CN104637091B - A kind of method that manifold is created by rarefaction representation - Google Patents
A kind of method that manifold is created by rarefaction representation Download PDFInfo
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- CN104637091B CN104637091B CN201510085550.2A CN201510085550A CN104637091B CN 104637091 B CN104637091 B CN 104637091B CN 201510085550 A CN201510085550 A CN 201510085550A CN 104637091 B CN104637091 B CN 104637091B
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Abstract
The invention discloses a kind of method that manifold is created by rarefaction representation, structure for have input whole projection information, it is represented again so as to define base signal by carrying out parametrization to geometry signals in part, introduces shape function to represent feature while base signal is constructed；And the Coordinate Conversion between different local cards is defined by transfer function, so that two different expressions be linked together, the uniformity of global definition is then ensured by weighting function；The manifold structure for solving and obtaining based on rarefaction representation can be exported.The invention provides two kinds of other inputs simultaneously：The control grid and wire frame structure of subdivision curved surface.For both inputs, the present invention can be automatically according to the projection information required for input calculating so as to direct solution manifold structure.The invention provides simple interactive interface, user can be with the parameter required for adjustment algorithm, such as degree of rarefication etc..User can export manifold structure and carry out other operations.
Description
Technical field
The present invention relates to a kind of method that manifold is created by rarefaction representation, belong to machine learning, Techniques of Optimum field.
Background technology
Rarefaction representation, a kind of basic but algorithm of prevalence in machine learning, it is intended to remove line with as far as possible few base signal
Property represents given signal.
Rarefaction representation assumes that signal can be represented in the base signal by one group of redundancy, and this expression is simultaneously sparse
, you can to express input signal by the several base signals of only a few.This expression is widely used in machine learning, calculates
It is the basis of many algorithms, such as dictionary learning among machine vision and pattern-recognition, deep learning, neutral net, object is known
Not, image denoising, picture up-sampling etc..
As it is assumed that input signal can be represented that problem belongs to integer optimization problem in itself, is by few base signal
NP-hard problems, it is impossible to optimal algorithm is realized in polynomial time.So many approximate datas are used in, solution is this kind of to ask
Topic.Generally there are two major class methods, one is by greedy algorithm, base signal optimal at that time is added every time to expand expression
Set, such as matching pursuit (MP) algorithm, orthogonal matching pursuit (OMP) algorithm；Secondly
It is that Integer constrained characteristic is converted into appropriate constraints, such as 1 mould or p moulds, such algorithm include basis pursuit (BP),
Compressed sensing (CS) etc..
When with rarefaction representation, generally there is a necessary premise：Signal, which is assumed first that, to be parameterized
Some specific theorem in Euclid space, it is generally one-dimensional（Such as voice signal）Or two dimension（Such as picture signal）.Should in geometric object
The problem of operation is forward position and prevalence is carried out with rarefaction representation.But for the two-dimensional manifold in three dimensions, remove
Special signal, can not typically be embedded into a regular two-dimentional theorem in Euclid space.
The content of the invention
The present invention exactly in view of the deficienciess of the prior art, provide it is a kind of by rarefaction representation create manifold method,
Input model can be subdivision curved surface or specific geometry wire frame structure with feature constraint, by being defined on three dimensions
Line composition.
To solve the above problems, the technical solution used in the present invention is as follows：
A kind of method that manifold is created by rarefaction representation, comprises the following steps：
Step A：Given geological information and its domain of definition grid projection coordinate；
Step B：Calculate the projection coordinate on locally card：Geometry signals are carried out with parametrization to define base letter in part
Number it is represented again, introduce shape function to represent feature while base signal is constructed；
Step C：Solve Global Optimal Problem：Coordinate Conversion between different local cards is defined by transfer function, so that
Two different expressions are linked together, the uniformity of global definition is then ensured by weighting function；
Step D：Generate result：By global sparse optimization problem iterative, final rarefaction representation is obtained.
Specifically, in a kind of described method that manifold is created by rarefaction representation：
The method of the step A includes：Obtained localized parameterization coordinate is on locally card：, its is corresponding several
How signal is：；
The method of the step B includes：Each local definition basic function collection is combined into：, the inside is by multinomial and shape
Shape function is constituted；By obtaining the solution of rarefaction representation to three coordinate solving models respectively, to represent local geometric signal；
The method of the step C includes：Weight function is defined according to local coordinate, partial model is plus weight function progress
Solve, the coordinate of final partial points is depending on the weighted value in different charts, so as to define the overall situation.
