CN104637091A - Method for creating flow pattern through sparse representation - Google Patents
Method for creating flow pattern through sparse representation Download PDFInfo
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- CN104637091A CN104637091A CN201510085550.2A CN201510085550A CN104637091A CN 104637091 A CN104637091 A CN 104637091A CN 201510085550 A CN201510085550 A CN 201510085550A CN 104637091 A CN104637091 A CN 104637091A
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Abstract
The invention discloses a method for creating flow pattern through sparse representation. For a structure in which complete projection information is input, geometrical signals are subjected to parameterization in local areas, so that base signals are defined for realizing the re-representation, and during the base signal construction, a shape function is introduced for representing features; in addition, coordinate conversion between different local cards is defined through a conversion function, so that the two different representations are associated, and then, the global definition uniformity is ensured through a weighing function; a flow pattern obtained through sparse representation resolution can be output. Meanwhile, the invention provides two other inputs including a finely divided curve surface control grid and a line frame structure. For the two inputs, the method has the advantages that the required projection information can be automatically calculated according to the input, so that the flow pattern structure can be directly solved. A simple interaction interface is provided, and a user can regulate parameters, such as sparseness, required by the algorithm. The user can output the flow pattern structure for other operations.
Description
Technical field
The present invention relates to a kind of method being created flow pattern by rarefaction representation, belong to machine learning, optimization technique field.
Background technology
Rarefaction representation, the algorithm that a kind of basis in machine learning is still popular, is intended to the signal going linear expression given with few base signal of trying one's best.
Rarefaction representation putative signal can represent at the base signal by one group of redundancy, and this expression is sparse simultaneously, namely can express input signal by the several base signal of only a few.This expression is widely used in machine learning, in the middle of computer vision and pattern-recognition, is the basis of a lot of algorithm, and as dictionary learning, the degree of depth learns, neural network, object identification, image denoising, picture up-sampling etc.
Because supposition input signal can be represented by few base signal, problem itself belongs to integer optimization problem, is NP-hard problem, can not realizes optimal algorithm in polynomial time.So a lot of approximate data is used in solve this kind of problem.There are two large class methods generally, the first is by greedy algorithm, the optimum at that time base signal of each interpolation expands and represents set, as matching pursuit (MP) algorithm, orthogonal matching pursuit (OMP) algorithm etc.; It two is that Integer constrained characteristic is converted to appropriate constraints, and as 1 mould or p mould, this type of algorithm comprises basis pursuit (BP), compressed sensing (CS) etc.
When utilization rarefaction representation, usually there is the prerequisite that necessary: first signal supposes parameterized to certain specific theorem in Euclid space, is generally one dimension (as voice signal) or two dimension (as picture signal).In geometric object, apply that rarefaction representation carries out operating is forward position and popular problem.But for being in for three-dimensional two-dimentional flow pattern, except special signal, a regular two-dimentional theorem in Euclid space generally can not be embedded into.
Summary of the invention
The present invention, just for the deficiency that prior art exists, provides a kind of and creates the method for flow pattern by rarefaction representation, and input model can be subdivision curved surface with feature constraint or specific geometrical line mount structure, is made up of the line be defined on three dimensions.
For solving the problem, the technical solution used in the present invention is as follows:
Created a method for flow pattern by rarefaction representation, comprise the following steps:
Steps A: given geological information and its projection coordinate at field of definition grid;
Step B: calculate the projection coordinate on the card of local: carry out parametrization in local to geometry signals thus define base signal heavily representing it, introduce shape function and carry out representation feature while structure base signal;
Step C: solve Global Optimal Problem: by the coordinate conversion between the card of transfer function definition different local, thus two different expressions are linked together, the unitarity of global definition is then guaranteed by weighting function;
Step D: generate result: by the sparse optimization problem iterative of the overall situation, obtain final rarefaction representation.
Particularly, in a kind of described method by rarefaction representation establishment flow pattern:
The method of described steps A comprises: the localized parameterization coordinate obtained on the card of local is: { p
i, the geometry signals of its correspondence is: { (x
i, y
i, z
i);
The method of described step B comprises: the basis function set of each local definition is: { d
j(p) }, the inside is made up of polynomial expression and shape function; By obtaining the solution of rarefaction representation respectively to three coordinate solving models, to represent local geometric signal;
The method of described step C comprises: add that weight function solves according to local coordinate definition weight function ω (p) partial model, the coordinate of final partial points is determined by the weighted value in different chart, thus the definition overall situation.
