CN109816771A - A kind of automatic recombination method of cultural relic fragments of binding characteristic point topology and geometrical constraint - Google Patents
A kind of automatic recombination method of cultural relic fragments of binding characteristic point topology and geometrical constraint Download PDFInfo
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Abstract
The invention discloses the automatic recombination method of cultural relic fragments of a kind of binding characteristic point topology and geometrical constraint, method includes: that n characteristic point of each plane of disruption of each fragment of historical relic is extracted using curvature function；Topology reconstruction is carried out to characteristic point, constructs n rank cum rights complete graph；The minimum, maximum spanning tree using Prime algorithm and improved Prime algorithm construction；Calculate minimum cost and and maximum cost and, quickly screen potential matching fragment using adjacent constraint；Best match fragment is found out using the maximum Hausdorff distance for mismatching formula and calculating two feature strings with the maximum curvature of characteristic point, minimum curvature construction feature string again, finally fragment is completed using rigid body translation and recombinates.The method recombinated the present invention overcomes tradition based on geometric drive leads to the problem of error hiding vulnerable to influence of noise, and fragment relatively complete for Fracture Surface Information has the advantages that recombination efficiency height and result accuracy rate are high.
Description
Technical field
The present invention relates to computer graphic image process field, in particular to a kind of binding characteristic point topology and geometrical constraint
The automatic recombination method of cultural relic fragments.
Background technique
Historical relic is the time-honored cultural infrastructure in China and wisdom crystallization.Due to the influence of the factors such as natural and artificial, lead
Cause most of historical relics that broken or imperfect state is presented.Traditional historical relic reparation repairs speed by manual operations of gaining knowledge of engaging in archaeological studies
Degree is slow, accuracy is low, there are secondary destructions.In recent years, there is high speed, convenient, nothing using area of computer aided historical relic Virtual restora- tion
The advantages such as destruction, improve the efficiency of historical relic reparation, have vital meaning to historical relic's protection and recovery.
According to the thickness information of historical relic, automate historical relic Virtual restora- tion object and be broadly divided into two classes: thin wall historical relic is broken
Piece and non-thin wall cultural relic fragments two major classes.Either thin wall cultural relic fragments are also non-thin wall cultural relic fragments, and recombination is asked
Topic is extensive, non-linear, multiple target a Combinatorial Optimization np hard problem.For thin wall cultural relic fragments, base is generallyd use
In the geometrical characteristic search pairing fragment of contour curve, fragment recombination is realized；For the recombination of non-thin wall fragment, generally use
Pairing fragment is searched for based on fragment plane of disruption geometrical characteristic, realizes the recombination of fragment.
However, being directed to non-thin wall cultural relic fragments, the above method matches clock synchronization in search, is using fracture facial contour mostly
The geological information on all vertex on line or relief region, geological information are easy affected by noise in estimation；Secondly, based on single
The geometrical characteristic matching of a point has randomness, ignores topology information between points, will cause error hiding, causes to recombinate
Journey will appear phenomena such as dislocation, infiltration.
Summary of the invention
It is an object of the invention to be easy affected by noise to generate mistake based on the method for geometric drive recombination for tradition
The problem of matching, provides the automatic recombination method of cultural relic fragments of a kind of binding characteristic point topology and geometrical constraint.
In order to achieve the above objectives, the invention adopts the following technical scheme:
A kind of automatic recombination method of cultural relic fragments of binding characteristic point topology and geometrical constraint, comprising the following steps:
Step 1, for the fragment of historical relic, plane of disruption segmentation is carried out respectively, obtains multiple planes of disruption of each fragment, then
N characteristic point of each plane of disruption is extracted respectively；
Step 2, topology reconstruction is carried out to n characteristic point of each plane of disruption, using each characteristic point as node, with characteristic point
Euclidean distance between spatial position connects the weight on side between two nodes, obtains n rank cum rights Undirected graph on each plane of disruption；
Step 3, for the cum rights Undirected graph, generate on each plane of disruption respectively the minimum spanning tree of characteristic point and
Maximum spanning tree；
Step 4, calculate separately the minimum spanning tree, maximum spanning tree minimum cost and and maximum cost and, utilize
Adjacent constraint, screens potential matching fragment, forms potential fragment collection；
Step 5, on fragment to be matched each plane of disruption and potential fragment concentrate each fracture of each fragment
Face calculates separately the feature string of the plane of disruption, then by calculating Hausdorff distance, find potential fragment concentrate with it is to be matched broken
The fragment of each plane of disruption best match of on piece carries out fragment recombination.
