CN106485783A - One kind is based on rarefaction representation and parameterized curved surface fitting method - Google Patents
One kind is based on rarefaction representation and parameterized curved surface fitting method Download PDFInfo
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- CN106485783A CN106485783A CN201610904734.1A CN201610904734A CN106485783A CN 106485783 A CN106485783 A CN 106485783A CN 201610904734 A CN201610904734 A CN 201610904734A CN 106485783 A CN106485783 A CN 106485783A
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- rarefaction representation
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- curved surface
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
- G06T17/20—Finite element generation, e.g. wire-frame surface description, tesselation
Abstract
The present invention discloses one kind based on rarefaction representation and parameterized curved surface fitting method, comprises the following steps：Input model；Model is split, and calculates the initial parameter coordinate in local surface piece, optimizes the linear combination coefficient of rarefaction representation, carries out parameter optimization, obtain composite function optimization；Solve Global Optimal Problem；Surface fitting result.One kind of the present invention is based on rarefaction representation and parameterized curved surface fitting method, by the use of simple monomial function as basic function, good approximation to different geometric properties is realized by the introducing of parameter optimization, input model can be three-dimensional grid model or point cloud.The present invention combines the linear combination coefficient and parameter optimization for optimizing rarefaction representation, obtains composite function Optimized model, by introducing auxiliary quantity, is solved using the mode of loop iteration.
Description
Technical field
The invention belongs to machine learning, Techniques of Optimum field, specifically one kind is based on rarefaction representation and parameterized song
Face approximating method.
Background technology
Rarefaction representation assumes that input signal can be represented by the base signal of one group of redundancy, while requiring that this expression is
Sparse, i.e., input signal is expressed by the several base signals of only a few.This expression is widely used in machine learning, calculates
In the middle of machine vision and pattern-recognition, it is the basis of a lot of learning algorithms, such as dictionary learning, deep learning, neutral net, object
Identification, image denoising, picture up-sampling etc..
How given input signal, go to select the base signal of only a few to be indicated belonging to integer optimization problem, be NP-
Hard problem, it is impossible to realize optimal algorithm in polynomial time, such issues that naturally a lot of approximate datas are suggested solution.
May be generally divided into two classes：One kind is to utilize greedy algorithm, adds base signal optimum at that time every time and represents collection to expand
Close, such as matching pursuit (MP), orthogonal matching pursuit (OMP) algorithm etc.；Second
It is that Integer constrained characteristic is converted to appropriate constraints, such as 1 mould or p mould, mainly include basis pursuit (BP), compressed
Sensing (CS) etc..
Additionally, as most of fitting algorithms, the basic function adopted during rarefaction representation determines fitting effect.Such as,
Smooth basic function can only be combined into smooth signal, and can not possibly produce signal of the Non-smooth surface with feature.
When with rarefaction representation, generally there is a necessary premise：Assume first that signal is parameterized to arrive
Certain specific theorem in Euclid space, generally one-dimensional（As voice signal）Or two dimension（As picture signal）.Parametrization is in several where
Important research topic is always in reason, as geometry does not have the parametrization of inherence in itself, different parametric method meeting
Different effects, such as conformal are obtained, protects area, anti-canting etc..As for sharp features in geometric object, most of method is also all
It is to rely on feature detection and realizes the good approximation to feature.Also, for three-dimensional geometric object, except special
Signal, can not typically be embedded into a regular two-dimentional theorem in Euclid space.
Content of the invention
It is an object of the invention to provide a kind of be based on rarefaction representation and parameterized curved surface fitting method.
