDA00038379321900000111
Mean. Mu.of (A) m And standard deviation sigma m ：
Figure FDA00038379321900000112
Figure FDA0003837932190000021
Step 2-4: judging the current point p is Neighbor distance average of (2)
Figure FDA0003837932190000022
Whether or not in the threshold range (mu) m -Qσ m ,μ m +Qσ m ) In which Q is a preset weight value, if not in the range, the current point p is Regarded as outliers, the current point p is From cultural relic fragment PC m Removing the point cloud data of the cultural relic fragments to obtain the cultural relic fragments PC m Is a non-abnormal point cloud data of +.>
Figure FDA0003837932190000023
Step 3: extracting each cultural relic fragment PC one by one m The contour points of the non-abnormal point cloud data of m=1, …, M consist of the following specific steps:
step 3-1: fitting a plane: PC for cultural relic fragments m Current target point p in non-outlier point cloud data of (2) tar With other points p oth The distances of (2) are ordered from small to large,
Figure FDA0003837932190000024
oth is not equal to tar, and the first k' points p corresponding to the distances are taken js Put into the current target point p tar K ' neighborhood point set { Pk ' NN ' tar In { Pk 'NN' using the k 'neighborhood point set' tar Fitting the data in the current target point p tar Is a plane adjacent to the plane of the substrate;
step 3-2: will be the current target point p tar And its k ' neighborhood point set Pk ' NN ' * tar Each neighborhood point in the map is projected to the current target point p tar To obtain the current target point p tar Is (are) projected points of (a)
Figure FDA0003837932190000025
And the projection point set of each neighborhood point in the k' neighborhood point set +.>
Figure FDA0003837932190000026
Step 3-3: constructing an included angle sequence: to be used for
Figure FDA0003837932190000027
As a reference vector, a neighborhood vector is calculated>
Figure FDA0003837932190000028
Angle with reference vector->
Figure FDA0003837932190000029
Thereby generating the sequence of included angles->
Figure FDA00038379321900000210
Figure FDA00038379321900000211
Step 3-4: calculating adjacent included angle difference value sequence
Figure FDA00038379321900000212
Figure FDA00038379321900000213
Figure FDA00038379321900000214
Figure FDA00038379321900000215
Step 3-5: find the adjacent included angle difference value sequence theta tar Maximum value of (2)
Figure FDA0003837932190000031
Comparing with a preset included angle threshold value, if
Figure FDA0003837932190000032
If the included angle is larger than the preset included angle threshold value, the current target point p is set tar Adding cultural relic fragments PC as contour points m Is set of contour points { P ] edge } m’ edge＝1,…k m ，k m PC for cultural relic fragments m Is defined by the number of contour points;
step 4: calculating each contour point set { P }, one by one edge } m Is composed of the following steps:
step 4-1: at the contour point set { P edge } m Is selected randomly by K subL The points are used as initial values of the centers of the contour lines and are moved into corresponding contour line sets; adopting an iterative clustering method to collect the contour point set { P edge } m Divided into K subL Contour lines K subL Is an integer greater than 1; when the change value of the center of each contour line is smaller than a preset center change threshold value or reaches the preset iteration times, ending the iterative clustering;
the iterative clustering process is as follows: calculating the contour point set { P }, one by one edge } m The distance between the points in (a) and the center of each contour line is added into the contour line set closest to the points in (b) and (c); calculating the mean value of the coordinates of the middle points of the centers of the outlines, and updating the centers of the corresponding outlines by using the mean value;
step 4-2: sequencing contour points in each contour line to obtain an ordered contour line point set
Figure FDA0003837932190000033
Figure FDA0003837932190000034
Figure FDA0003837932190000035
Is the ith contour line subl i The number of contour points in (a);
step 4-3: for each ordered contour line point set one by one
