CN108305289B - Three-dimensional model symmetry characteristic detection method and system based on least square method - Google Patents
Three-dimensional model symmetry characteristic detection method and system based on least square method Download PDFInfo
- Publication number
- CN108305289B CN108305289B CN201810073992.9A CN201810073992A CN108305289B CN 108305289 B CN108305289 B CN 108305289B CN 201810073992 A CN201810073992 A CN 201810073992A CN 108305289 B CN108305289 B CN 108305289B
- Authority
- CN
- China
- Prior art keywords
- plane
- dimensional model
- symmetry
- symmetrical
- points
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired - Fee Related
Links
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/60—Analysis of geometric attributes
- G06T7/68—Analysis of geometric attributes of symmetry
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06V—IMAGE OR VIDEO RECOGNITION OR UNDERSTANDING
- G06V10/00—Arrangements for image or video recognition or understanding
- G06V10/70—Arrangements for image or video recognition or understanding using pattern recognition or machine learning
- G06V10/74—Image or video pattern matching; Proximity measures in feature spaces
- G06V10/75—Organisation of the matching processes, e.g. simultaneous or sequential comparisons of image or video features; Coarse-fine approaches, e.g. multi-scale approaches; using context analysis; Selection of dictionaries
- G06V10/757—Matching configurations of points or features
Landscapes
- Engineering & Computer Science (AREA)
- Theoretical Computer Science (AREA)
- Computer Vision & Pattern Recognition (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Computing Systems (AREA)
- Evolutionary Computation (AREA)
- General Health & Medical Sciences (AREA)
- Medical Informatics (AREA)
- Software Systems (AREA)
- Databases & Information Systems (AREA)
- Artificial Intelligence (AREA)
- Health & Medical Sciences (AREA)
- Multimedia (AREA)
- Geometry (AREA)
- Image Analysis (AREA)
Abstract
The invention discloses a three-dimensional model symmetry characteristic detection method and a system based on a least square method, comprising the following steps of: establishing a minimum bounding box of the three-dimensional model, and establishing a new coordinate system; dividing the plane of the minimum bounding box according to the spatial resolution, setting opposite planes in the divided six planes into a group, taking a plurality of equidistant mark points on each plane of the minimum bounding box, projecting each group of mark points onto the surface of a three-dimensional model to obtain projection points, calculating the matching degree of the mark points and the projection points, and screening a symmetrical data group according to the matching degree; detecting the plane reflection symmetry of the symmetrical data set according to a least square method to find an initial symmetrical plane; and checking and correcting the initial symmetry plane, and continuously refining the initial symmetry plane until an accurate symmetry plane is obtained. The method comprises four parts of calculating a minimum bounding box, screening a symmetrical data set, detecting plane reflection symmetry and detecting and correcting a symmetrical plane, and is used for detecting the symmetrical plane of a three-dimensional model.
Description
Technical Field
The invention relates to a three-dimensional model symmetry characteristic detection method and system based on a least square method.
Background
The computer group simulation has important significance for the research of the modern society, along with the improvement of the attention, the field of group simulation application is wider and wider, and the related technology is developed and matured gradually. Therefore, people have higher and higher requirements on the models applied in group simulation, the accuracy of the models is maintained, too much memory space cannot be occupied, and the three-dimensional mesh simplification algorithm is gradually transited from initial global simplification to a simplification method for local feature preservation. Considering that most of the three-dimensional models have symmetrical characteristics, such as animals, furniture, people, automobiles and the like, how to reduce the calculation amount in the simplification step by using the symmetry of the objects has very important significance for improving the performance of the three-dimensional model simplification algorithm. However, in the actual application step, not all three-dimensional models are perfectly symmetrical. The method has important research significance on how to efficiently and accurately detect the symmetric surface of the model for the non-perfectly symmetric three-dimensional model.
Disclosure of Invention
In order to solve the defects of the prior art, the invention provides a three-dimensional model symmetry characteristic detection method and a three-dimensional model symmetry characteristic detection system based on a least square method.
In order to achieve the purpose, the invention adopts the following scheme:
the three-dimensional model symmetry characteristic detection method based on the least square method comprises the following steps:
dividing each plane of six planes of a minimum bounding box of the three-dimensional model into cells according to spatial resolution, selecting a plurality of equidistant mark points on each plane of the divided minimum bounding box, setting each two opposite surfaces of the divided six planes into a group, projecting each group of mark points onto the surface of the three-dimensional model to obtain projection points, calculating the matching degree of the mark points and the projection points, and screening a symmetrical data group according to the matching degree;
and detecting the plane reflection symmetry of the symmetrical data set according to a least square method to find an initial symmetrical plane.
Preferably, before the dividing step is performed on each plane of the six planes of the minimum bounding box of the three-dimensional model according to the spatial resolution, the method further includes: and establishing a minimum bounding box of the three-dimensional model and establishing a new coordinate system.
Preferably, after the step of finding the initial symmetry plane, the method further comprises:
and checking and correcting the initial symmetry plane, and continuously refining the initial symmetry plane until an accurate symmetry plane is obtained.
Preferably, the establishing of the new coordinate system is to establish the new coordinate system by using the central point of the minimum bounding box as the origin of the coordinate axis.