When control grid of the input for subdivision curved surface, it is necessary to be finely divided the local coordinate construction of curved surface, the step A
Following steps are specifically included in this case：
Step A11：Given subdivision curved surface control grid；
Step A12：Two layers of subdivision simultaneously calculates local coordinate：The geometry for the point that record domain of definition grid subdivision is obtained afterwards twice
Coordinate and these Local grid relative coordinate；
Step A13：Constructive geometry coordinate and its projection coordinate：Know and utilize phase after the projection of coarse grid among local card
The partial projection coordinate of these refinement points is extrapolated to coordinate.
When input is wire frame structure, it is necessary to carry out the local coordinate construction in wire-frame model, the step A is in such a feelings
Following steps are specifically included under condition：
Step A21：Given wire frame structure：Wire-frame model is made up of three-dimensional line；
Step A22：Domain of definition grid is constructed according to step A21 structure：Three-dimensional line in step A21 is constructed naturally
One domain of definition network, extracts this structure；
Step A23：Calculate the projection coordinate put on line：The local coordinate of the point on three-dimensional line in step A21 is
The coordinate on line on domain of definition grid, the coordinate of partial projection is calculated with this.
It is described as the improvement of above-mentioned technical proposal.
It is described as the improvement of above-mentioned technical proposal.
Compared with prior art, implementation result of the invention is as follows by the present invention：
A kind of method that manifold is created by rarefaction representation of the present invention, can be generated according to given geological information
Manifold structure, can also directly generate manifold structure according to subdivision curved surface or wire frame structure.Except have input whole projection letter
The structure of breath, the present invention is additionally provided using two kinds of other inputs simultaneously（That is the control grid and wire frame structure of subdivision curved surface）When
Solution；, can with method of the present invention for both inputs of the control grid and wire frame structure of subdivision curved surface
With the projection information required for being calculated automatically according to input so as to direct solution manifold structure.
Brief description of the drawings
Fig. 1 is a kind of flow chart for the algorithm core that manifold is created by rarefaction representation of the present invention；
Fig. 2 is generated the stream of manifold for a kind of method for creating manifold by rarefaction representation of the present invention by subdivision curved surface
Cheng Tu；
Fig. 3 is generated the stream of manifold for a kind of method for creating manifold by rarefaction representation of the present invention by wire frame structure
Cheng Tu；
Fig. 4 is the definition figure of manifold in a kind of method that manifold is created by rarefaction representation of the present invention；
Fig. 5 is the shape function geometry of core algorithm use in the specific embodiment of the invention；
Fig. 6 is the relation of the length and its gradient of printable support in the specific embodiment of the invention；
The simple browser interface that Fig. 7 provides for the specific embodiment of the invention；
Fig. 8 is manifold result in the specific embodiment of the invention 1；
Fig. 9 is the input of wire frame structure in the specific embodiment of the invention 2；
Figure 10 is the manifold structure result of wire frame structure generation in the specific embodiment of the invention 2.
Embodiment
Illustrate present disclosure below in conjunction with specific embodiments.
The main contents of the present invention are the provision of the algorithm frame that a kind of basis gives geological information and generates manifold structure
Frame and the algorithm that manifold structure is directly generated according to subdivision curved surface or wire frame structure.There is provided input subdivision curved surface control net
The interface of lattice and wire frame structure, user can obtain manifold by inputting these structures, and preserve.
The Thoughts of the present invention：Because manifold structure is defined in the function structure on some domain of definition grid.For
Some locally blocks（chart）For can be embedded into two dimensional surface.If three-dimensional geometry can be defined to the projection of local card, in office
Portion can just be parameterized to geometry signals and it is represented again so as to define base signal.Because geometry signals have sometimes
There is only continuous feature, be relatively difficult to portray such signal with traditional batten.So the present invention is while base signal is constructed
Introduce the shape function among finite element（shape function）More effectively represent feature.Then the dilute of the overall situation is passed through
Optimization problem iterative is dredged, final rarefaction representation is obtained.
In order to which local expression is changed into global, the concept of transfer function is inventor introduced（transition
function).Transfer function defines the Coordinate Conversion between different local cards, so as to which two different expressions are contacted
Together.Then the uniformity of global definition is ensure that by weighting function.