Figure FDA0003837932190000036
Fitting a B-spline function parameter equation, and sequentially selecting w wheelsProfile point fitting B-spline function parameter equation
Figure FDA0003837932190000037
Step 4-4: calculating the curvature of each contour line at each contour point one by one to obtain a curvature sequence
Figure FDA0003837932190000038
Step 4-5: extracting each ordered contour line point set one by one
Figure FDA0003837932190000039
Is characterized by: for curvature sequence->
Figure FDA0003837932190000041
Equal length segmentation, K c For the segment length, the local curvature maximum value is determined segment by segment, and the contour point corresponding to the local curvature maximum value is used for +.>
Figure FDA0003837932190000042
Building contour lines subl for elements i Feature point set->
Figure FDA0003837932190000043
The corresponding feature point index set is +.>
Figure FDA0003837932190000044
Step 4-6: calculating the current contour line subl one by one i To be compared with characteristic points
Figure FDA0003837932190000045
Figure FDA0003837932190000046
Is a mathematical geometric feature of (a):
characteristic points to be compared
Figure FDA0003837932190000047
Curvature of->
Figure FDA0003837932190000048
Figure FDA0003837932190000049
Figure FDA00038379321900000410
From the curvature sequence->
Figure FDA00038379321900000411
Extracting;
characteristic points to be compared
Figure FDA00038379321900000412
Flexibility ratio of->
Figure FDA00038379321900000413
The method comprises the following steps:
Figure FDA00038379321900000414
wherein ,
Figure FDA00038379321900000415
Figure FDA00038379321900000416
characteristic points to be compared
Figure FDA00038379321900000417
Feature points adjacent to the left side->
Figure FDA00038379321900000418
Constituent left neighbor vector->
Figure FDA00038379321900000419
Is a mold of (2)
Figure FDA00038379321900000420
The method comprises the following steps:
Figure FDA00038379321900000421
wherein ,
Figure FDA00038379321900000422
for->
Figure FDA00038379321900000423
Three-dimensional space coordinates of>
Figure FDA00038379321900000424
Is taken as a point
Figure FDA00038379321900000425
Is a three-dimensional space coordinate of (2);
characteristic points to be compared
Figure FDA00038379321900000426
Feature points adjacent to the right side->
Figure FDA00038379321900000427
Right neighbor vector of the composition->
Figure FDA0003837932190000051
Is->
Figure FDA0003837932190000052
The method comprises the following steps:
Figure FDA0003837932190000053
wherein ,
Figure FDA0003837932190000054
for->
Figure FDA0003837932190000055
Three-dimensional space coordinates of>
Figure FDA0003837932190000056
For->
Figure FDA0003837932190000057
Is a three-dimensional space coordinate of (2);
characteristic points to be compared
Figure FDA0003837932190000058
Included angle of vector formed by the adjacent characteristic points>
Figure FDA0003837932190000059
Is vector quantity
Figure FDA00038379321900000510
Vector->
Figure FDA00038379321900000511
Included angle of (2):
Figure FDA00038379321900000512
characteristic points to be compared
Figure FDA00038379321900000513
The feature vectors of (a) are:
Figure FDA00038379321900000514
building a contour line subl i Characteristic representation matrix of (a)
Figure FDA00038379321900000515
The r-th behavior in the matrix is to be compared with the feature point +.>
Figure FDA00038379321900000516
Feature vector +.>
Figure FDA00038379321900000517
Figure FDA00038379321900000518
Figure FDA00038379321900000519
Step 5: the contour line rough comparison comprises the following specific steps:
step 5-1: PC for breaking cultural relics m Sequentially with PC n Pairing, m=1, …, M; n=m+1, …, M; PC for calculating cultural relic fragments one by one m Is a contour line subl of (2) i And cultural relic fragment PC n Is a contour line subl of (2) j Differences between pairs of feature points:
calculating contour lines subl i And subl j Curvature variability of (c):
Figure FDA00038379321900000520
Figure FDA0003837932190000061
wherein i=1, …, K subL ；j＝1,…,K subL ；
Figure FDA0003837932190000062
Figure FDA0003837932190000063
Figure FDA0003837932190000064
Respectively the contour lines subl i And subl j The number of points involved; the D function is calculated by the following steps:
Figure FDA0003837932190000065
and->
Figure FDA0003837932190000066
Figure FDA0003837932190000067
Calculating contour lines subl i And subl j Flexibility ratio variability of (c):
Figure FDA0003837932190000068
the D function calculation mode is as follows:
Figure FDA0003837932190000069
and->
Figure FDA00038379321900000610
Figure FDA00038379321900000611
Calculating contour lines subl i And subl j Left neighbor vector mode difference of (c):
Figure FDA00038379321900000612
Figure FDA00038379321900000613
Figure FDA0003837932190000071
calculating contour lines subl i And subl j Right neighbor vector mode difference of (c):
Figure FDA0003837932190000072
Figure FDA0003837932190000073
Figure FDA0003837932190000074
calculating contour lines subl i And subl j Is different from the left and right adjacent vector included angles:
Figure FDA0003837932190000075
Figure FDA0003837932190000076
wherein ,
Figure FDA0003837932190000077
is a contour line subl i The included angle formed by the q-th feature point and the left and right adjacent vectors,/>
Figure FDA0003837932190000078
is a contour line subl j An included angle formed by the q-th feature point and left and right adjacent vectors;
step 5-2: calculating contour lines subl i And subl j Crude alignment variability of (c):
Figure FDA0003837932190000079
if the contour line subl i And subl j The rough alignment difference of (2) is smaller than the rough alignment difference threshold epsilon, and the contour line subl i And subl j Adding a rough matching result set as a matching contour pair;
step 6: contour line similarity fine matching:
step 6-1: match contour line pairs subl in a coarse comparison result set one by one i and sublj Segmentation is carried out: contour points contained between two adjacent feature points on each contour line
Figure FDA0003837932190000081
Respectively forming a section, calculating the chord diameter length in each section>
Figure FDA0003837932190000082
and />
Figure FDA0003837932190000083
Construction of subl i and sublj Is a set of chord and perpendicular diameter lengths of the contour section>
Figure FDA0003837932190000084
And->
Figure FDA0003837932190000085
Figure FDA0003837932190000086
Figure FDA0003837932190000087
wherein ,
Figure FDA0003837932190000088
and->
Figure FDA0003837932190000089
Point +.>
Figure FDA00038379321900000810
And (4) point->
Figure FDA00038379321900000811
Corresponding to the length of the chord diameter, the +.>
Figure FDA00038379321900000812
Is a contour line subl i Contour points in the upper segi segment, zi=1, …, e segi ；/>
Figure FDA00038379321900000813
Is a contour line subl j Contour points in the upper segj segment zj=1, …, e segj ；e segi 、e segj Respectively the contour lines subl i Middle segi segment and contour line subl j The number of contour points contained in the segj section; />
Figure FDA00038379321900000814
Figure FDA00038379321900000815
Respectively represent contour lines subl i ,subl i The upper section number,/->
Figure FDA00038379321900000816
and />
Figure FDA00038379321900000817
Two contour lines subl respectively i ,subl j The number of segments in (a);
subl i and sublj Profile segment chord sag length
Figure FDA00038379321900000818
And->
Figure FDA00038379321900000819
Is calculated by the same method as that of the subl i Length of chord diameter of contour segment +.>
Figure FDA00038379321900000820
The calculation method of (1) is as follows:
Figure FDA00038379321900000821
wherein ,
Figure FDA00038379321900000822
for vectors in the segi segment with the 1 st feature point as the source point and the last feature point as the end point +.>
Figure FDA00038379321900000823
The 1 st feature point is taken as a source point in the segi segment, and the zi contour point contained in the segment is taken as a +.>
Figure FDA00038379321900000824
Is the vector of the end point and,
Figure FDA00038379321900000825
for vector->
Figure FDA00038379321900000826
Is (are) mould>
Figure FDA00038379321900000827
For vector->
Figure FDA00038379321900000828
Is a mold of (2);
step 6-2: calculating contour lines subl one by using a dynamic programming method i ,subl j Inner chord perpendicular diameter length set of middle corresponding section
Figure FDA0003837932190000091
And->