Preferably, the dividing the plane of the minimum bounding box according to the spatial resolution includes the following steps:
calculating the ratio of the number of the vertexes of the three-dimensional model to the volume of the minimum bounding box, comparing the ratio with a set threshold, and if the ratio is greater than or equal to the set threshold, dividing six planes of the minimum bounding box into a plurality of cells at equal intervals according to the ratio; if the ratio is smaller than the set threshold, the six planes of the minimum bounding box are divided into a plurality of cells according to pixels.
Preferably, the calculating the matching degree between the mark point and the projection point includes the following steps:
the two symmetrical mark points are provided with two projection points, if two items of values in the horizontal coordinate, the vertical coordinate and the vertical coordinate of the two projection points are consistent, and only one item is inconsistent, whether the inconsistent coordinate value deviation is within a set deviation measurement range is judged, if so, the two mark points are judged to be matched, otherwise, the two mark points are not matched.
If the two symmetrical mark points only have one projection point or no projection point, the two mark points are directly judged to be not matched.
If the two mark points are matched, calculating the ratio of the matched mark point logarithm to the group of mark point logarithms, and obtaining the ratio which is the matching degree of the mark point and the projection point.
Preferably, the step of screening the symmetric data sets according to the matching degree is as follows:
and the projection point set corresponding to the mark point group with the highest matching degree value is the symmetric data group.
Preferably, the symmetry data set is subjected to plane reflection symmetry detection according to a least square method, and the step of finding an initial symmetry plane is as follows:
and fitting the discrete data points in each symmetrical data set to obtain corresponding straight lines, and connecting all the straight lines into a plane to obtain an initial symmetrical plane.
Preferably, the step of checking the corrected initial symmetry plane is as follows:
comparing the initial symmetry plane with a preset symmetry plane, wherein the initial symmetry plane is partially parallel to or overlapped with the preset symmetry plane, the parallel or overlapped part is defined as a completely symmetrical part, and the rest part is defined as a non-completely symmetrical part;
and for the part which is not completely symmetrical, reducing the equal spacing by half, and repeating the step of searching the initial symmetrical plane.
Three-dimensional model symmetry characteristic detection system based on least square method includes: a memory, a processor and a computer program stored on the memory and running on the processor, the computer program, when executed by the processor, performing the steps of any of the methods described above.
A computer readable storage medium having computer instructions embodied thereon, which, when executed by a processor, perform the steps of any of the above methods.
The invention has the beneficial effects that:
(1) according to the three-dimensional model symmetry characteristic detection method based on the least square method, in the preprocessing stage, a new coordinate system is established by redefining the coordinate axis direction according to model distribution, so that the coordinates of corresponding points are different only in a certain coordinate, convenience is provided for subsequent calculation, and time is saved;
(2) according to the three-dimensional model symmetry characteristic detection method based on the least square method, the calculation range is reduced at equal intervals according to the spatial resolution of the model, the original points traversing the whole model are calculated and reduced into small-range data, the calculation amount is greatly reduced, and the symmetry characteristic of the model is not lost;
(3) according to the three-dimensional model symmetry characteristic detection method based on the least square method, the concept of calculus is utilized, the whole is firstly subdivided into parts, and then the parts are collected into the whole, so that the complexity of the algorithm is reduced, repeated iteration is avoided, the symmetrical detail characteristics are well reserved, the symmetrical curved surface of the model is found to the greatest extent according to the symmetry of the model, and convenience is provided for the follow-up simplification work of the three-dimensional model in the practical application step.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the application and, together with the description, serve to explain the application and are not intended to limit the application.
FIG. 1 is a schematic block diagram of the present invention;
FIGS. 2(a) and 2(b) are conceptual illustrations of bounding boxes in the present invention;
FIG. 3 is a schematic diagram of the meshing in the present invention;
FIGS. 4(a) and 4(b) are schematic diagrams comparing the change of a model bounding box and a coordinate system in the present invention;
FIG. 5 is a schematic diagram of meshing of a model of the present invention;
FIG. 6 is a diagram illustrating the effect of a certain model-oriented projection in the present invention;
FIG. 7 is a schematic plan view of a subset of a model of the present invention;
FIG. 8 is a schematic illustration of a subset of the flat-fit lines of a model of the present invention;
fig. 9(a), 9(b) and 9(c) are schematic diagrams of symmetry detection of a model in the present invention.
Detailed Description
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
The embodiments and features of the embodiments in the present application may be combined with each other without conflict. The invention is further described with reference to the following figures and examples.
The invention is further illustrated by the following examples in conjunction with the accompanying drawings:
the invention can be applied to the field of 3D printing and can also be applied to the field of three-dimensional animation design.
As shown in fig. 1, the method for detecting symmetry characteristics of a three-dimensional model based on a least square method includes the following steps:
step (1): establishing a minimum bounding box of the three-dimensional model, and establishing a new coordinate system;
step (2): dividing the plane of the minimum bounding box according to the spatial resolution, taking a plurality of equidistant mark points on each plane of the minimum bounding box, projecting the mark points to the surface of a three-dimensional model to obtain symmetrical feature points, calculating the matching degree of the mark points and the symmetrical feature points, and screening a symmetrical data group according to the matching degree;
and (3): detecting the plane reflection symmetry of the symmetrical data set according to a least square method to find an initial symmetrical plane;
and (4): and checking and correcting the initial symmetry plane, and continuously refining the initial symmetry plane until an accurate symmetry plane is obtained.