The purpose of the present invention can be achieved through the following technical solutions：
One kind is comprised the following steps based on rarefaction representation and parameterized curved surface fitting method：
（1）Input model；
（2）Model is split, and calculates the initial parameter coordinate in local surface piece, optimizes the linear combination coefficient of rarefaction representation,
Parameter optimization is carried out, composite function optimization is obtained, Optimized model is：
Wherein,For being input into Grid Signal,For the parametrization coordinate of signal,For linear combination coefficient,Fixed monomial basic function,Represent parameter transformation,It is the area of t-th triangle,Refer to t-th triangle
The corresponding Jacobi singular values of a matrix of fractal transform,、For scalar parameter,For degree of rarefication, Section 1 is data fit term,
Afterwards two be used for ensure parameter field convert when triangle gridding quality；
（3）Solve Global Optimal Problem；
（4）Surface fitting result.
As the present invention further preferably, the model is three-dimensional grid model or point cloud.
Optimized model of the present invention is solved by way of loop iteration, and formula is as follows：
Wherein, f is auxiliary variable,For penalty factor,For Lagrange multiplier,、For scalar parameter,For dilute
Dredge degree,It is the area of t-th triangle,Refer to that t-th triangle converts corresponding Jacobi singular values of a matrix.
Iterative step of the present invention is：
（1）Input model is read, and initial parameter coordinate is calculated using LSCM method；
（2）Iteration optimization is solved：The initial parametrization coordinate of fixation, optimizes the linear combination coefficient of rarefaction representation, fixes afterwards dilute
Dredge and represent, Optimal Parameters domain；
（3）Through 15 iteration optimization, you can obtain final surface fitting result.
Beneficial effects of the present invention：One kind of the present invention is based on rarefaction representation and parameterized curved surface fitting method,
By the use of simple monomial function as basic function, well forcing to different geometric properties is realized by the introducing of parameter optimization
Closely, input model for three-dimensional grid model or can put cloud.
The present invention combines the linear combination coefficient and parameter optimization for optimizing rarefaction representation, obtains composite function Optimized model,
By introducing auxiliary quantity, solved using the mode of loop iteration.
Larger for summit quantity, the more complicated model of structure, model can be divided into multiple local surface pieces, phase
Sympathize between patch and there is coincidence surface information, the present invention directly adopts Mean Method, reach the global effect of definition.
Description of the drawings
Fig. 1 is that the present invention is a kind of is based on rarefaction representation and parameterized curved surface fitting method flow chart.
Fig. 2 is a kind of part monomial base letter adopted based on rarefaction representation and parameterized curved surface fitting method of the present invention
Number schematic diagram.
Fig. 3 is a kind of iterative schematic diagram based on rarefaction representation and parameterized curved surface fitting method of the present invention.
Fig. 4 is that the present invention is a kind of based on simply browsing in rarefaction representation and parameterized curved surface fitting method embodiment 1
Interface.
Fig. 5 is that a kind of grid based on rarefaction representation and parameterized curved surface fitting method embodiment 1 of the present invention is input into.
Fig. 6 represents knot for a kind of optimization based on rarefaction representation and parameterized curved surface fitting method embodiment 1 of the present invention
Really.
Fig. 7 represents knot for a kind of optimization based on rarefaction representation and parameterized curved surface fitting method embodiment 2 of the present invention
Really.
Specific embodiment
For the ease of it will be appreciated by those skilled in the art that the present invention is further illustrated below in conjunction with the accompanying drawings.
The invention reside in there is provided the curved surface fitting method optimized based on rarefaction representation and parameter field and corresponding model
Derivation algorithm.The introducing of parameter field optimization improves the ability to express of rarefaction representation, even with simple monomial function,
The good approximation to geometric properties can be completed.
One kind is comprised the following steps based on rarefaction representation and parameterized curved surface fitting method：
（1）Input model；
（2）Model is split, and calculates the initial parameter coordinate in local surface piece, optimizes the linear combination coefficient of rarefaction representation,
Parameter optimization is carried out, composite function optimization is obtained, Optimized model is：
Wherein,For being input into Grid Signal,For the parametrization coordinate of signal,For linear combination coefficient,Fixed monomial basic function,Represent parameter transformation,It is the area of t-th triangle,Refer to t-th triangle
The corresponding Jacobi singular values of a matrix of fractal transform,、For scalar parameter,For degree of rarefication, Section 1 is data fit term,
Afterwards two be used for ensure parameter field convert when triangle gridding quality；
（3）Solve Global Optimal Problem；
（4）Surface fitting result.