Further, each plane of disruption on fragment to be matched and potential fragment concentrate each fragment
Each plane of disruption, calculate separately the feature string of the plane of disruption, then by calculating Hausdorff distance, find potential fragment and concentrate
With the fragment of plane of disruption best match each on fragment to be matched, fragment recombination is carried out, comprising:
For each plane of disruption on fragment to be matched, by all characteristic points on the plane of disruption, using maximum curvature, most
Small curvature is configured with ordered pair, obtains the feature string of the plane of disruption；Potential fragment is obtained using same method and concentrates each plane of disruption
Feature string；
The fracture that formula calculates the plane of disruption feature string of fragment to be matched, potential fragment concentrates fragment is mismatched using maximum
Hausdorff distance between region feature string finds out potential fragment and concentrates this with the minimum person of outstanding talent of the plane of disruption of fragment to be matched generation more
Then the fragment of husband's distance carries out the recombination of fragment to be matched and best match fragment as best match fragment.
Further, the formula of the corresponding adjacency matrix of n rank cum rights Undirected graph are as follows:
Wherein, D is the corresponding adjacency matrix of n rank cum rights Undirected graph, dijIndicate the power between any two characteristic point
Value,I, j=1,2 ..., n, n are characterized number a little, pi,pjFor fragment
Any two characteristic point on the plane of disruption, coordinate are respectively (xi,yi,zi),(xj,yj,zj)。
Further, in step 3, the minimum spanning tree of characteristic point on each plane of disruption is generated, comprising:
Step 3.1, to G=(V, { E }), initial p={ p0}(p0∈ V), FE=Φ；
Wherein, G=(V, { E }) is the cum rights Undirected graph of one of plane of disruption characteristic point construction of any fragment, V
Refer to all set of characteristic points of one of plane of disruption of any fragment, the set on the side of { E } between all characteristic points, FE is
The set on the side in minimum spanning tree, P are characterized the subset of point set V, p0For the arbitrary characteristics point in V, Φ is empty set；
Step 3.2, from (p when selecting a weight the smallest in of all p ∈ P, v ∈ V-P0,v0) and be added set FE,
Simultaneously by v0P is added；
Wherein, p is characterized the characteristic point in a subset P, and v is a characteristic point in V-P, (p0,v0) it is minimum weight
Side；
Step 3.3, it repeats step 3.2 to stop operation when p=v, obtain on one of plane of disruption of any fragment
The minimum spanning tree T of characteristic pointmin={ P, { FE } }.
Further, in step 3, the maximum spanning tree of characteristic point on each plane of disruption is generated, comprising:
Step 3.4, to G=(V, { E }), initial p={ p0}(p0∈ V), FEM=Φ；
Wherein, G=(V, { E }) is the cum rights Undirected graph of the one of plane of disruption characteristic point construction of any fragment, and V refers to
Be feature point set on the fragment plane of disruption, the set on the side of { E } between all characteristic points, FEM is the side in maximum spanning tree
Set, P is characterized the subset of point set V, p0For the arbitrary characteristics point in V, Φ is empty set；
Step 3.5, from the while (p for selecting a maximum weight in of all p ∈ P, v ∈ V-P0,v0) and be added set FEM,
Simultaneously by v0P is added；Wherein p is characterized the characteristic point in a subset P, v0It is a characteristic point in V-P；
3.6, it repeats step 3.5 and stops operation when p=v, obtain characteristic point on each plane of disruption of each fragment
Maximum spanning tree Tmax={ P, { FEM } }.
Further, in step 4, the formula of the adjacent constraint are as follows:
Wherein, A, B are respectively the plane of disruption of two fragments, the minimum cost of the minimum spanning tree of characteristic point on the A plane of disruption
With and maximum spanning tree maximum cost and respectively MinA, MaxA；The minimum generation of the minimum spanning tree of characteristic point on the B plane of disruption
Valence and and maximum spanning tree maximum cost and respectively MinB, MaxB.
Further, in step 5, the maximum mismatched degree formula are as follows:
H (S1, S2)=max (h (S1, S2), h (S2, S1)) formula 4
Wherein, S1 is the feature string of the plane of disruption of fragment to be matched, and S2 is the feature that potential fragment concentrates the fragment plane of disruption
String, h (S1, S2) are the oriented Hausdorff distance of S1 to S2, and h (S2, S1) is the oriented Hausdorff distance of S2 to S1, and a is
The ordered pair that the maximum principal curvatures k1 of any feature point and minimum principal curvatures k2 is constituted in S1；B be S2 in any feature point most
The ordered pair that big principal curvatures k1 and minimum principal curvatures k2 is constituted.