When being input as the control mesh of subdivision curved surface, need the local coordinate structure carrying out subdivision curved surface, described steps A is specifically comprising the following steps in such cases:
Steps A 11: given subdivision curved surface control mesh;
Steps A 12: two-layer segmentation also calculates local coordinate: the geometric coordinate of the point obtained after record field of definition grid subdivision twice and these relative coordinates at Local grid;
Steps A 13: constructive geometry coordinate and projection coordinate thereof: utilize relative coordinate to extrapolate these partial projection coordinates with choice refreshments after knowing the projection of coarse grid in the middle of the card of local.
When being input as wire frame structure, need the local coordinate structure carried out in wire-frame model, described steps A is specifically comprising the following steps in such cases:
Steps A 21: given wire frame structure: wire-frame model is made up of the line of three-dimensional;
Steps A 22: the structure structure field of definition grid according to steps A 21: the line of the three-dimensional in steps A 21 constructs a field of definition network naturally, extracts this structure;
Steps A 23: calculate the projection coordinate that line is put: the local coordinate of the point on the line of the three-dimensional in steps A 21 is the coordinate on the line on field of definition grid, calculates the coordinate of partial projection with this.
As the improvement of technique scheme, described in.
As the improvement of technique scheme, described in.
Compared with prior art, implementation result of the present invention is as follows in the present invention:
A kind of method being created flow pattern by rarefaction representation of the present invention, can be generated flow structure according to given geological information, also directly can generate flow structure according to subdivision curved surface or wire frame structure.Except have input the structure of whole projection information, the present invention additionally provides solution during other inputs of employing two kinds (i.e. the control mesh of subdivision curved surface and wire frame structure) simultaneously; For control mesh and wire frame structure these two kinds inputs of subdivision curved surface, use method of the present invention can automatically according to input calculate required for projection information thus direct solution flow structure.
Accompanying drawing explanation
Fig. 1 is a kind of process flow diagram being created the algorithm core of flow pattern by rarefaction representation of the present invention;
Fig. 2 is a kind of method being created flow pattern by rarefaction representation of the present invention is generated flow pattern process flow diagram by subdivision curved surface;
Fig. 3 is a kind of method being created flow pattern by rarefaction representation of the present invention is generated flow pattern process flow diagram by wire frame structure;
Fig. 4 is a kind of definition figure being created flow pattern in the method for flow pattern by rarefaction representation of the present invention;
Fig. 5 is the shape function geometry that in the specific embodiment of the invention, core algorithm adopts;
Fig. 6 is the length of printable support and the relation of its degree of tilt in the specific embodiment of the invention;
The simple and easy browser interface that Fig. 7 provides for the specific embodiment of the invention;
Fig. 8 is flow pattern 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 flow structure result that in the specific embodiment of the invention 2, wire frame structure generates.
Embodiment
Below in conjunction with specific embodiments content of the present invention is described.
Main contents of the present invention there are provided and a kind ofly generate the algorithm frame of flow structure according to given geological information and directly generate the algorithm of flow structure according to subdivision curved surface or wire frame structure.Provide the interface of input subdivision curved surface control mesh and wire frame structure, user obtains flow pattern by inputting these structures, and preserves.
Thoughts of the present invention: because flow structure is defined in the function structure on certain field of definition grid.Two dimensional surface can be embedded into for certain local card (chart).If the projection of three-dimensional geometry to local card can be defined, just can carry out parametrization to geometry signals thus base signal can be defined heavily representing it in local.Because geometry signals has only continuous print feature sometimes, compare with traditional batten and be difficult to portray such signal.So the present invention's shape function (shape function) introduced in the middle of finite element while structure base signal carrys out more effective representation feature.Then by the sparse optimization problem iterative of the overall situation, final rarefaction representation is obtained.
In order to the expression of local is become the overall situation, inventor introduce the concept (transition function) of transfer function.Transfer function defines the coordinate conversion between the card of different local, thus two different expressions can be linked together.Then the unitarity of global definition is ensure that by weighting function.
As shown in Figure 1 to Figure 3, main realization of the present invention comprises three aspects: learn that the flow pattern in partial projection coordinate situation solves; The local coordinate structure of subdivision curved surface; Local coordinate structure in wire-frame model.Wherein Part I is core content of the present invention, and concrete technical scheme is: on certain local card, obtain one group of localized parameterization coordinate { p
i, and the geometry signals of these some correspondences is: { (x
i, y
i, z
i).The basis function set of each local definition is: { d
j(p) }, the inside is made up of polynomial expression and shape function.In order to represent local geometric signal, the present invention is by obtaining the solution of rarefaction representation respectively to three coordinate solving models.For the overall situation, certain partial points may be positioned in the middle of the card of multiple local, according to local coordinate, weight function ω (p) can be defined, thus in the middle of partial model, add that weight function solves, the coordinate of final partial points is determined by the weighted value in different chart, thus reaches the effect of global definition.
