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 PDFInfo
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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
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 Wherein M is the total number of fragments, +.>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 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,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)
step 2-3: calculate cultural relic fragment PC m Neighbor distance average value of all points in point cloud data of (a)Mean. Mu.of (A) m And standard deviation sigma m :
Step 2-4: judging the current point p is Neighbor distance average of (2)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 +.>
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,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)And the projection point set of each neighborhood point in the k' neighborhood point set +.>
Step 3-3: constructing an included angle sequence: to be used forAs a reference vector, a neighborhood vector is calculated>Angle with reference vector->Thereby generating the sequence of included angles->
Step 3-5: find the adjacent included angle difference value sequence theta tar Maximum value of (2)Comparing with a preset included angle threshold value, if +.>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 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 oneFitting the B-spline function parameter equation, and sequentially selecting w contour points to fit the B-spline function parameter equation
Step 4-4: calculating the curvature of each contour line at each contour point one by one to obtain a curvature sequence
Step 4-5: extracting each ordered contour line point set one by oneIs characterized by: for curvature sequence->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 +.>Building contour lines subl for elements i Feature point set->The corresponding feature point index set is +.>
Step 4-6: calculating the current contour line subl one by one i To be compared with characteristic points Is a mathematical geometric feature of (a):
characteristic points to be comparedFeature points adjacent to the left side->Constituent left-neighbor vectorIs->The method comprises the following steps:
wherein ,for->Three-dimensional space coordinates of>Is taken as a pointIs a three-dimensional space coordinate of (2);
characteristic points to be comparedFeature points adjacent to the right side->Right neighbor vector of the compositionIs->The method comprises the following steps:
wherein ,for->Three-dimensional space coordinates of>For->Is a three-dimensional space coordinate of (2);
characteristic points to be comparedIncluded angle of vector formed by the adjacent characteristic points>Is vector quantityVector->Included angle of (2):
building a contour line subl i Characteristic representation matrix of (a)The r-th behavior in the matrix is to be compared with the feature point +.>Feature vector +.>
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):
The number of points involved; the D function is calculated by the following steps:
Calculating contour lines subl i And subl j Flexibility ratio variability of (c):
the D function calculation mode is as follows:
Calculating contour lines subl i And subl j Left neighbor vector mode difference of (c):
calculating contour lines subl i And subl j Right neighbor vector mode difference of (c):
calculating contour lines subl i And subl j Is different from the left and right adjacent vector included angles:
wherein ,is a contour line subl i The included angle formed by the q-th feature point and the left and right adjacent vectors,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):
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 lineRespectively forming a section, calculating the chord diameter length in each section> and />Construction of subl i and sublj Is a set of chord and perpendicular diameter lengths of the contour section>And (3) with
wherein ,and->Point +.>And (4) point->Corresponding to the length of the chord diameter, the +.>Is a contour line subl i Contour points in the upper segi segment, zi=1, & e segi ;/>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; /> Respectively represent contour lines subl i ,subl i The upper section number,/-> and />Two contour lines subl respectively i ,subl j The number of segments in (a);
subl i and sublj Profile segment chord sag lengthAnd->Is calculated by the same method as that of the subl i Length of chord diameter of contour segment +.>The calculation method of (1) is as follows:
wherein ,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 +.>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 +.>Is the vector of the endpoint, +.>For vector->Is (are) mould>For vector->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 sectionAnd->Length of the longest common subsequence of +.> For matrix->Zj column element, zi=1,.. segi ;zj=1,...,e segj ;/>If it isv_lcs is a preset threshold value, contour line subl i ,subl j The corresponding segment in (a) is a common subsequence; /> Otherwise, let go of>
Step 6-3: segment similarity judgment: calculating a threshold ω for similarity discrimination sim :
ω sim =|setl max -setl min | (22)
If it isJudging that the segments are similar; setl min 、setl max Respectively is a chord diameter length set +.>And->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 distributionTransformation relationTransformation parameters->From the rotation parameter->Translation parameter->Scaling parameter->Composition;