Compared with prior art, the present invention has following technical effect that
1. feature of present invention point negligible amounts, calculation amount is small, fragment recombination efficiency can be effectively improved, in historical relic repair process
In, it using the present invention, can effectively improve recovery speed, reduce restored cycle；
2. the present invention combines the topology and geometrical characteristic of selected characteristic point, pairing fragment can be effectively searched for, with tradition
Recombination method based on single geometric drive is compared, and is avoided and is generated error hiding, recombination result has infiltration, texture are discontinuous to ask
Topic.
Detailed description of the invention
Fig. 1 is the automatic recombination method flow chart of cultural relic fragments of binding characteristic point topology and geometrical constraint of the invention；
Fig. 2 is cultural relic fragments model schematic；Wherein, (a) is the fragment 1 of the unearthed G10-57 figurines in terra cotta warriors and horses 1 hole,
(b) be fragment 2, (c) of the unearthed G10-57 figurines in terra cotta warriors and horses 1 hole be the broken of the G10-57 figurines that terra cotta warriors and horses 1 hole is unearthed
Piece 3, (d) are the fragment 4 of the unearthed G10-57 figurines in terra cotta warriors and horses 1 hole；
Fig. 3 is the schematic diagram that potential fragment is quickly screened using minimum, maximum spanning tree；Wherein, (a) be A fragment some
The minimum spanning tree of the plane of disruption is (c) maximum spanning tree of some plane of disruption of A fragment, (b) most for some plane of disruption of B fragment
Small spanning tree is (d) maximum spanning tree of some plane of disruption of B fragment；
Fig. 4 is the characteristic point corresponding relationship of fragment 3 and fragment 4；
Fig. 5 is fragment model recombination result figure and its recombination details display diagram；Wherein, (a) is that fragment 1 and fragment 2 recombinate
Result figure (b) recombinates result figure and its detail view for fragment 1 and fragment 2, (c) recombinates result figure for fragment 3 and fragment 4, (d)
Result figure and its detail view are recombinated for fragment 3 and fragment 4；It (e) is that fragment 1, fragment 2, fragment 3 and fragment 4 recombinate result figure,
It (f) is fragment 1, fragment 2, fragment 3 and fragment 4 recombinate result figure and its detail view.
Specific embodiment
The object of the present invention is to provide the automatic recombination method of cultural relic fragments of a kind of binding characteristic point topology and geometrical constraint,
Pairing fragment is searched for using two-stage matching strategy, flow chart of the invention is as shown in Figure 1, gradually judge the syntople of fragment；
Fragment relatively complete for Fracture Surface Information, the topology and geological information of present invention combination fragment plane of disruption characteristic point are realized broken
The automatic recombination of piece.
As shown in Figures 1 to 5, the invention discloses the cultural relic fragments of a kind of binding characteristic point topology and geometrical constraint are automatic
Recombination method, detailed step are as follows:
Step 1, for the fragment of historical relic, plane of disruption segmentation is carried out respectively, obtains multiple planes of disruption of each fragment, then
N characteristic point of each plane of disruption is extracted respectively.
According to the thickness information of historical relic, automate historical relic Virtual restora- tion object and be broadly divided into two classes: thin wall fragment and
Non- thin wall fragment two major classes, this programme is non-thin wall fragment model, i.e. the fragment of the historical relic refers to non-thin-walled
The fragment model of class historical relic.In the present embodiment, using the fragment model of historical relic terra cotta warriors and horses, Q fragment, Q >=2 are shared；Tool
Body, the fragment 1 for choosing terra cotta warriors and horses 1 unearthed G10-57 figurines in hole arrives fragment 4, and each fragment has the Z plane of disruption, Z >=1.
The plane of disruption number of each fragment is determined according to practical historical relic, can be the same or different, the plane of disruption point based on method arrow
It cuts algorithm and carries out plane of disruption segmentation, refer to and correctly identify fragment with the plane of disruption partitioning algorithm based on method arrow that Lie group brightness proposes
The plane of disruption and original face, all planes of disruption are split, and extract the plane of disruption respectively to each fragment, are extracted using curvature function
The significant n characteristic point of the concavity and convexity of each plane of disruption out is to extract n spy to each plane of disruption respectively using curvature function
Sign point.Each extracted feature point number of the plane of disruption is identical, if feature point number is not identical, may generate error hiding or
Person is the incorrect situation of matching, and n characteristic point value range is 10-15.
