CN109785440A - A kind of curved surface distorted pattern - Google Patents
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- CN109785440A CN109785440A CN201811549419.7A CN201811549419A CN109785440A CN 109785440 A CN109785440 A CN 109785440A CN 201811549419 A CN201811549419 A CN 201811549419A CN 109785440 A CN109785440 A CN 109785440A
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Abstract
The invention discloses a kind of curved surface distorted patterns, are related to curved surface deformation technology field.Present invention assumes that the vertex movements that curved surface distorted pattern is each vertex and one neighborhood are by a rotary motion RiS is converted with a scalingiIt is compound to portray f (vi)=RiSipi；And curved surface partial transformation during deformation is controlled by the relative rotation in vertex and one neighborhoodThen with (dRij,Sj) be major parameter surface deformation model: v'i‑v'j=f (vi)‑f(vj)=RtdRtiSi(vi‑vj).The present invention is by establishing with (dRij,Sj) be major parameter surface deformation model；Compared to the spin matrix R on each vertexi, in parameter dR in modelijHave to the partial transformation of curved surface deformation and portray well, so the model has a wide range of applications ability in finding the relevant application of curved surface deformation corresponding points；The application for being related to corresponding points tracking mainly has grid nature deformation, the model synthesis of data-driven and non-rigid cloud registration.
Description
Technical field
The invention belongs to curved surface deformation technology fields, more particularly to a kind of curved surface distorted pattern.
Background technique
The correspondence point tracking of variation curved surface is very important technology in the movement and deformation of 3D grid, and distortion of the mesh is dynamic
The keyframe interpolation of picture, the model tormulation technology of object scanning modeling and database-driven in non-rigid motion is not all from
Open the corresponding points tracking of variation curved surface.One good corresponding points tracking is the basis of nature and accurate model sport deformation.Appoint
The movement and deformation of what surface mesh can be expressed as the motion profile combination of corresponding vertex at any time.The change of whole surface
Change combines generation by the mass motion and local motion that form the vertex on surface, and mass motion corresponds to object in space
In location track variation, local motion correspond to object itself accordingly deform.
In the case of no prior information, the target point on each vertex can be arbitrary, model surface deformation from
By spending for 3*N, N is the number on curved surface vertex.Therefore it needs to add prior information to curved surface modification, so that the freedom degree of movement
Decline can solve whole corresponding points using given part deformation constraint.Common curved surface modification constraint has rigid body fortune
It is dynamic, affine motion, local rigid motion campaign, local affine invariant movement etc..Constraining in for curved surface deformation from front to back is gradually cut
Weak, the freedom degree of deformation is gradually increasing, and the expression ability of distorted pattern is also gradually increasing.For the song in practical application
How face Deformation Demands establish the pass that suitable balance is corresponding points tracking technique between model freedom degree and expression ability
Key.
Summary of the invention
The purpose of the present invention is to provide a kind of curved surface distorted patterns, by establishing with (dRij,Sj) it is major parameter
Surface deformation model: vi'-v'j=f (vi)-f(vj)=RtdRtiSi(vi-vj)；Compared to the spin matrix R on each vertexi,
dRijThe partial transformation in curved surface deformation process can be more embodied, the accuracy of curved surface deformation midpoint tracking is improved and improves model
The popularity of application.
In order to solve the above technical problems, the present invention is achieved by the following technical solutions:
The present invention is a kind of curved surface distorted pattern, it is assumed that curved surface distorted pattern is the vertex on each vertex and one neighborhood
Movement is by a rotary motion RiS is converted with a scalingiIt is compound to portray, it may be assumed that f (vi)=RiSipi；Wherein, viFor vertex,
piFor vertex viThe vertex in one field；
And curved surface partial transformation during deformation is controlled by the relative rotation in vertex and one neighborhood, it may be assumed that
dRij=Ri TRj；Compared to the spin matrix R on each vertexi, dRijThe partial transformation in curved surface deformation process can more be embodied；Then
With (dRij,Sj) be major parameter surface deformation model:
vi'-v'j=f (vi)-f(vj)=RtdRtiSi(vi-vj)；
Wherein, vi' and v'jIndicate two vertex positions of the neighborhood on target surface；viAnd vjIt indicates on former curved surface
Corresponding neighborhood two o'clock position；RtIn t correspond to viAny one of neighborhood point.