Preferably, the establishing of the new coordinate system is to establish the new coordinate system by using the central point of the minimum bounding box as the origin of the coordinate axis.
Preferably, in the step (1), the step of establishing a minimum bounding box of the three-dimensional model is as follows:
step (1-1): let the vertex set P of the three-dimensional model be { P ═ P1,p2,...,pnIn which p isi＝(xi，yi，zi) ∈ R, i is 1,2, n, and the order is
Is the centroid of the three-dimensional model;
step (1-2): according to the properties of the points in the minimum bounding box, setting the maximum value of the points in the minimum bounding box as positive infinity, and setting the minimum value of the points in the minimum bounding box as negative infinity;
step (1-3): all points are traversed and the bounding box of the minimum bounding box is expanded until it contains all points of the three-dimensional model.
As shown in fig. 2(a) and 2(b), preferably, in step (1-2), the property of the point within the minimum bounding box is:
(1-2-1): the points within the minimum bounding box satisfy the following inequality:
Xmin≤X≤Xmax；(1-1)
Ymin≤Y≤Ymax；(1-2)
Zmin≤Z≤Zmax；(1-3)
wherein the content of the first and second substances,
x represents the X coordinate of a point of the three-dimensional model within the minimal bounding box,
y represents the Y coordinate of the point of the three-dimensional model within the minimal bounding box,
z represents the X coordinate of a point of the three-dimensional model within the minimum bounding box,
Xmina minimum value of the X coordinate representing a point of the three-dimensional model within the minimum bounding box,
Ymina minimum value of the Y coordinate representing a point of the three-dimensional model within the minimum bounding box,
Zmina minimum value of the Z coordinate representing a point of the three-dimensional model within the minimum bounding box,
Xmaxthe maximum value of the X-coordinate representing the point of the three-dimensional model within the minimum bounding box,
Ymaxthe maximum value of the Y coordinate representing the point of the three-dimensional model within the minimum bounding box,
Zmaxthe maximum value of the Z coordinate representing a point of the three-dimensional model within the minimum bounding box.
(1-2-2): two points within the minimum bounding box:
Pmin＝[XminYminZmin]；(2-1)
Pmax＝[XmaxYmaxZmax]；(2-2)
wherein the content of the first and second substances,
Pmina point at which each coordinate value representing a point of the three-dimensional model within the minimum bounding box takes a minimum value is also one vertex at which each coordinate value is minimum among the eight vertices of the minimum bounding box,
Pmaxa point where each coordinate value representing a point of the three-dimensional model in the minimum bounding box takes the maximum value,one vertex with the largest coordinate value among the eight vertices of the minimum bounding box is represented by PminAnd PmaxThe two vertices define the minimum bounding box.
(1-2-3): the center point C of the minimum bounding box is:
C＝(Pmin+Pmax)/2；(3)
(1-2-4): the size vector S is from PminPoint of direction PmaxSize vector S contains the length, width and height of the minimum bounding box rectangle boundary;
S＝Pmax-Pmin；(4)
(1-2-5): calculating a centroid point pmThe distance from the center point C is taken as the deviation measure E.
Preferably, in step (1), the method for establishing the new coordinate system is as follows:
step (1-4): moving the original point position of the coordinate axis to the calculated central point C;
step (1-5): adjusting the coordinates of the three-dimensional model by adopting Hotelling transformation to ensure that the geometric shape of the three-dimensional model is unchanged, forming a new coordinate system, and updating P simultaneouslyminAnd PmaxCoordinate values of (2):
Pmin＝(xmin,ymin,zmin)；
Pmax＝(xmax,ymax,zmax)；
wherein x isminMinimum value of X coordinate, y, representing points of the three-dimensional model within the minimum bounding box under the new coordinate systemminA minimum value of a Y coordinate representing a point of the three-dimensional model within the minimum bounding box under the new coordinate system; z is a radical ofminMinimum value, x, of Z coordinates representing points of the three-dimensional model within the minimum bounding box under the new coordinate systemmaxMaximum value of X coordinate, y, representing point of three-dimensional model within minimum bounding box under new coordinate systemmaxMaximum value of Y coordinate, z, representing point of three-dimensional model within minimum bounding box under new coordinate systemmaxA maximum value of a Z coordinate representing a point of the three-dimensional model within the minimum bounding box under the new coordinate system;
the expression for each plane of the minimum bounding box is:
F1:x＝a；F2:y＝b；F3:z＝c；
F4:x＝-a；F5:y＝-b；F6:z＝-c，
wherein, F1And F4、F2And F5、F3And F6Respectively two opposite planes in the minimum bounding box, wherein a, b and c are constants; a pair of the model bounding box and the coordinate system variation in this example is shown in fig. 4(a) and 4 (b).