Step 2, topology reconstruction is carried out to n characteristic point of each plane of disruption, using each characteristic point as node, with characteristic point
Euclidean distance between spatial position connects the weight on side between two nodes, obtains n rank cum rights Undirected graph on each plane of disruption；
Specifically, the building method of the corresponding adjacency matrix of n rank cum rights Undirected graph is as follows:
If the n characteristic point extracted on any one plane of disruption is respectively p1,p2,...,pn, coordinate is respectively (x1,y1,
z1),(x2,y2,z2),…,(xn,yn,zn), it take the Euclidean distance between any two characteristic point as the weight on the side of two nodes,
Construct the corresponding adjacency matrix of n rank cum rights Undirected graph are as follows:
Wherein, D is the corresponding adjacency matrix of n rank cum rights Undirected graph, dijIndicate the power between any two characteristic point
Value,Wherein i, j=1,2 ..., n, n are characterized number a little, pi,pjFor
Any two characteristic point on the fragment plane of disruption, coordinate are respectively (xi,yi,zi),(xj,yj,zj)。
Analog reconstruction is being carried out in the present solution, cultural relic fragments are input in computer, n rank cum rights Undirected graph exists
Computer-internal is stored by the way of adjacency matrix, thus provide be n rank cum rights Undirected graph adjacency matrix；
The weight for connecting side between two nodes with the Euclidean distance between characteristic point spatial position is obtained as the element in adjacency matrix
To adjacency matrix, it is equivalent to the n rank cum rights Undirected graph constructed；N rank cum rights Undirected graph and adjacency matrix are one
One-to-one correspondence, the corresponding adjacency matrix of a n rank cum rights complete graph；Adjacency matrix is by belonging on the same plane of disruption
Any two characteristic point between weight a matrix being combined into of collection.
Step 3, for the cum rights Undirected graph, generate on each plane of disruption respectively the minimum spanning tree of characteristic point and
Maximum spanning tree.
Specifically, Prime is utilized to the n rank cum rights Undirected graph on each plane of disruption of each fragment in this programme
(Pu Limu) algorithm is handled, and the minimum spanning tree of characteristic point on each plane of disruption of each fragment is obtained；To each fragment
Each plane of disruption on n rank cum rights Undirected graph, using improve Prime algorithm handled, obtain the every of each fragment
The maximum spanning tree of characteristic point on a plane of disruption.
Specifically, to the n rank cum rights Undirected graph on each plane of disruption of each fragment, using Prime algorithm construction
Minimum spanning tree, the specific steps are as follows:
Assuming that G=(V, { E }) is the cum rights Undirected graph of one of plane of disruption characteristic point construction of any fragment,
In, V refers to all set of characteristic points of one of plane of disruption of any fragment, the set on the side of { E } between all characteristic points,
If FE is the set on the side in minimum spanning tree；
Step 3.1, to G=(V, { E }), initial p={ p0}(p0∈ V), FE=Φ, P are characterized the subset of point set V, p0For
Arbitrary characteristics point in V, Φ is empty set, completes initialization operation；
Step 3.2, from (p when selecting a weight the smallest in of all p ∈ P, v ∈ V-P0,v0) and be added set FE,
Simultaneously by v0P is added；Wherein, p is characterized the characteristic point in a subset P, and v is a characteristic point in V-P, (p0,v0) it is minimum
The side of weight can get the intermediate state of minimum spanning tree by step 3.2；
Step 3.3, it repeats step 3.2 to stop operation when p=v, obtains one of plane of disruption of any fragment
Minimum spanning tree Tmin={ P, { FE } }.
In the present solution, Prime algorithm is all utilized to the n rank cum rights Undirected graph on each plane of disruption of each fragment,
Obtain the minimum spanning tree of the n rank cum rights Undirected graph on each plane of disruption of each fragment, detailed process are as follows: to any broken
The cum rights Undirected graph G=(V, { E }) of one of plane of disruption characteristic point construction of piece, in a plane of disruption of any fragment
All set of characteristic points V in, select any one characteristic point initialize, by the point p of initialization0It is put into characteristic point subset P, this
A characteristic point subset P is the subset of all set of characteristic points V, and the set FE on the side established in minimum spanning tree is simultaneously set as empty
Collection completes initialization operation；Belong in characteristic point subset p ∈ P and all set of characteristic points from characteristic point and is not belonging to feature idea
In all sides of the set v ∈ V-P of collection, the smallest side (p of a weight is selected0,v0), and the collection on the side of minimum spanning tree is added
FE is closed, can get the intermediate state of minimum spanning tree；When characteristic point subset is identical as all set of characteristic points, that is, P=V
When, stop the operation for obtaining the intermediate state of minimum spanning tree, obtains the minimum of one of plane of disruption of any fragment and generate
Set Tmin={ P, { FE } }；To the n rank cum rights Undirected graph on each plane of disruption of each fragment, Prime algorithm is all utilized,
Finally obtain the minimum spanning tree of the n rank cum rights Undirected graph on each plane of disruption of each fragment.