The invention has the following advantages:
The present invention is by establishing with (dRij,Sj) be major parameter surface deformation model: vi'-v'j=f (vi)-f(vj)
=RtdRtiSi(vi-vj)；Compared to the spin matrix R on each vertexi, in parameter dR in modelijThe part of curved surface deformation is become
It has changed and has portrayed well, so the model has a wide range of applications energy in finding the relevant application of curved surface deformation corresponding points
Power；The application for being related to corresponding points tracking mainly has grid nature deformation, the model synthesis of data-driven and non-rigid cloud
Registration.
Certainly, it implements any of the products of the present invention and does not necessarily require achieving all the advantages described above at the same time.
Specific embodiment
Technical scheme in the embodiment of the invention is clearly and completely described, it is clear that described embodiment is only
It is only a part of the embodiment of the present invention, instead of all the embodiments.Based on the embodiments of the present invention, the common skill in this field
Art personnel all other embodiment obtained without creative efforts belongs to the model that the present invention protects
It encloses.
The present invention is a kind of curved surface distorted pattern, it is assumed that curved surface distorted pattern is the vertex on each vertex and one neighborhood
Movement is by a rotary motion RiS is converted with a scalingiIt is compound to portray, it may be assumed that f (vi)=RiSipi；Wherein, viFor vertex,
piFor vertex viThe vertex in one field；
And curved surface partial transformation during deformation is controlled by the relative rotation in vertex and one neighborhood, it may be assumed that
dRij=Ri TRj；Compared to the spin matrix R on each vertexi, dRijThe partial transformation in curved surface deformation process can more be embodied；Then
With (dRij,Sj) be major parameter surface deformation model:
vi'-v'j=f (vi)-f(vj)=RtdRtiSi(vi-vj)；
Wherein, vi' and v'jIndicate two vertex positions of the neighborhood on target surface；viAnd vjIt indicates on former curved surface
Corresponding neighborhood two o'clock position；RtIn t correspond to viAny one of neighborhood point.
Specific embodiment one:
Grid deforms the initial and final state for referring to given grid naturally, utilizes the model (dRij,Sj) and grid
The equivalence of local deformation in deformation, for initial and final state intermediate state, the grid local deformation of intermediate state is equivalent to
(dRij,Sj) intermediate state, it can obtained with model parameter interpolation that is initial and terminating.
Algorithm steps are as follows:
1. the initial position v of given gridi, we approach initial position using distorted pattern to the perseverance of initial position
It Deng mapping I, is remained unchanged according to the length of each edge and establishes corresponding energy equation group, least square solves to obtain model ginseng
Number (dRij,Sj)；
2. according to the (dR solvedij,Sj), according to partial dot of the grid from initial position to final position to constraint, build
Corresponding soft-constraint or hard constraint equation are found, solution obtains whole transformation matrix.
Specific embodiment two:
By taking the modeling of the face of data priori as an example, curved surface distorted pattern proposed by the present invention can be by model in database
The vertex of series correspond generate in each model local deformation (dRij,Sj), and the face of data priori models
It is then the coarse point cloud that input is approached by the linear combination of database model, the linear combination of database model can be used
(dRij,Sj) linear combination replace, with parameter linear combination can be very good to keep in model partial transformation, in turn
So that the effect approached is more preferable.
Algorithm steps are as follows:
Given faceform's database, i.e., intermediate face f0 and other expressions f1, f2 ... fn, with identical as specific example one
Method find out f0 to fk model deformation parameter pk:(dRij,Sj)；
The point cloud data for now giving acquisition, the curved surface mapping approached by intermediate face is formed by the linear combination of parameter pk
, we are overlapped model and collection point cloud after mapping as far as possible using the iteration closest approach algorithm of point cloud to point cloud, most
Small two multiply the weighting weight for estimating combination.
Specific embodiment three:
In given curved surface distorted pattern (dRij,Sj) under, the constraint of any curved surface deformation can be expressed as being limited in
The position on certain vertex or energy constraint can both be propagated on neighborhood to generate by the partial transformation that partial model is portrayed
Other vertex positions, the reasonable registration applied under the imperfect situation of scanning element cloud.And model proposed by the present invention both may be used
To indicate whole movement, local surface variation can also be contained, can sufficiently track object in scanning registration process
Non-rigid motion.