Preferably, in the step (2), the step of dividing the minimum bounding box according to the spatial resolution is:
calculating the ratio of the number n of the vertexes of the three-dimensional model to the volume M of the minimum bounding box, and dividing the minimum bounding box according to the ratio:
when in use
When the minimum bounding box is used, the six surfaces of the minimum bounding box are divided into a plurality of cells at equal intervals according to the ratio;
when in use
Then, the six faces of the minimum bounding box are divided into cells according to pixels, as shown in fig. 3.
Grouping the opposing faces into three sets of labeled dot sets A, B, C each having 2 × X '× Y', 2 × Y '× Z', 2 × X '× Z', wherein a ═ a ″, Z ″, respectively1∪A2,B＝B1∪B2,C＝C1∪C2；
Wherein the content of the first and second substances,
set A1Is a dividing plane F1Then the set of the marking points is obtained,
set A2Is a dividing plane F4Then the set of the marking points is obtained,
set B1Is a dividing plane F2Then the set of the marking points is obtained,
set B2Is a dividing plane F5Then the set of the marking points is obtained,
set C1Is a dividing plane F3Then the set of the marking points is obtained,
set C2Is a dividing plane F6Then the set of the marking points is obtained,
A1＝{aij(x,y,z)|x＝a,-b≤y≤b,-c≤z≤c},
A2＝{aij'(x,y,z)|x＝-a,-b≤y≤b,-c≤z≤c},
wherein, aijIs set A1Point of (a)ijIs a set A2In (1), i is more than or equal to 0 and less than or equal to X '-1, and j is more than or equal to 0 and less than or equal to Y' -1;
B1＝{bmn(x,y,z)|y＝b,-c≤z≤c,-a≤x≤a},
B2{bmn'(x,y,z)|y＝-b,-c≤z≤c,-a≤x≤a},
wherein, bmnIs a set B1Point of (b)mnIs a set B2M is more than or equal to 0 and less than or equal to Y '-1, n is more than or equal to 0 and less than or equal to Z' -1;
C1＝{cpq(x,y,z)|z＝c,-a≤x≤a,-b≤y≤b},
C2＝{cpq'(x,y,z)|z＝-c,-a≤x≤a,-b≤y≤b},
wherein, cpqIs a set C1Point of (1), cpqIs a set C2Wherein p is more than or equal to 0 and less than or equal to X '-1, and q is more than or equal to 0 and less than or equal to Z' -1;
the points with the same subscript in the two sets of each group are a pair of symmetrical mark points, i.e. the points
Set A1A in (a)ijAnd set A2A in (a)ij', when ij is the same, aijAnd aij' is a pair of symmetrical marker points;
set B1B in (1)mnAnd set B2B in (1)mn', when mn is the same, bmnAnd bmn' is a pair of symmetrical marker points;
set C1C in (1)pqAnd set C2C in (1)pq', when pq is the same, cpqAnd cpq' is a pair of symmetrical marker points.
Example (b): in the step (2), the step of dividing the bounding box according to the spatial resolution is:
calculating the ratio N/M12365 of the number N5844126 of the vertexes of the three-dimensional model and the volume M520 of the bounding box>100, the six faces of the bounding box are divided into cells, and this example division effect is shown in fig. 5, and three sets of data sets a ═ a, i.e., three sets of labeled points, i.e., 2 × 30 × 20, 2 × 20 × 11, and 2 × 30 × 11, are obtained by setting the opposite faces of the divided six faces as one set1∪A2,B＝B1∪B2,C＝C1∪C2,
A schematic projection of one face of this example is shown in fig. 6;
preferably, in the step (2), the step of calculating the matching degree between the mark point and the symmetric feature point includes:
step (2-1): all the mark points are projected and mapped to the surface of the three-dimensional model, and the three sets of data sets A, B, C respectively take the projection points to form three sets of projection point sets F according to the positions of the projection points on the three-dimensional modelfa、Ffb、Ffc：
A→Ffa(A1→Ffa1,A2→Ffa2)；
B→Ffb(B1→Ffb1,B2→Ffb2)；
C→Ffc(C1→Ffc1,C2→Ffc2)；
Ffa＝Ffa1∪Ffa2；
Ffb＝Ffb1∪Ffb2；
Ffc＝Ffc1∪Ffc2；
Wherein the content of the first and second substances,
Ffais a set of projection points from which set a maps to the surface of the three-dimensional model,
Ffbis a set of projection points that set B maps to the surface of the three-dimensional model,
Ffcis a set of projection points from which the set C is mapped onto the surface of the three-dimensional model,
Ffa1is set A1A set of projection points mapped to the surface of the three-dimensional model,
Ffa2is set A2A set of projection points mapped to the surface of the three-dimensional model,
Ffb1is a set B1A set of projection points mapped to the surface of the three-dimensional model,
Ffb2is a set B2A set of projection points mapped to the surface of the three-dimensional model,
Ffc1is a set C1A set of projection points mapped to the surface of the three-dimensional model,
Ffc2is a set C2A set of projection points mapped to a surface of the three-dimensional model.