Using improved Prime algorithm construction maximum spanning tree, the specific steps are as follows:
Assuming that G=(V, { E }) be to the cum rights that constructs of the one of plane of disruption characteristic point of any fragment it is undirected completely
Figure, wherein V refers to feature point set on the fragment plane of disruption, the set on the side of { E } between all characteristic points, if FEM is maximum
The set on the side in spanning tree.
Step 3.4, to G=(V, { E }), initial p={ p0}(p0∈ V), FEM=Φ, P are characterized the subset of point set V, p0
For the arbitrary characteristics point in V, Φ is empty set, completes initialization operation；
Step 3.5, from the while (p for selecting a maximum weight in of all p ∈ P, v ∈ V-P0,v0) and be added set FEM,
Simultaneously by v0P is added, wherein p is characterized the characteristic point in a subset P, v0It is a characteristic point in V-P, by step 3.4
It can get the intermediate state of maximum spanning tree；
Step 3.6, it repeats step 3.5 to stop operation when p=v, obtains feature on each plane of disruption of each fragment
The maximum spanning tree Tmax={ P, { FEM } } of point.
In the present solution, all utilizing improvement Prime to the n rank cum rights Undirected graph on each plane of disruption of each fragment
Algorithm obtains the maximum spanning tree of the n rank cum rights Undirected graph on each plane of disruption of each fragment, detailed process are as follows: right
The cum rights Undirected graph G=(V, { E }) of one of plane of disruption characteristic point construction of any fragment, at one of any fragment
In all set of characteristic points V of the plane of disruption, any one characteristic point is selected to initialize, by the point p of initialization0It is put into feature idea
Collect P, this characteristic point subset P is the subset of all set of characteristic points V, and the set FEM on the side established in maximum spanning tree is simultaneously set
It is set to empty set, completes initialization operation；Belong in characteristic point subset p ∈ P and all set of characteristic points from characteristic point and is not belonging to spy
In all sides of the set v ∈ V-P of sign point subset, the side (p an of maximum weight is selected0,v0), and maximum spanning tree is added
The set FEM on side can get the intermediate state of maximum spanning tree；When characteristic point subset is identical as all set of characteristic points,
When being exactly P=V, stops the operation for obtaining the intermediate state of maximum spanning tree, obtain one of plane of disruption of any fragment
Maximum spanning tree Tmax={ P, { FEM } }；To the n rank cum rights Undirected graph on each plane of disruption of each fragment, all utilize
Prime algorithm finally obtains the minimum spanning tree of the n rank cum rights Undirected graph on each plane of disruption of each fragment.
Step 4, the minimum spanning tree to characteristic point on each plane of disruption and maximum spanning tree calculate separately the most your pupil
Cheng Shu, maximum spanning tree minimum cost and and maximum cost and, constrained using adjacent, screen potential matching fragment, formed latent
In fragment collection.
In the present solution, to the minimum spanning tree of characteristic point on each plane of disruption of each fragment, calculate minimum cost and, it is right
The maximum spanning tree of characteristic point on each plane of disruption of each fragment, calculate maximum cost and；Utilize the minimum of minimum spanning tree
Cost and and maximum spanning tree maximum cost and as binary group, define adjacent constraint with binary group, quickly screen potential
With fragment, potential matching fragment refers to the matching fragment for meeting adjacent constraint, these potentially match fragment and form potential fragment
Collection.Using the method for adjacent constraint are as follows:
If A, B is respectively the plane of disruption of two fragments, on the A plane of disruption minimum cost of the minimum spanning tree of characteristic point and and
The maximum cost of maximum spanning tree and respectively MinA, MaxA；On the B plane of disruption minimum cost of the minimum spanning tree of characteristic point and
And the maximum cost and respectively MinB, MaxB of maximum spanning tree.Ideally, if A, B plane of disruption are the disconnected of exact matching
Broken face, then MinA=MinB and MaxA=MaxB.However under actual conditions, there are certain errors, therefore define adjacent constraint
Formula are as follows:
In formula 2, formula 3, ε1,ε2For empirical value, ε1And ε2Value is between 0.3-0.8.