Figure FDA0003837932190000092
Length of the longest common subsequence of +.>
Figure FDA0003837932190000093
Figure FDA0003837932190000094
Figure FDA0003837932190000095
For matrix->
Figure FDA0003837932190000096
Zj column element, zi=1, …, e segi ；zj＝1,…,e segj ；/>
Figure FDA0003837932190000097
If it is
Figure FDA0003837932190000098
Delta_lcs is a preset threshold value, contour line subl i ,subl j The corresponding segment in (a) is a common subsequence; />
Figure FDA0003837932190000099
Figure FDA00038379321900000910
Otherwise, let go of>
Figure FDA00038379321900000911
Figure FDA00038379321900000912
Step 6-3: segment similarity judgment: calculating a threshold ω for similarity discrimination sim :
ω sim ＝|setl max -setl min | (22)
If it is
Figure FDA00038379321900000913
Judging that the segments are similar; setl min 、setl max Respectively is a chord diameter length set +.>
Figure FDA00038379321900000914
And->
Figure FDA00038379321900000915
Middle e segi And e segj Minimum and maximum values of (a);
step 6-4: if the contour line subl i And subl j All the sections are similar, the contour line subl i And subl j Is similarly matchable;
step 7: virtually splicing fragments, namely, matching similar contour lines subl i And subl j Virtual splicing is carried out, and the method comprises the following specific steps:
step 7-1: transform parameters using gaussian mixture distribution
Figure FDA00038379321900000916
Transformation relation
Figure FDA00038379321900000917
Transformation parameters->
Figure FDA00038379321900000918
From the rotation parameter->
Figure FDA00038379321900000919
Translation parameter->
Figure FDA00038379321900000920
Scaling parameter->
Figure FDA00038379321900000921
Composition;
building a contour line subl j Contour point set PL of (1) j Likelihood function of (2)
Figure FDA00038379321900000922
Figure FDA00038379321900000923
Figure FDA0003837932190000101
wherein ,
Figure FDA0003837932190000102
the weight value is preset; omega 2 Is a preset model parameter;
solving maximized contour subl j Contour point set PL of (1) j Obtaining a gaussian mixture distribution transformation parameter from likelihood functions of (a)
Figure FDA0003837932190000103
Transformation relation->
Figure FDA0003837932190000104
Step 7-2: virtual splicing:
Figure FDA0003837932190000105
wherein ,PLi ' PL i Iterating the transformed result;
the deviation is:
Figure FDA0003837932190000106
step 7-3: if the number of iterative transformations reaches the preset maximum value iter max Or |delta' 2 -δ 2 Whether or not is smaller than the deviation tolerance t e ，|δ′ 2 -δ 2 |<t e Stopping the iteration; otherwise, update value delta 2 and PLj ：
δ 2 ＝δ′ 2
PL i ＝PL i ′ (27)
Figure FDA0003837932190000107
Figure FDA0003837932190000108
For PL i Points in'; turning to step 7-1.
2. The intelligent splicing method for the cultural relic fragments based on the contour line features as claimed in claim 1, wherein the method comprises the following steps: contour line subl i And subl j Is set of contour points of (a)
Figure FDA0003837932190000109
Figure FDA00038379321900001010
And->
Figure FDA00038379321900001011
Is equal to->
Figure FDA00038379321900001012
The step 7 can be simplified as the following steps:
step 7-1: calculating contour lines subl i And contour line subl j Transform relation PL of (2) j ＝R ij PL i +T ij Rotation parameter R in (a) ij And a displacement parameter T ij ：
R ij ＝VU T (28)
Figure FDA0003837932190000111
Figure FDA0003837932190000112
And->
Figure FDA0003837932190000113
Outline subl respectively i And subl j The centroid of the contour point set of (2) is calculated by:
Figure FDA0003837932190000114
Figure FDA0003837932190000115
wherein ,
Figure FDA0003837932190000116
respectively contour point sets PL i With PL j Point in->
Figure FDA0003837932190000117
The matrices V and U are defined by the matrix->
Figure FDA0003837932190000118
Performing SVD decomposition h=u Σv T The sigma is obtained as a diagonal matrix; />
Figure FDA0003837932190000119
and />
Figure FDA00038379321900001110
The method comprises the following steps of:
Figure FDA00038379321900001111
Figure FDA00038379321900001112
step 7-2: virtual splicing: contour line subl j Using transformation relation PL j Transformed and contour line subl i And (5) splicing.