Ffa1＝{faij(x,y,z)|x≤a,-b≤y≤b,-c≤z≤c},
Ffa2＝{faij'(x,y,z)|-a≤x,-b≤y≤b,-c≤z≤c},
Wherein fa isijIs a set Ffa1Point of (a)ijIs a set Ffa2In (1), i is more than or equal to 0 and less than or equal to X '-1, and j is more than or equal to 0 and less than or equal to Y' -1;
Ffb1＝{fbmn(x,y,z)|y≤b,-a≤x≤a,-c≤z≤c},
Ffb2＝{fbmn'(x,y,z)|-b≤y,-a≤x≤a,-c≤z≤c},
wherein fbmnIs a set Ffb1Point of (5), fbmnIs a set Ffb2M is more than or equal to 0 and less than or equal to Y '-1, n is more than or equal to 0 and less than or equal to Z' -1;
Ffc1＝{fcpq(x,y,z)|z≤c,-a≤x≤a,-b≤y≤b},
Ffc2＝{fcpq'(x,y,z)|-c≤z,-a≤x≤a,-b≤y≤b},
where fcpqIs a set Ffc1Point of center, fcpqIs a set Ffc2Wherein p is more than or equal to 0 and less than or equal to X '-1, and q is more than or equal to 0 and less than or equal to Z' -1;
in the two sets of each group, the points with the same subscript are a pair of symmetric projection points, that is:
set Ffa1In (fa)ijAnd set Ffa2In (fa)ij', when ij are the same, faijAnd faij' is a pair of symmetric proxels;
set Ffb1Fb inmnAnd set Ffb2Fb inmn', fb when mn is the samemnAnd fbmn' is a pair of symmetric proxels;
set Ffc1Fc inpqAnd set Ffc2Fc inpq', fc when pq is the samepqAnd fcpq' is a pair of symmetric proxels.
Step (2-2): judging whether each pair of mark points in each group of the three groups of mark point sets has projections on the surface of the three-dimensional model:
if there is a pair of projection points for each pair of mark points, the coordinates (x) of the pair of projection points1,y1,z1) And (x)2,y2,z2) Only one pair of values is different, provided that z is1And z2Different (the A group mark point set is x1And x2In contrast, the set of B markers is y1And y2In contrast, the set of C markers is z1And z2Different), and the numerical deviation e ═ z1-z2If the | is less than or equal to the deviation measure E, recording as matching;
conversely, if the numerical deviation e is | z1-z2If | is greater than the deviation measure E, the result is recorded as mismatching;
if at least one of the pair of mark points has no projection point on the three-dimensional model, the coordinates of the projection point are marked as (0,0,0) and
it is considered to be mismatched.
Step (2-3): the ratio of the matched mark point logarithm R to the group mark point logarithm G is used as the group matching degree H, namely
Wherein the content of the first and second substances,
the higher the matching degree H is, the more obvious the symmetry of the group data is, and the group max (H) with the highest matching degree H is takena,Hb,Hc) The corresponding set of projection points is a symmetric dataset T,
when max (H)a,Hb,Hc)＝HaWhen T is equal to Ffa；
When max (H)a,Hb,Hc)＝HbWhen T is equal to Ffb；
When max (H)a,Hb,Hc)＝HcWhen T is equal to Ffc。
Step (2-4): the parallel plane of the centroid making plane and the plane of the symmetrical data set is a preset symmetrical plane.
In the step (2), the step of calculating the matching degree is:
the first step is as follows: if two opposite marked points have projection points on the three-dimensional model, namely the point coordinates are not equal to (0,0,0), taking FaFor example, the following steps are carried out: ffa1Point of (fa)ijSubscripts ij and F offa2Point of (fa)ij' when the subscripts ij are equal, the two points are a set of opposite points, and the coordinates (x) of the two points are equal1,y1,z1) And (x)2,y2,z2) Only the value of z is different, and the deviation e ═ z1-z2I in error measurementIf the degree is within the E degree, recording as a matched symmetrical point, otherwise, not a matched pair; if at least one of the two opposite marked points has no projected point on the three-dimensional model, i.e. at least one of the coordinates is (0,0,0), it is not considered as a matching pair.
The second step is that: the ratio of the matched symmetrical point pairs to the mark point pairs is used as the matching degree P, the higher the matching degree is, the more obvious the symmetry of the group of data is, and then the symmetrical point set with the highest matching degree P is used as a symmetrical data set; in this example, the matching degree of T1 is 421, the matching degree of T2 is 95, and the matching degree of T3 is 113, so the set T1 is taken as a symmetric data group.