Algorithm steps are as follows:
1. the truncation distance field of a given upper hardwood fused registration utilizes marching cube algorithm from the distance field
Generate grid surface at this time；
2. selecting suitably to sample the anchor point registered as next frame point cloud on vertex from grid surface；
3. the anchor point selected using 2 and next hardwood collection point cloud do the registration of iteration closest approach, due to proposed by the present invention
What deformation model was portrayed is to maintain the transformation of curved surface local property, first fixed model parameter (dRij,Sj) use whole minimum two
Multiplication algorithm provides the initial estimation of anchor point；
4. using the method for global parameter alternative optimization find out cloud be overlapped energy minimum anchorage spin matrix and
Deformation model (dRij,Sj) representated by partial transformation.
It is worth noting that, included each unit is only drawn according to function logic in the above system embodiment
Point, but be not limited to the above division, as long as corresponding functions can be realized；In addition, each functional unit is specific
Title is also only for convenience of distinguishing each other, the protection scope being not intended to restrict the invention.
In addition, those of ordinary skill in the art will appreciate that realizing all or part of step in the various embodiments described above method
It suddenly is that relevant hardware can be instructed to complete by program, corresponding program can store computer-readable deposits in one
In storage media.
Present invention disclosed above preferred embodiment is only intended to help to illustrate the present invention.There is no detailed for preferred embodiment
All details are described to the greatest extent, are not limited the invention to the specific embodiments described.Obviously, according in this specification
Hold, can make many modifications and variations.These embodiments are chosen and specifically described to this specification, is in order to preferably explain this
The principle and practical application of invention, so that skilled artisan be enable to better understand and utilize the present invention.This hair
It is bright to be limited only by the claims and their full scope and equivalents.
Claims (1)
1. a kind of curved surface distorted pattern, which is characterized in that
Assuming that the vertex movements that curved surface distorted pattern is each vertex and one neighborhood are by a rotary motion RiWith a scaling
Convert SiIt is compound to portray, it may be assumed that f (vi)=RiSipi；
Wherein, viFor vertex, piFor vertex viThe vertex in one field；
And curved surface partial transformation during deformation is controlled by the relative rotation in vertex and one neighborhood, it may be assumed that
Then with (dRij,Sj) be major parameter surface deformation model:
v′i-v'j=f (vi)-f(vj)=RtdRtiSi(vi-vj)；
Wherein, v 'iAnd v'jIndicate two vertex positions of the neighborhood on target surface；viAnd vjIndicate corresponding on former curved surface
One neighborhood two o'clock position；RtIn t correspond to viAny one of neighborhood point.
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113554559A (en) * | 2021-06-21 | 2021-10-26 | 中国人民解放军空军工程大学 | Three-dimensional reconstruction method and device with multiple complex curved surface rotational symmetry models |
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| US20150219902A1 (en) * | 2014-02-06 | 2015-08-06 | Samsung Electronics Co., Ltd. | Electronic device including flexible display unit and operation method thereof |
| WO2015193617A1 (en) * | 2014-06-18 | 2015-12-23 | Morel Julien | Wing for the propulsion of a vehicle |
| CN106934824A (en) * | 2017-03-16 | 2017-07-07 | 天津大学 | The global non-rigid registration and method for reconstructing of deformable bodies |
| CN108711185A (en) * | 2018-05-15 | 2018-10-26 | 清华大学 | Joint rigid moves and the three-dimensional rebuilding method and device of non-rigid shape deformations |
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2018
- 2018-12-18 CN CN201811549419.7A patent/CN109785440A/en active Pending
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101522530A (en) * | 2006-10-13 | 2009-09-02 | 宝洁公司 | Method and apparatus for aplying indicia to a curved surface |
| US20150219902A1 (en) * | 2014-02-06 | 2015-08-06 | Samsung Electronics Co., Ltd. | Electronic device including flexible display unit and operation method thereof |
| WO2015193617A1 (en) * | 2014-06-18 | 2015-12-23 | Morel Julien | Wing for the propulsion of a vehicle |
| CN106934824A (en) * | 2017-03-16 | 2017-07-07 | 天津大学 | The global non-rigid registration and method for reconstructing of deformable bodies |
| CN108711185A (en) * | 2018-05-15 | 2018-10-26 | 清华大学 | Joint rigid moves and the three-dimensional rebuilding method and device of non-rigid shape deformations |
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| ANUJ SRIVASTAVA等: "Shape Analysis of Elastic Curves in Euclidean Spaces" * |
| GANG XU等: "Direct manipulation of free-form deformation using curve-pairs" * |
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| CN113554559A (en) * | 2021-06-21 | 2021-10-26 | 中国人民解放军空军工程大学 | Three-dimensional reconstruction method and device with multiple complex curved surface rotational symmetry models |
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Application publication date: 20190521 |