3. The intelligent splicing method for the cultural relic fragments based on the contour line features as claimed in claim 1, wherein the method comprises the following steps: step 2-1 Point p is ＝(x is ,y is ,z is ) The distance is Euclidean distance when k neighbor sampling is carried out, and the point p js And the current point p is The Euclidean distance of (2) is:
Figure FDA00038379321900001113
4. the intelligent splicing method for the cultural relic fragments based on the contour line features as claimed in claim 1, wherein the method comprises the following steps: threshold Range (μ) in Steps 2-4 m -Qσ m ,μ m +Qσ m ) The value range of the weight value Q of (1, 5)]。
5. The intelligent splicing method for the cultural relic fragments based on the contour line features as claimed in claim 1, wherein the method comprises the following steps: threshold Range (μ) in Steps 2-4 m -Qσ m ,μ m +Qσ m ) The value range of the weight value Q of the (E) is [1,10]。
6. The intelligent splicing method for the cultural relic fragments based on the contour line features as claimed in claim 1, wherein the method comprises the following steps: step 3-1 for each Point p tar ＝(x tar ,y tar ,z tar )，
Figure FDA0003837932190000121
Performing k 'neighbor sampling to construct a k' neighborhood point set { Pk 'NN' tar When the value of k' is [10,60 ]]And selecting positive integers in the same.
7. The intelligent splicing method for the cultural relic fragments based on the contour line features as claimed in claim 1, wherein the method comprises the following steps: initial value number K of contour line center in step 4-1 subL In [2,10]And selecting positive integers in the same.
8. The intelligent splicing method for the cultural relic fragments based on the contour line features as claimed in claim 1, wherein the method comprises the following steps: step 4-2, sequencing contour points in each contour line to obtain an ordered contour line point set
Figure FDA0003837932190000122
Through the visual window interface, according to the contour point selected by the user +.>
Figure FDA0003837932190000123
And (3) taking the outline points as starting points, and sequencing from the near to the far according to the Euclidean space distance between other residual outline points and the starting points.
9. The intelligent splicing method for the cultural relic fragments based on the contour line features as claimed in claim 1, wherein the method comprises the following steps: step 6-2 comparing contour lines subl one by one using a dynamic programming method i ,subl j The chord diameter length set of the corresponding section in the middle is calculated, and the chord diameter length set in the corresponding section is calculated
Figure FDA0003837932190000124
And->
Figure FDA0003837932190000125
Length of the longest common subsequence of +.>
Figure FDA0003837932190000126
When in use, will->
Figure FDA0003837932190000127
In the lower segment, the value of the threshold delta_lcs in the segment is equal to the average value of the corresponding two-segment chord diameter length sets ∈>
Figure FDA0003837932190000128
And->
Figure FDA0003837932190000129
{ e segi ,e segj The larger value in }:
Figure FDA00038379321900001210
wherein ,esegj Is a contour line subl j The number of contour points contained in the second segi segment;
Figure FDA0003837932190000131
Figure FDA0003837932190000132
respectively represent contour lines subl i ,subl i The upper segment number.
10. The intelligent splicing method for the cultural relic fragments based on the contour line features as claimed in claim 1, wherein the method comprises the following steps: in step 7-3, judging whether the iterative conversion times reach a preset maximum value iter max The value is [20,50 ]]A positive integer therebetween.
CN202211100410.4A 2022-09-08 2022-09-08 Ceramic fragment three-dimensional intelligent splicing method based on contour features Pending CN116310244A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116602664A (en) * 2023-07-17 2023-08-18 青岛市胶州中心医院 Comprehensive diagnosis and treatment nursing system for neurosurgery patients

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116602664A (en) * 2023-07-17 2023-08-18 青岛市胶州中心医院 Comprehensive diagnosis and treatment nursing system for neurosurgery patients
CN116602664B (en) * 2023-07-17 2023-09-22 青岛市胶州中心医院 Comprehensive diagnosis and treatment nursing system for neurosurgery patients

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