Preferably, the step (3) is as follows:
step (3-1): two data point sets F of a symmetrical data set Tfr1＝fruv(x, y, z) and Ffr2＝fruv'(x,y,z)
When T ═ FfaWhere r is a, u is i, v is j, Ffa1＝faij(x,y,z),Ffa2＝faij'(x,y,z)；
When T ═ FfbWhere r is b, u is m, v is n, Ffb1＝fbmn(x,y,z),Ffb2＝fbmn'(x,y,z)；
When T ═ FfcWhere r is c, u is p, v is q, Ffc1＝fcpq(x,y,z),Ffc2＝fcpq'(x,y,z)。
According to the subscript uv of the point, the larger number of u and v is taken as the number of subsets, T is divided into a plurality of subsets, and T is { T ═ T0',T1',...,TW' } for example:
when u > v, W ═ 0.. u-1,
T0'＝fr0v(x,y,z)∪fr0v'(x,y,z)；
T1'＝fr1v(x,y,z)∪fr1v'(x,y,z)；
……
Tu-1'＝fr(u-1)v(x,y,z)∪fr(u-1)v'(x,y,z)；
when u < v, W ═ 0.. v-1,
T0'＝fru0(x,y,z)∪fru0'(x,y,z)；
T1'＝fru1(x,y,z)∪fru1'(x,y,z)；
……
Tv-1'＝fru(v-1)(x,y,z)∪fru(v-1)'(x,y,z)；
namely Tw'＝Tw'1∪Tw'2，Tw'1Representing each subset from the set Ffr1＝fruvA subset of points in (x, y, z), Tw'2Representing each subset from the set Ffr2＝fruvA subset of points in (x, y, z); each subset TwThe points in' are all distributed on the same plane, which is perpendicular to the two opposite surfaces for obtaining the symmetrical data set T, and the plan views of the subsets divided by a certain model in this example are shown in FIG. 7, that is, there are several discrete data points (x) in a certain planev,yv,zv) V-0, 1.., n-1, the equation of the plane is expressed as the interval in which the plane is located
A1x+B1y+C1z+D1＝0，(5)
x, y, z are variables, a ', b', c ', d' are constants;
step (3-2): one straight line in the three-dimensional plane is represented by two intersected planes, and the other plane equation is set as follows:
A'x+B'y+C'z+D'＝0,(6)
wherein, A'2+B'2+C'2Not equal to 0, x, y, z are variables, A ', B', C ', D' are constants;
the method is simplified and can be obtained:
recording:
substitution (7)
Obtaining: a is0x+a1y+a2， (8)
Step (3-3): for each subset Tw' discrete n data points, n ≧ 3, (x)v,yv,zv) v-0, 1,. n-1; point of interest (x)v,yv,zv) N-1 fits the plane equation of calculation formula (7), in the geometrical sense, that is, looks for a fitted line that minimizes the sum of the squares of the distances to the given data points, minimizing S:
where S represents the sum of the squares of the distances of the straight lines to the given data point; to minimize S, it should be satisfied
k＝0,1,2，
Represents a pair ofkCalculating a partial derivative of S;
namely:
comprises the following steps:
or the like, or, alternatively,
solving the linear equation set of equations (10) - (12) yields: a is0,a1,a2Is substituted into (8) to obtain
z＝a0x+a1y+a2，(13)
The resulting fitted straight line can be expressed by equation (5) and equation (13):
A1,B1,C1,D1,a0,a1,a2is constant, x, y, z are variables.
Step (3-4): and fitting discrete data points in the plurality of symmetrical data groups to obtain a plurality of straight lines, and connecting the straight lines into a plane to obtain an initial symmetrical plane.
In this example, a schematic diagram of a subset of planes of a model fitting straight lines is shown in FIG. 8;
after fitting the discrete data points in the 30 data sets, obtaining 30 straight lines, and forming a connecting line into a plane to obtain an initial symmetry plane, wherein in the example, the initial symmetry plane of a certain model is shown in fig. 9 (a);
preferably, in the step (4), the step of checking the corrected initial symmetry plane is as follows:
step (4-1): comparing the initial symmetry plane with a preset symmetry plane, wherein the initial symmetry plane is partially parallel to or overlapped with the preset symmetry plane, the parallel or overlapped part is defined as a completely symmetrical part, and the rest part is defined as a non-completely symmetrical part;
step (4-2): and (4) reducing the equal spacing in the step (2) by half for the non-completely symmetrical part, and repeatedly executing the steps (2) - (4). The comparison of the symmetry detection effect of a model in this example is shown in fig. 9(b) and 9 (c).
The above description is only a preferred embodiment of the present application and is not intended to limit the present application, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present application shall be included in the protection scope of the present application.
Claims (10)
1. The three-dimensional model symmetry characteristic detection method based on the least square method is characterized by comprising the following steps of:
dividing each plane of six planes of a minimum bounding box of the three-dimensional model into cells according to spatial resolution, selecting a plurality of equidistant mark points on each plane of the divided minimum bounding box, setting each two opposite planes of the divided six planes into a group, projecting each group of mark points to the surface of the three-dimensional model to obtain projection points, calculating the matching degree of the two mark points according to whether the projection points form matched symmetrical points or not, and screening a symmetrical data group according to the matching degree;
and detecting the plane reflection symmetry of the symmetrical data set according to a least square method to find an initial symmetrical plane.
2. The method for detecting the symmetry characteristics of the three-dimensional model based on the least square method as claimed in claim 1, wherein before the step of dividing each of the six planes of the minimum bounding box of the three-dimensional model according to the spatial resolution, the method further comprises: and establishing a minimum bounding box of the three-dimensional model and establishing a new coordinate system.
3. The method for detecting the symmetry characteristics of the three-dimensional model based on the least square method as claimed in claim 1, wherein after the step of finding the initial symmetry plane, the method further comprises the following steps:
and checking and correcting the initial symmetry plane, and continuously refining the initial symmetry plane until an accurate symmetry plane is obtained.