This programme be according to formula 2 and formula 3, quickly to screen potential matching fragment, characteristic point institute structure on the plane of disruption of fragment
At minimum spanning tree minimum cost and and maximum spanning tree maximum cost and simultaneously meet formula 2 and formula 3, then two fracture
Face is possible to match, and two fragments where two planes of disruption belong to potential matching fragment, will meet formula 2 and formula 3 simultaneously
The set of matching fragment composition forms potential fragment collection；The minimum spanning tree constituted for characteristic point on the plane of disruption of fragment
Minimum cost and and maximum spanning tree maximum cost and only meet formula 2 or formula 3, and be unsatisfactory for formula 2 and formula 3, then two fractures
Two fragments where face are not belonging to matching fragment, and two planes of disruption centainly mismatch.
Step 5, on fragment to be matched each plane of disruption and potential fragment concentrate each fracture of each fragment
Face calculates separately the feature string of the plane of disruption, then by calculating Hausdorff distance, find potential fragment concentrate with it is to be matched broken
The fragment of each plane of disruption best match of on piece carries out fragment recombination.
In the present solution, to each fragment that the potential fragment that step 4 obtains is concentrated, by each plane of disruption of each fragment
On all characteristic points, utilize maximum curvature k1, minimum curvature k2Ordered pair is constructed, each plane of disruption of each fragment is obtained
Feature string.Similarly, to all characteristic points on each plane of disruption of fragment to be matched, maximum curvature k is utilized1, minimum curvature k2
Ordered pair is constructed, the feature string of each plane of disruption is obtained；Formula, which is mismatched, using maximum calculates fragment to be matched and potential fragment
Hausdorff (Hao Siduofu) distance for concentrating the feature string of the plane of disruption of fragment is measured to be matched using Hausdorff distance
Fragment and potential fragment concentrate the similarity degree of the feature string of the plane of disruption of fragment, find out potential fragment and concentrate and fragment to be matched
The plane of disruption generates the fragment of minimum Hausdorff distance, is exactly best match fragment, then carries out fragment to be matched and best
Recombination with fragment.
The similarity degree of two feature strings is measured using Hausdorff distance, the method for use is as follows:
If TP1={ p11,p12,...,p1nBe the plane of disruption to be matched feature point set, p1nIndicate the of the plane of disruption to be matched
N characteristic point calculates the maximum curvature k of each characteristic point1, minimum curvature k2, ordered pair is constituted, the plane of disruption to be matched is obtained
Feature string S1 are as follows: Represent one in multiple planes of disruption of fragment to be matched
The maximum principal curvatures of n-th of characteristic point of a plane of disruption,Represent a plane of disruption in multiple planes of disruption of fragment to be matched
N-th of characteristic point minimum principal curvatures；TP2={ p21,p22,...,p2nIt is the feature that potential fragment concentrates the fragment plane of disruption
Point set, p2nIndicate n-th of characteristic point of the plane of disruption, the feature string S2 of the plane of disruption are as follows: Represent potential fragment concentrate fragment multiple planes of disruption one of them is disconnected
The maximum principal curvatures of n-th of characteristic point of broken face,Represent one of plane of disruption that fragment concentrates multiple planes of disruption of fragment
N-th of characteristic point minimum principal curvatures；The similarity degree between two feature strings is measured using Hausdorff distance,
Maximum mismatched degree between Hausdorff distance two set of reflection, apart from similarity degrees smaller, then that explanation two is gathered
It is bigger.The formula of maximum mismatched degree are as follows:
H (S1, S2)=max (h (S1, S2), h (S2, S1)) formula 4
Wherein, S1 is the feature string of the plane of disruption of fragment to be matched, and S2 is the feature that potential fragment concentrates the fragment plane of disruption
String, h (S1, S2) are known as the oriented Hausdorff distance of S1 to S2, h (S2, S1) be known as the oriented Hausdorff of S2 to S1 away from
From H (S1, S2) is known as the oriented Hausdorff distance of maximum of S1 to S2, and also referred to as maximum mismatched degree, a is any in S1
The ordered pair that the maximum principal curvatures k1 and minimum principal curvatures k2 of characteristic point are constituted,Generation respectively
The maximum principal curvatures of the ith feature point of a plane of disruption in multiple planes of disruption of table fragment to be matched, minimum principal curvatures；b
For any feature point in S2 maximum principal curvatures k1 and minimum principal curvatures k2 constitute ordered pair,Respectively represent the jth for the plane of disruption that potential fragment is concentrated in multiple planes of disruption of fragment
The maximum principal curvatures of a characteristic point, minimum principal curvatures；Wherein, i, j=1,2 ..., n. definitionWherein | | | | it is vector field homoemorphism operation.