solving maximized contour subl j Contour point set PL of (1) j Obtaining a gaussian mixture distribution transformation parameter from likelihood functions of (a)Transformation relation->
Step 7-2: virtual splicing:
wherein ,PLi ' PL i Iterating the transformed result;
the deviation is:
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)
Further, a contour line subl i And subl j Is set of contour points of (a) And (3) withIs equal to->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)
And->Outline subl respectively i And subl j The centroid of the contour point set of (2) is calculated by:
wherein ,respectively contour point sets PL i With PL j Point in->The matrices V and U are defined by the matrix->Performing SVD decomposition h=u Σv T The sigma is obtained as a diagonal matrix; /> and />The method comprises the following steps of:
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:
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 ),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 setThrough the visual window interface, according to the contour point selected by the user +.>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 calculatedAnd->Length of the longest common subsequence of +.>When in use, will->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 ∈>And->{ e segi ,e segj The larger value in }:
wherein ,esegj Is a contour line subl j The number of contour points contained in the second segi segment; 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 Wherein M is the total number of fragments, +.>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 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,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) areCalculating the current point p is =(x is ,y is ,z is ),/>With current cultural relic fragment PC m Other points p in the point cloud data of (a) js =(x js ,y js ,z js ),And is not equal to js distance is,js :
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)
step 2-3: calculate cultural relic fragment PC m Neighbor distance average value of all points in point cloud data of (a)Mean. Mu.of (A) m And standard deviation sigma m :
Step 2-4: judging the current point p is Neighbor distance average of (2)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 +.>
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 containsThe 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,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)Calculating the current point p tar =(x tar ,y tar ,z tar ),/>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 ,/> And tar+. oth:
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:
after matrixing, solving for X' to obtain (o 1 ,o 2 ,o 3 ):
AX′=b
wherein ,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)And the projection point set of each neighborhood point in the k' neighborhood point set +.>
Step 3-3: constructing an included angle sequence: to be used forAs a reference vector, a neighborhood vector is calculated>Angle with reference vector->Thereby generating the sequence of included angles->
Step 3-5: find the adjacent included angle difference value sequence theta tar Maximum value of (2)Comparing with a preset included angle threshold value, if +.>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;
wherein ,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 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 pointsAs the source point, with the current contour line subl i Middle unordered point +.> And (2) the source point->Distance of (2) start,nos Sequencing from small to large to obtain ordered contour line point set +.> Is the ith contour line subl i Profile points in (a):
wherein ,(xstart ,y start ,z start ) Is taken as a pointCoordinates of (x) nos ,y nos ,z nos ) For->Is used for the purpose of determining the coordinates of (a),
storing the ordered contour line point set;
step 4-3: for each ordered contour line point set one by oneFitting the B-spline function parameter equation, and sequentially selecting w contour points to fit the B-spline function parameter equation
The present embodiment uses the current wheelPart point of the profile 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:
step 4-4: calculating the curvature of each contour line at each contour point one by one to obtain a curvature sequence
The solving process comprises the following steps:
step 4-5: extracting each ordered contour line point set one by oneIs characterized by: for curvature sequence->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 +.>Building contour lines subl for elements i Feature point set->The corresponding feature point index set is +.>
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 Is a mathematical geometric feature of (a):
characteristic points to be comparedFeature points adjacent to the left side->Constituent left-neighbor vectorIs->The method comprises the following steps:
wherein ,for->Three-dimensional space coordinates of>Is taken as a pointIs a three-dimensional space coordinate of (2);
characteristic points to be comparedFeature points adjacent to the right side->Right neighbor vector of the compositionIs->The method comprises the following steps:
wherein ,for->Three-dimensional space coordinates of>Is taken as a pointIs a three-dimensional space coordinate of (2);
characteristic points to be comparedIncluded angle of vector formed by the adjacent characteristic points>For vector->Vector->Included angle of (2):