As shown in Figure 1 to Figure 3, main realization of the invention includes three aspects：In the case of learning partial projection coordinate
Manifold is solved；The local coordinate construction of subdivision curved surface；Local coordinate construction in wire-frame model.Wherein Part I is the present invention
Core content, concrete technical scheme is：In some locally card, one group of localized parameterization coordinate is obtained, and these points
Corresponding geometry signals are：.Each local definition basic function collection is combined into：, the inside is by multinomial and shape
Shape function is constituted.In order to represent local geometric signal, the present invention obtains the solution of rarefaction representation, the model difference by model
Three coordinates are solved.For the overall situation, some partial points is likely located among multiple local cards, can according to local coordinate
To define weight function, so as to be solved among partial model plus weight function, the coordinate of final partial points is by difference
Depending on weighted value in chart, so as to reach the effect of global definition.
For the processing of subdivided meshes：Subdivision curved surface is frequency of use very high a kind of curved surface in computer graphics, is made
Widely used for the three-dimensional version of spline function the field such as rendering and have.In order to which the manifold for obtaining subdivision curved surface is represented, record
The geometric coordinate for the point that domain of definition grid subdivision is obtained afterwards twice and these Local grid relative coordinate（Triangle gridding
Or the barycentric coodinates in quadrilateral mesh）.Know and extrapolated among local card after the projection of coarse grid using relative coordinate
The partial projection coordinate of these refinement points.Then manifold is tried to achieve using these projection coordinates to represent.
For the processing of wire-frame model：Wire-frame model is made up of the line in three-dimensional.These natural structures of three-dimensional line
A domain of definition network has been made, this structure is extracted first with existing algorithm.The local coordinate of point so on line
It is exactly the coordinate on the line on domain of definition grid（Inside does not have）, so as to be easy to the coordinate for calculating partial projection.
These three final parts constitute the major part of the present invention.
Fig. 4 simply describes the definition of manifold structure；Fig. 5 illustrates dictionary geometry used.
Specific embodiment 1
Using with subdivision curved surface as input as embodiment 1.User needs the control grid of given subdivision curved surface, such as Fig. 6 institutes
Show.Here subdivision curved surface allows to carryConstraint.Do not mark c line in wherein Fig. 6 is for the line that no constraint indicates cConstraint.
Simultaneously the invention provides simple interactive interface, as shown in fig. 7, shirtsleeve operation step is as follows：
Step 101：Opening button above user's click is that the control grid of subdivision curved surface can be loaded into internal memory.With
Family can be translated by mouse action object, and rotate and stretch the grid, and select a suitable visual angle to check object.
Step 102：It is that can directly generate subdivided meshes projection information that user, which clicks on keyboard shortcut J keys,.
Step 103：User, which clicks on right side solve buttons, can solve manifold structure.
Generate manifold result as shown in Figure 8.The generating principle of manifold structure is based on global rarefaction representation.Step first
102 generate the projection information required in solution, the i.e. observation of signal and the partial projection in locally card, then basis
Transfer function and weighting function solve the rarefaction representation problem of the overall situation.
Step 104：The manifold structure of generation can be shown in interactive interface.User can by mouse action without
Product, can be translated, rotation and the scaling manifold structure, and select a suitable visual angle to check object.
Step 105：Manifold structure can be preserved out by user by the save button in left side.
Specific embodiment 2
The specific embodiment 2 that wire frame structure is generated to manifold structure as input is described below.Fig. 9 illustrates embodiment 2
The wire frame structure of middle input.The structure is made up of the lines in three-dimensional.And manifold can equally be generated by the interface of the present invention
Structure, can input wire frame structure input of the suffix for dh by opening button first.It may then pass through click solve buttons
Carry out the solution of manifold structure.User can set the parameter of some algorithms of the inside, such as degree of rarefication.Then can be at interface
It is middle to show obtained manifold structure, while user can preserve the manifold structure tried to achieve.
End user can obtain the operation that desired manifold structure is wanted.
Above content is made for the present invention in conjunction with specific embodiments describes in detail, it is impossible to assert that the present invention is specific real
Apply and be only limitted to these explanations.For those skilled in the art, before present inventive concept is not departed from
Put, some simple deduction or replace can also be made, the scope of protection of the invention should be all considered as belonging to.