In the present solution, fragment to be matched and potential fragment can be obtained as final Hausdorff distance in H (S1, S2)
The similarity degree between the feature string of the plane of disruption of fragment is concentrated, concentrates each of fragment disconnected fragment to be matched and potential fragment
Broken face calculate Hausdorff distance, best match fragment can be found, then by rigid body translation by best match fragment with it is potential
Matching fragment is recombinated, and the recombination of partial piece can be completed by repeating the above steps.
It is illustrated in figure 3 the schematic diagram using the potential matching fragment of fast search of the present invention, (a) is some fracture of A fragment
The minimum spanning tree in face, minimum cost and be 15 (c) are the maximum spanning tree of some plane of disruption of A fragment, maximum cost and are
35, (b) be some plane of disruption of B fragment minimum spanning tree, minimum cost and be 15, (d) be some plane of disruption of B fragment maximum
Spanning tree, maximum cost and be 35, respectively by the minimum of some plane of disruption of A fragment, maximum cost and, some plane of disruption of B fragment
Minimum, maximum cost and it is found that the fragment concurrent fracture face A and B fragment concurrent fracture face may match, then carry out next
The geometric match of step can be obtained final best pairing by geometric match and cheat out as a result, being illustrated in figure 4 terra cotta warriors and horses 1
The characteristic point corresponding relationship of the fragment 3 of G10-57 figurines of soil, fragment 4；It is illustrated in figure 5 and utilizes method progress of the invention
Fragment recombination as a result, fragment be G10-57 figurines in partial piece, the fragment Fracture Surface Information is relatively complete, wherein black surround
Region is recombination position, but due to fragment texture and colouring information serious loss, the partial result after can not seeing recombination clearly, in order to
Convenient for observing and analyzing, position details being recombinated to it and is amplified, arrow meaning is respectively to recombinate details, can by recombination detail view
Know, infiltration, inconsistent phenomenon can't be generated with the method for the present invention.The experimental results showed that this method is opposite to Fracture Surface Information
Completely, the apparent fragment of feature can obtain good matching and recombination effect.
Claims (7)
1. the automatic recombination method of cultural relic fragments of a kind of binding characteristic point topology and geometrical constraint, which is characterized in that including following
Step:
Step 1, for the fragment of historical relic, plane of disruption segmentation is carried out respectively, the plane of disruption of each fragment is obtained, then extracts respectively
N characteristic point of each plane of disruption out；
Step 2, topology reconstruction is carried out to n characteristic point of each plane of disruption, using each characteristic point as node, with the feature space of points
Euclidean distance between position connects the weight on side between two nodes, obtains n rank cum rights Undirected graph on each plane of disruption；
Step 3, for the cum rights Undirected graph, the minimum spanning tree of characteristic point and maximum on each plane of disruption are generated respectively
Spanning tree；
Step 4, calculate separately the minimum spanning tree, maximum spanning tree minimum cost and and maximum cost and, utilize adjoining
Constraint, screens potential matching fragment, forms potential fragment collection；
Step 5, on fragment to be matched each plane of disruption and potential fragment concentrate each plane of disruption of each fragment,
The feature string of the plane of disruption is calculated separately, then by calculating Hausdorff distance, potential fragment is found and concentrates and fragment to be matched
The fragment of upper each plane of disruption best match, carries out fragment recombination.
2. the automatic recombination method of cultural relic fragments of binding characteristic point topology as described in claim 1 and geometrical constraint, feature
Be, on fragment to be matched each plane of disruption and potential fragment concentrate each plane of disruption of each fragment, count respectively
The feature string of the plane of disruption is calculated, then by calculating Hausdorff distance, is found each on potential fragment concentration and fragment to be matched
The fragment of plane of disruption best match carries out fragment recombination, comprising:
Maximum curvature, most Chinese yeast are utilized by all characteristic points on the plane of disruption for each plane of disruption on fragment to be matched
Rate constructs ordered pair, obtains the feature string of the plane of disruption；The spy that potential fragment concentrates each plane of disruption is obtained using same method
Sign string；
Utilize the maximum plane of disruption spy for mismatching formula and calculating the plane of disruption feature string of fragment to be matched, potential fragment concentration fragment
Hausdorff distance between sign string, find out potential fragment concentrate with the plane of disruption of fragment to be matched generate minimum Hao Siduofu away from
From fragment as best match fragment, then carry out the recombination of fragment to be matched and best match fragment.