4. The method for detecting the symmetry characteristics of the three-dimensional model based on the least square method as claimed in claim 2, wherein the establishing of the new coordinate system is performed by using the central point of the minimum bounding box as the origin of the coordinate axis.
5. The method for detecting the symmetry characteristics of the three-dimensional model based on the least square method as claimed in claim 1, wherein the cell division is performed according to the spatial resolution, comprising the steps of:
calculating the ratio of the number of the vertexes of the three-dimensional model to the volume of the minimum bounding box, comparing the ratio with a set threshold, and if the ratio is greater than or equal to the set threshold, dividing six planes of the minimum bounding box into a plurality of cells at equal intervals according to the ratio; if the ratio is smaller than the set threshold, the six planes of the minimum bounding box are divided into a plurality of cells according to pixels.
6. The method for detecting the symmetry characteristics of the three-dimensional model based on the least square method as claimed in claim 1, wherein the matching degree of the mark points and the projection points is calculated, and the method comprises the following steps:
the two symmetrical mark points are provided with two projection points, if two items of values in the horizontal coordinate, the vertical coordinate and the vertical coordinate of the two projection points are consistent, and only one item is inconsistent, whether the inconsistent coordinate value deviation is within a set deviation measure range is judged, if so, the two mark points are judged to be matched, otherwise, the two mark points are not matched;
if the two symmetrical mark points only have one projection point or do not have the projection point, directly judging that the two mark points are not matched;
if the two mark points are matched, calculating the ratio of the matched mark point logarithm to the group of mark point logarithms, and obtaining the ratio which is the matching degree of the mark point and the projection point.
7. The method for detecting the symmetry characteristics of the three-dimensional model based on the least square method as claimed in claim 1, wherein the step of screening the symmetrical data sets according to the matching degree comprises the following steps:
the projection point set corresponding to the mark point group with the highest matching degree value is a symmetrical data group;
alternatively, the first and second electrodes may be,
and (3) detecting the plane reflection symmetry of the symmetrical data set according to a least square method, and finding an initial symmetrical plane according to the following steps:
and fitting the discrete data points in each symmetrical data set to obtain corresponding straight lines, and connecting all the straight lines into a plane to obtain an initial symmetrical plane.
8. The method for detecting the symmetry characteristics of the three-dimensional model based on the least square method as claimed in claim 3, wherein the step of checking and correcting the initial symmetry plane comprises the following steps:
comparing the initial symmetry plane with a preset symmetry plane, wherein the initial symmetry plane is partially parallel to or overlapped with the preset symmetry plane, the parallel or overlapped part is defined as a completely symmetrical part, and the rest part is defined as a non-completely symmetrical part;
and for the part which is not completely symmetrical, reducing the equal spacing by half, and repeating the step of searching the initial symmetrical plane.
9. Three-dimensional model symmetry characteristic detecting system based on least square method, characterized by includes: memory, processor and computer program stored on the memory and executed on the processor, the computer program, when executed by the processor, performing the steps of the method of any of claims 1 to 8.
10. A computer readable storage medium having computer instructions embodied thereon, which when executed by a processor, perform the steps of the method of any one of claims 1 to 8.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201810073992.9A CN108305289B (en) | 2018-01-25 | 2018-01-25 | Three-dimensional model symmetry characteristic detection method and system based on least square method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201810073992.9A CN108305289B (en) | 2018-01-25 | 2018-01-25 | Three-dimensional model symmetry characteristic detection method and system based on least square method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN108305289A CN108305289A (en) | 2018-07-20 |
| CN108305289B true CN108305289B (en) | 2020-06-30 |
Family
ID=62866464
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201810073992.9A Expired - Fee Related CN108305289B (en) | 2018-01-25 | 2018-01-25 | Three-dimensional model symmetry characteristic detection method and system based on least square method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN108305289B (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP4086849A1 (en) * | 2021-12-24 | 2022-11-09 | Univerza v Mariboru | Procedure for detecting the reflectional symmetry of geometrical objects |
Families Citing this family (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110377997B (en) * | 2019-07-10 | 2022-11-18 | 武汉理工大学 | Method and system for inspecting bushing for mold matching design of building aluminum template |
| CN110706276B (en) * | 2019-09-27 | 2022-05-10 | 中国科学院软件研究所 | Skeleton guidance-based three-dimensional model intrinsic symmetry detection method |
| CN112802201B (en) * | 2019-10-25 | 2023-12-29 | 北京博超时代软件有限公司 | Method and device for obtaining parallel nearest distance between entity models |