Claims (3)
1. a kind of method that manifold is created by rarefaction representation, it is characterized in that, comprise the following steps：
Step A：Given geological information and its domain of definition grid projection coordinate；And step A method includes：In local card
On obtained localized parameterization coordinate be：, its corresponding geometry signals is：；
Step B：Calculate the projection coordinate on locally card：Carry out parametrization to geometry signals to define base signal pair in part
It is represented again, introduces shape function to represent feature while base signal is constructed；And step B method includes：Each
Local definition's basic function collection is combined into：, the inside is made up of multinomial and shape function；Sparse table is obtained by model
The solution shown, the model is solved to three coordinates respectively, to represent local geometric signal；
Step C：Solve Global Optimal Problem：Coordinate Conversion between different local cards is defined by transfer function, so that by two
Individual different expression is linked together, and the uniformity of global definition is then ensured by weighting function；And step C method bag
Include：Weight function is defined according to local coordinate, partial model solved plus weight function, the coordinates of final partial points by
Depending on weighted value in different charts, so as to define the overall situation；
Step D：Generate result：By global sparse optimization problem iterative, final rarefaction representation is obtained.
2. a kind of method that manifold is created by rarefaction representation as claimed in claim 1, it is characterized in that, the step A includes
Following steps：
Step A11：Given subdivision curved surface control grid；
Step A12：Two layers of subdivision simultaneously calculates local coordinate：The geometric coordinate for the point that record domain of definition grid subdivision is obtained afterwards twice
And these are in the relative coordinate of Local grid；
Step A13：Constructive geometry coordinate and its projection coordinate：Know and utilize relative seat among local card after the projection of coarse grid
Mark extrapolates the partial projection coordinate of these refinement points.
3. a kind of method that manifold is created by rarefaction representation as claimed in claim 1, it is characterized in that, the step A includes
Following steps：
Step A21：Given wire frame structure：Wire-frame model is made up of three-dimensional line；
Step A22：Domain of definition grid is constructed according to step A21 structure：Three-dimensional line in step A21 constructs one naturally
Domain of definition network, extracts this structure；
Step A23：Calculate the projection coordinate put on line：The local coordinate of the point on three-dimensional line in step A21 is definition
The coordinate on line on the grid of domain, the coordinate of partial projection is calculated with this.
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Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102163330A (en) * | 2011-04-02 | 2011-08-24 | 西安电子科技大学 | Multi-view face synthesis method based on tensor resolution and Delaunay triangulation |
| CN103034868A (en) * | 2012-11-29 | 2013-04-10 | 中国地质大学（武汉） | Classification method aiming at small sample and high dimensional images |
| US8483492B2 (en) * | 2005-10-25 | 2013-07-09 | William Marsh Rice University | Method and apparatus for signal detection, classification and estimation from compressive measurements |
| CN103714526A (en) * | 2013-12-24 | 2014-04-09 | 西安电子科技大学 | Super-resolution image reconstruction method based on sparse multi-manifold embedment |
| CN104076332A (en) * | 2014-06-25 | 2014-10-01 | 西安电子科技大学 | Estimation method for magnitudes and phases of radar uniform linear array |
-
2015
- 2015-02-17 CN CN201510085550.2A patent/CN104637091B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US8483492B2 (en) * | 2005-10-25 | 2013-07-09 | William Marsh Rice University | Method and apparatus for signal detection, classification and estimation from compressive measurements |
| CN102163330A (en) * | 2011-04-02 | 2011-08-24 | 西安电子科技大学 | Multi-view face synthesis method based on tensor resolution and Delaunay triangulation |
| CN103034868A (en) * | 2012-11-29 | 2013-04-10 | 中国地质大学（武汉） | Classification method aiming at small sample and high dimensional images |
| CN103714526A (en) * | 2013-12-24 | 2014-04-09 | 西安电子科技大学 | Super-resolution image reconstruction method based on sparse multi-manifold embedment |
| CN104076332A (en) * | 2014-06-25 | 2014-10-01 | 西安电子科技大学 | Estimation method for magnitudes and phases of radar uniform linear array |
Non-Patent Citations (1)
| Title |
|---|
| 基于流形学习的正交稀疏保留投影;刘茜等;《计算机技术与发展》;20140731;第24卷(第7期);全文 * |
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Effective date of registration: 20210108 Address after: Room 902, 9 / F, building F, Tianhe Software Park, Tianhe District, Guangzhou 510000 Patentee after: GUANGDONG 3VJIA INFORMATION TECHNOLOGY Co.,Ltd. Address before: Room 606, floor A-3, innovation industrial park, No. 800, Wangjiang West Road, high tech Zone, Hefei City, Anhui Province 230000 Patentee before: HEFEI ABACI SCIENCE & TECHNOLOGY Co.,Ltd. |