The model is three-dimensional grid model or point cloud.
Optimized model of the present invention is solved by way of loop iteration, and formula is as follows：
Wherein, f is auxiliary variable,For penalty factor,For Lagrange multiplier,、For scalar parameter,For
Degree of rarefication,It is the area of t-th triangle,Refer to that t-th triangle converts corresponding Jacobi singular values of a matrix.
Above-mentioned iterative step is：
（1）Input model is read, and initial parameter coordinate is calculated using LSCM method；
（2）Iteration optimization is solved：The initial parametrization coordinate of fixation, optimizes the linear combination coefficient of rarefaction representation, fixes afterwards dilute
Dredge and represent, Optimal Parameters domain；
（3）Through 15 iteration optimization, you can obtain final surface fitting result.
Embodiment 1
Fig. 2 shows part monomial basic function；Fig. 3 is the iterative synoptic chart of the inventive method algorithm, and primary iteration is walked
Rapid as follows：
Step 31：Input model is read, and initial parameter coordinate is calculated using LSCM method.
Step 32：Iteration optimization is solved.The initial parametrization coordinate of fixation, optimizes the linear combination coefficient of rarefaction representation,
The combined effect of basic function is as shown in 321；Rarefaction representation, Optimal Parameters domain 322 are fixed afterwards；After completing an iteration, sparse table
Show and parameterize the compound expression of coordinate as shown in 323.
Step 33：Optimization is completed, and obtains final surface fitting result 33.
The invention provides simple interactive interface, as shown in figure 4, shirtsleeve operation step is as follows：
Step 41：User clicks on the button of opening of top and is loaded into model.User passes through mouse action object, can translate, rotation
With the flexible model, and a suitable visual angle is selected to check object.
Step 42：User clicks on the compound sparse representation model that keyboard shortcut A key may wait for solving the present invention.
Step 43：The result of Function Fitting can be shown in interactive interface.User can pass through mouse action nothing
Product, can translate, and rotate and the scaling flow structure, and select a suitable visual angle to check object.
Step 44：The curved surface result of fitting can be preserved by user by the save button in left side.
Fig. 5 is the input model of the embodiment of the present invention 1, and Fig. 6 is corresponding Optimal Fitting result.
Embodiment 2
One of the present invention directly applies, and point cloud is rebuild.
As shown in fig. 7, step is as follows：
Step 71：Read the point cloud model of input.
Step 72：By existing method for reconstructing, discrete grid block is output as, obtains simple three-legged structure 72；Cloud will be put
Project to structure 72, obtain local gravity center coordinate of each point in projected triangle；Process side such as 1 complex model of embodiment
Method, is carried out splitting laggard line parameter to structure 72, and the barycentric coodinates according to a cloud obtain the parametrization coordinate initial value of a cloud, after
All fixed points of a cloud are solved as input signal.
73：Optimization is completed, and obtains final surface fitting result 73.
Above content is only to present configuration example and explanation, affiliated those skilled in the art couple
Described specific embodiment is made various modifications or supplements or substituted using similar mode, without departing from invention
Structure surmounts scope defined in the claims, all should belong to protection scope of the present invention.
Claims (4)
1. one kind is characterized in that, be comprised the following steps based on rarefaction representation and parameterized curved surface fitting method：
（1）Input model；
（2）Model is split, and calculates the initial parameter coordinate in local surface piece, optimizes the linear combination coefficient of rarefaction representation,
Parameter optimization is carried out, composite function optimization is obtained, Optimized model is：
Wherein,For being input into Grid Signal,For the parametrization coordinate of signal,For linear combination coefficient,Fixed monomial basic function,Represent parameter transformation,It is the area of t-th triangle,Refer to t-th three
The corresponding Jacobi singular values of a matrix of angular conversion,、For scalar parameter,For degree of rarefication, Section 1 is data fitting
, latter two are used for ensureing the quality of triangle gridding during parameter field conversion；
（3）Solve Global Optimal Problem；
（4）Surface fitting result.