| CN110986788B (en) * | 2019-11-15 | 2020-10-23 | 华南农业大学 | Automatic measurement method based on three-dimensional point cloud livestock phenotype body size data |
| CN112652075B (en) * | 2021-01-30 | 2022-08-09 | 上海汇像信息技术有限公司 | Symmetric fitting method of symmetric object 3D model |
| CN116597117B (en) * | 2023-07-18 | 2023-10-13 | 中国石油大学(华东) | Hexahedral mesh generation method based on object symmetry |
| CN117876554B (en) * | 2024-03-12 | 2024-05-28 | 中南建筑设计院股份有限公司 | Convex hull-based plate minimum bounding box calculation method and system |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102945569A (en) * | 2012-10-23 | 2013-02-27 | 西北工业大学 | Three-dimensional model symmetry analysis method based on heat kernel signal |
| WO2013075339A1 (en) * | 2011-11-25 | 2013-05-30 | Thomson Licensing | Methods and apparatus for reflective symmetry based 3d model compression |
| CN103729510A (en) * | 2013-12-25 | 2014-04-16 | 合肥工业大学 | Method for computing accurate mirror symmetry of three-dimensional complex model on basis of internal implication transformation |
| CN105631932A (en) * | 2015-12-22 | 2016-06-01 | 北京航空航天大学 | Three-dimensional model re-construction method with contour line guidance |
| CN107146251A (en) * | 2017-03-28 | 2017-09-08 | 浙江大学 | A kind of symmetrical analysis method of three-dimensional face model |
-
2018
- 2018-01-25 CN CN201810073992.9A patent/CN108305289B/en not_active Expired - Fee Related
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2013075339A1 (en) * | 2011-11-25 | 2013-05-30 | Thomson Licensing | Methods and apparatus for reflective symmetry based 3d model compression |
| CN102945569A (en) * | 2012-10-23 | 2013-02-27 | 西北工业大学 | Three-dimensional model symmetry analysis method based on heat kernel signal |
| CN103729510A (en) * | 2013-12-25 | 2014-04-16 | 合肥工业大学 | Method for computing accurate mirror symmetry of three-dimensional complex model on basis of internal implication transformation |
| CN105631932A (en) * | 2015-12-22 | 2016-06-01 | 北京航空航天大学 | Three-dimensional model re-construction method with contour line guidance |
| CN107146251A (en) * | 2017-03-28 | 2017-09-08 | 浙江大学 | A kind of symmetrical analysis method of three-dimensional face model |
Non-Patent Citations (3)
| Title |
|---|
| Efficient 3D reflection symmetry detection: A view-based approach;Bo Li 等;《Graphical Models》;20150926;2-14 * |
| 一种结构对称的破碎青铜文物的数字修复方法;税午阳 等;《文物保护与考古科学》;20151130;第27卷(第4期);113-117 * |
| 医疗三维几何模型的对称面定位研究;程小富;《中国优秀硕士学位论文全文数据库 信息科技辑》;20180115(第01期);I138-1246 * |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP4086849A1 (en) * | 2021-12-24 | 2022-11-09 | Univerza v Mariboru | Procedure for detecting the reflectional symmetry of geometrical objects |
Also Published As
| Publication number | Publication date |
|---|---|
| CN108305289A (en) | 2018-07-20 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN108305289B (en) | Three-dimensional model symmetry characteristic detection method and system based on least square method | |
| CN106909877B (en) | Visual simultaneous mapping and positioning method based on dotted line comprehensive characteristics | |
| CN107610061B (en) | Edge-preserving point cloud hole repairing method based on two-dimensional projection | |
| CN102930246B (en) | Indoor scene identifying method based on point cloud fragment division | |
| CN108171780A (en) | A kind of method that indoor true three-dimension map is built based on laser radar | |
| Mokhtarian et al. | Multi-scale free-form 3D object recognition using 3D models | |
| CN112347550B (en) | Coupling type indoor three-dimensional semantic graph building and modeling method | |
| JP2007502473A (en) | Computer vision system for classification and spatial localization of bounded 3D objects | |
| CN107622530B (en) | Efficient and robust triangulation network cutting method | |
| US20240153123A1 (en) | Isogeometric Analysis Method Based on a Geometric Reconstruction Model | |
| CN105678252A (en) | Iteration interpolation method based on face triangle mesh adaptive subdivision and Gauss wavelet | |
| CN116662600B (en) | Visual positioning method based on lightweight structured line map | |
| Lee et al. | Region matching and depth finding for 3D objects in stereo aerial photographs | |
| CN111369682A (en) | Method, apparatus and computer-readable storage medium for generating leaf-like structures | |
| CN111681300A (en) | Method for obtaining target area composed of outline sketch lines | |
| Lee et al. | A new hybrid method for 3D object recovery from 2D drawings and its validation against the cubic corner method and the optimisation-based method | |
| CN115861247A (en) | High-resolution remote sensing image contour multistage regularization method, system and application | |
| CN115661374A (en) | Rapid retrieval method based on space division and model voxelization | |
| Ruan et al. | Efficient exact collision detection between ellipsoids and superquadrics via closed-form Minkowski sums | |
| CN113744324A (en) | Stereo matching method combining multiple similarity measures | |
| CN106909874A (en) | A kind of nose localization method and device | |
| CN114926536B (en) | Semantic-based positioning and mapping method and system and intelligent robot | |
| CN106023314A (en) | B spline master curve fitting method based on rotary axis direction mapping | |
| CN113313629B (en) | Automatic intersection identification method and system and model storage method and system thereof | |
| CN105678708A (en) | Integrative optimization method suitable for registered multi-view ordered point clouds |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant | ||
| CF01 | Termination of patent right due to non-payment of annual fee | ||
| CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20200630 Termination date: 20220125 |