building a contour line subl i Characteristic representation matrix of (a)The r-th behavior in the matrix is to be compared with the feature point +.>Feature vector +.>
And->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):
wherein i=1,.. subL ;j=1,...,K subL ; Respectively the contour lines subl i And subl j The number of points involved; the D function is calculated by the following steps:
Calculating contour lines subl i And subl j Flexibility ratio variability of (c):
the D function calculation mode is as follows:
Calculating contour lines subl i And subl j Left neighbor vector mode difference of (c):
calculating contour lines subl i And subl j Right neighbor vector mode difference of (c):
calculating contour lines subl i And subl j Is different from the left and right adjacent vector included angles:
wherein ,is a contour line subl i The included angle formed by the q-th feature point and the left and right adjacent vectors,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):
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 lineRespectively forming a section, calculating the chord diameter length in each section> and />Construction of subl i and sublj Is a set of chord and perpendicular diameter lengths of the contour section>And (3) with
wherein ,and->Point +.>And (4) point->Corresponding to the length of the chord diameter, the +.>Is a contour line subl i Contour points in the upper segi segment, zi=1, & e segi ;/>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; /> Respectively represent contour lines subl i ,subl i The upper section number,/-> and />Two contour lines subl respectively i ,subl j The number of segments in (a);
subl i and sublj Profile segment chord sag lengthAnd->Is calculated by the same method as that of the subl i Length of chord diameter of contour segment +.>The calculation method of (1) is as follows:
wherein ,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 +.>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 +.>Is the vector of the endpoint, +.>For vector->Is (are) mould>For vector->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 sectionAnd->Length of the longest common subsequence of +.> For matrix->Zj column element, zi=1,.. segi ;zj=1,...,e segj ;/>If->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 +.>Otherwise, let go of>
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 isJudging that the segments are similar; setl min 、setl max Respectively is a chord diameter length set +.>And->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 distributionTransformation relation->Transformation parameters->From the rotation parameter->Translation parameter->Scaling parameter->Composition;
wherein ,the weight value is preset; delta 2 Is a preset model parameter; />The method is obtained by the following steps: from the following components
solving maximized contour subl j Contour point set PL of (1) j Obtaining a gaussian mixture distribution transformation parameter from likelihood functions of (a)Transformation relation->
Step 7-2: virtual splicing:
wherein ,PLi ' PL i Iterating the transformed result;
the deviation is:
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)
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) And->Are equal to each other in the number of pointsThe 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)
And->Outline subl respectively i And subl j The centroid of the contour point set of (2) is calculated by:
wherein ,respectively contour point sets PL i With PL j Point in->The matrices V and U are defined by the matrix->Performing SVD decomposition h=u Σv T The sigma is obtained as a diagonal matrix; /> and />The method comprises the following steps of:
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 calculatedAnd->Length of the longest common subsequence of +.>When in use, will->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 +.>And->{ e segi ,e segj The larger value in }:
wherein ,esegj Is a contour line subl j The number of contour points contained in the second segi segment; 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 setThrough the visual window interface, according to the contour point selected by the user +.>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 Wherein M is the total number of fragments, +.>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 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,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)
step 2-3: calculate cultural relic fragment PC m Neighbor distance average value of all points in point cloud data of (a)Mean. Mu.of (A) m And standard deviation sigma m :
Step 2-4: judging the current point p is Neighbor distance average of (2)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 +.>
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,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)And the projection point set of each neighborhood point in the k' neighborhood point set +.>
Step 3-3: constructing an included angle sequence: to be used forAs a reference vector, a neighborhood vector is calculated>Angle with reference vector->Thereby generating the sequence of included angles->
Step 3-5: find the adjacent included angle difference value sequence theta tar Maximum value of (2)Comparing with a preset included angle threshold value, ifIf 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 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 oneFitting a B-spline function parameter equation, and sequentially selecting w wheelsProfile point fitting B-spline function parameter equation