2. described in claim 1 based on rarefaction representation and parameterized curved surface fitting method, it is characterized in that, the model be three
Dimension grid model or point cloud.
3. according to based on rarefaction representation and parameterized curved surface fitting method described in claim 1, it is characterized in that, the optimization mould
Type is solved by way of loop iteration, and formula is as follows：
Wherein, f is auxiliary variable,For penalty factor,For Lagrange multiplier,、For scalar parameter,For dilute
Dredge degree,It is the area of t-th triangle,Refer to that t-th triangle converts corresponding Jacobi singular values of a matrix.
4. according to claim 3 based on rarefaction representation and parameterized curved surface fitting method, it is characterized in that, the iteration
Solution procedure is：
（1）Input model is read, and initial parameter coordinate is calculated using LSCM method；
（2）Iteration optimization is solved：The initial parametrization coordinate of fixation, optimizes the linear combination coefficient of rarefaction representation, fixes afterwards dilute
Dredge and represent, Optimal Parameters domain；
（3）Through 15 iteration optimization, you can obtain final surface fitting result.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109816789A (en) * | 2018-12-14 | 2019-05-28 | 合肥阿巴赛信息科技有限公司 | A kind of threedimensional model parametric method based on deep neural network |
| CN109961517A (en) * | 2019-03-01 | 2019-07-02 | 浙江大学 | A kind of triangle gridding weight parametric method for parametric surface fitting |
| CN116993925A (en) * | 2023-09-25 | 2023-11-03 | 安徽大学 | Distributed bundling adjustment method for large-scale three-dimensional reconstruction |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102222365A (en) * | 2011-07-29 | 2011-10-19 | 电子科技大学 | Method for reconstructing curved surface of complex space |
| CN104268934A (en) * | 2014-09-18 | 2015-01-07 | 中国科学技术大学 | Method for reconstructing three-dimensional curve face through point cloud |
-
2016
- 2016-10-18 CN CN201610904734.1A patent/CN106485783A/en active Pending
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102222365A (en) * | 2011-07-29 | 2011-10-19 | 电子科技大学 | Method for reconstructing curved surface of complex space |
| CN104268934A (en) * | 2014-09-18 | 2015-01-07 | 中国科学技术大学 | Method for reconstructing three-dimensional curve face through point cloud |
Non-Patent Citations (2)
| Title |
|---|
| LINLIN XU 等: "Surface approximation via sparse representation and parameterization optimization", 《COMPUTER-AIDED DESIGN》 * |
| 叶井飞 等: "基于Zernike多项式和径向基函数的自由曲面重构方法", 《光学学报》 * |
Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109816789A (en) * | 2018-12-14 | 2019-05-28 | 合肥阿巴赛信息科技有限公司 | A kind of threedimensional model parametric method based on deep neural network |
| CN109816789B (en) * | 2018-12-14 | 2023-02-07 | 广东三维家信息科技有限公司 | Three-dimensional model parameterization method based on deep neural network |
| CN109961517A (en) * | 2019-03-01 | 2019-07-02 | 浙江大学 | A kind of triangle gridding weight parametric method for parametric surface fitting |
| CN109961517B (en) * | 2019-03-01 | 2021-05-07 | 浙江大学 | Triangular mesh reparameterization method for parametric surface fitting |
| CN116993925A (en) * | 2023-09-25 | 2023-11-03 | 安徽大学 | Distributed bundling adjustment method for large-scale three-dimensional reconstruction |
| CN116993925B (en) * | 2023-09-25 | 2023-12-01 | 安徽大学 | Distributed bundling adjustment method for large-scale three-dimensional reconstruction |
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