3. the automatic recombination method of cultural relic fragments of binding characteristic point topology as described in claim 1 and geometrical constraint, feature
It is, in step 2, the formula of the corresponding adjacency matrix of n rank cum rights Undirected graph are as follows:
Wherein, D is the corresponding adjacency matrix of n rank cum rights Undirected graph, dijIndicate the weight between any two characteristic point,I, j=1,2 ..., n, n are characterized number a little, pi,pjIt is disconnected for fragment
Any two characteristic point on broken face, coordinate are respectively (xi,yi,zi),(xj,yj,zj)。
4. the automatic recombination method of cultural relic fragments of binding characteristic point topology as described in claim 1 and geometrical constraint, feature
It is, in step 3, generates the minimum spanning tree of characteristic point on each plane of disruption, comprising:
Step 3.1, to G=(V, { E }), initial p={ p0}(p0∈ V), FE=Φ；
Wherein, G=(V, { E }) is the cum rights Undirected graph of one of plane of disruption characteristic point construction of any fragment, and V, which refers to, to be appointed
All set of characteristic points of one of plane of disruption of meaning fragment, the set on the side of { E } between all characteristic points, FE are minimum
The set on the side in spanning tree, P are characterized the subset of point set V, p0For the arbitrary characteristics point in V, Φ is empty set；
Step 3.2, from (p when selecting a weight the smallest in of all p ∈ P, v ∈ V-P0,v0) and set FE is added, simultaneously
By v0P is added；
Wherein, p is characterized the characteristic point in a subset P, and v is a characteristic point in V-P, (p0,v0) be minimum weight side；
Step 3.3, it repeats step 3.2 to stop operation when p=v, obtains feature on one of plane of disruption of any fragment
The minimum spanning tree T of pointmin={ P, { FE } }.
5. the automatic recombination method of cultural relic fragments of binding characteristic point topology as described in claim 1 and geometrical constraint, feature
It is, in step 3, generates the maximum spanning tree of characteristic point on each plane of disruption, comprising:
Step 3.4, to G=(V, { E }), initial p={ p0}(p0∈ V), FEM=Φ；
Wherein, G=(V, { E }) is the cum rights Undirected graph of the one of plane of disruption characteristic point construction of any fragment, and V is referred to
Feature point set on the fragment plane of disruption, the set on the side of { E } between all characteristic points, FEM are the collection on the side in maximum spanning tree
It closes, P is characterized the subset of point set V, p0For the arbitrary characteristics point in V, Φ is empty set；
Step 3.5, from the while (p for selecting a maximum weight in of all p ∈ P, v ∈ V-P0,v0) and set FEM is added, simultaneously
By v0P is added；Wherein p is characterized the characteristic point in a subset P, v0It is a characteristic point in V-P；
3.6, it repeats step 3.5 and stops operation when p=v, obtain the maximum of characteristic point on each plane of disruption of each fragment
Spanning tree Tmax={ P, { FEM } }.
6. the automatic recombination method of cultural relic fragments of binding characteristic point topology as described in claim 1 and geometrical constraint, feature
It is, in step 4, the formula of the adjacent constraint are as follows:
Wherein, A, B are respectively the plane of disruption of two fragments, on the A plane of disruption minimum cost of the minimum spanning tree of characteristic point and and
The maximum cost of maximum spanning tree and respectively MinA, MaxA；On the B plane of disruption minimum cost of the minimum spanning tree of characteristic point and
And the maximum cost and respectively MinB, MaxB of maximum spanning tree.
7. the automatic recombination method of cultural relic fragments of binding characteristic point topology as described in claim 1 and geometrical constraint, feature
It is, in step 5, the maximum mismatched degree formula are as follows:
H (S1, S2)=max (h (S1, S2), h (S2, S1)) formula 4
Wherein, S1 is the feature string of the plane of disruption of fragment to be matched, and S2 is the feature string that potential fragment concentrates the fragment plane of disruption, h
(S1, S2) is the oriented Hausdorff distance of S1 to S2, and h (S2, S1) is the oriented Hausdorff distance of S2 to S1, and a is in S1
The ordered pair that the maximum principal curvatures k1 and minimum principal curvatures k2 of any feature point are constituted；B is that the maximum of any feature point in S2 is main
The ordered pair that curvature k1 and minimum principal curvatures k2 is constituted.
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