Step 4-4: calculating the curvature of each contour line at each contour point one by one to obtain a curvature sequence
Step 4-5: extracting each ordered contour line point set one by oneIs characterized by: for curvature sequence->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 +.>Building contour lines subl for elements i Feature point set->The corresponding feature point index set is +.>
Step 4-6: calculating the current contour line subl one by one i To be compared with characteristic points Is a mathematical geometric feature of (a):
characteristic points to be comparedFeature points adjacent to the left side->Constituent left neighbor vector->Is a mold of (2)The method comprises the following steps:
wherein ,for->Three-dimensional space coordinates of>Is taken as a pointIs a three-dimensional space coordinate of (2);
characteristic points to be comparedFeature points adjacent to the right side->Right neighbor vector of the composition->Is->The method comprises the following steps:
wherein ,for->Three-dimensional space coordinates of>For->Is a three-dimensional space coordinate of (2);
characteristic points to be comparedIncluded angle of vector formed by the adjacent characteristic points>Is vector quantityVector->Included angle of (2):
building a contour line subl i Characteristic representation matrix of (a)The r-th behavior in the matrix is to be compared with the feature point +.>Feature vector +.>
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):
wherein i=1, …, K subL ;j=1,…,K subL ; Respectively the contour lines subl i And subl j The number of points involved; the D function is calculated by the following steps:
Calculating contour lines subl i And subl j Flexibility ratio variability of (c):
the D function calculation mode is as follows:
Calculating contour lines subl i And subl j Left neighbor vector mode difference of (c):
calculating contour lines subl i And subl j Right neighbor vector mode difference of (c):
calculating contour lines subl i And subl j Is different from the left and right adjacent vector included angles:
wherein ,is a contour line subl i The included angle formed by the q-th feature point and the left and right adjacent vectors,/>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):
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 lineRespectively forming a section, calculating the chord diameter length in each section> and />Construction of subl i and sublj Is a set of chord and perpendicular diameter lengths of the contour section>And->
wherein ,and->Point +.>And (4) point->Corresponding to the length of the chord diameter, the +.>Is a contour line subl i Contour points in the upper segi segment, zi=1, …, e segi ;/>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; /> Respectively represent contour lines subl i ,subl i The upper section number,/-> and />Two contour lines subl respectively i ,subl j The number of segments in (a);
subl i and sublj Profile segment chord sag lengthAnd->Is calculated by the same method as that of the subl i Length of chord diameter of contour segment +.>The calculation method of (1) is as follows:
wherein ,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 +.>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 +.>Is the vector of the end point and,for vector->Is (are) mould>For vector->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 sectionAnd->Length of the longest common subsequence of +.> For matrix->Zj column element, zi=1, …, e segi ;zj=1,…,e segj ;/>If it isDelta_lcs is a preset threshold value, contour line subl i ,subl j The corresponding segment in (a) is a common subsequence; /> Otherwise, let go of>
Step 6-3: segment similarity judgment: calculating a threshold ω for similarity discrimination sim :
ω sim =|setl max -setl min | (22)
If it isJudging that the segments are similar; setl min 、setl max Respectively is a chord diameter length set +.>And->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 distributionTransformation relationTransformation parameters->From the rotation parameter->Translation parameter->Scaling parameter->Composition;
solving maximized contour subl j Contour point set PL of (1) j Obtaining a gaussian mixture distribution transformation parameter from likelihood functions of (a)Transformation relation->
Step 7-2: virtual splicing:
wherein ,PLi ' PL i Iterating the transformed result;
the deviation is:
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)
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) And->Is equal to->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)
And->Outline subl respectively i And subl j The centroid of the contour point set of (2) is calculated by:
wherein ,respectively contour point sets PL i With PL j Point in->The matrices V and U are defined by the matrix->Performing SVD decomposition h=u Σv T The sigma is obtained as a diagonal matrix; /> and />The method comprises the following steps of:
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:
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 ),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 setThrough the visual window interface, according to the contour point selected by the user +.>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 calculatedAnd->Length of the longest common subsequence of +.>When in use, will->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 ∈>And->{ e segi ,e segj The larger value in }:
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.
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