Process for subdivided meshes: subdivision curved surface is a kind of curved surface that in computer graphics, frequency of utilization is very high, to have in the field such as to play up as the three-dimensional version of splines and uses widely.In order to the flow pattern obtaining subdivision curved surface represents, the geometric coordinate of the point obtained after record field of definition grid subdivision twice and these relative coordinates at Local grid (barycentric coordinates in triangle gridding or quadrilateral mesh).Relative coordinate is utilized to extrapolate these partial projection coordinates with choice refreshments after knowing the projection of coarse grid in the middle of the card of local.Then utilize these projection coordinates to try to achieve flow pattern to represent.
Process for wire-frame model: wire-frame model is made up of the line in three-dimensional.The line of these three-dimensionals naturally constructs a field of definition network, first utilizes existing algorithm to extract this structure.The local coordinate of the point so on line is exactly the coordinate (inside does not have) on the line on field of definition grid, thus can be easy to the coordinate calculating partial projection.
These three parts final constitute major part of the present invention.
Fig. 4 simply describes the definition of flow structure; Fig. 5 illustrates dictionary geometry used.
Specific embodiment 1
Using with subdivision curved surface as being input as embodiment 1.User needs the control mesh of given subdivision curved surface, as shown in Figure 6.Here subdivision curved surface allows with C ° of constraint.The line wherein not marking c in Fig. 6 is the line indicating c without constraint is C ° of constraint.The invention provides simple interactive interface, as shown in Figure 7, shirtsleeve operation step is as follows simultaneously:
Step 101: user clicks opening button and namely the control mesh of subdivision curved surface can being loaded into internal memory of top.User, can translation by mouse action object, rotates and this grid flexible, and selects a suitable visual angle to check object.
Step 102: namely user clicks keyboard shortcut J key can directly generate subdivided meshes projection information.
Step 103: user clicks right side solve button can solve flow structure.
Generate flow pattern result as shown in Figure 8.The generating principle of flow structure is based on the rarefaction representation of the overall situation.First the projection information that step 102 is required in generating and solving, namely the observation of signal and the partial projection in the card of local, then solve the rarefaction representation problem of the overall situation according to transfer function and weighting function.
Step 104: the flow structure of generation can be shown in mutual interface.User can by mouse action without product, can translation, rotate and this flow structure of scaling, and select a suitable visual angle to check object.
Step 105: flow structure can be preserved out by the save button in left side by user.
Specific embodiment 2
Introduce the specific embodiment 2 wire frame structure being generated flow structure as input below.Fig. 9 illustrates the wire frame structure of input in embodiment 2.This structure is made up of the lines in three-dimensional.And flow structure can be generated equally by interface of the present invention, first can by opening the wire frame structure input that button input suffix is dh.Then solving of flow structure can be carried out by clicking solve button.User can set the parameter of some algorithms of the inside, as degree of rarefication etc.Then can show the flow structure obtained in interface, user can preserve the flow structure of trying to achieve simultaneously.
The flow structure that end user can obtain wanting carries out the operation wanted.
Above content is detailed description made for the present invention in conjunction with specific embodiments, can not assert that the present invention specifically implements to be only limitted to these explanations.For those skilled in the art, without departing from the inventive concept of the premise, some simple deduction or replace can also be made, all should be considered as belonging to the scope of protection of the invention.
Claims (4)
1. created a method for flow pattern by rarefaction representation, it is characterized in that, comprise the following steps:
Steps A: given geological information and its projection coordinate at field of definition grid;
Step B: calculate the projection coordinate on the card of local: carry out parametrization in local to geometry signals thus define base signal heavily representing it, introduce shape function and carry out representation feature while structure base signal;
Step C: solve Global Optimal Problem: by the coordinate conversion between the card of transfer function definition different local, thus two different expressions are linked together, the unitarity of global definition is then guaranteed by weighting function;
Step D: generate result: by the sparse optimization problem iterative of the overall situation, obtain final rarefaction representation.
2. a kind ofly as claimed in claim 1 create the method for flow pattern by rarefaction representation, it is characterized in that,
The method of described steps A comprises: the localized parameterization coordinate obtained on the card of local is: { p
t, the geometry signals of its correspondence is: { (x
t, y
t, z
t);
The method of described step B comprises: the basis function set of each local definition is: { d
f(p) }, the inside is made up of polynomial expression and shape function; By obtaining the solution of rarefaction representation respectively to three coordinate solving models, to represent local geometric signal;
The method of described step C comprises: according to local coordinate definition weight function ω (p), partial model adds that weight function solves, and the coordinate of final partial points is determined by the weighted value in different chart, thus the definition overall situation.
3. a kind ofly as claimed in claim 1 create the method for flow pattern by rarefaction representation, it is characterized in that, described steps A comprises the following steps:
Steps A 11: given subdivision curved surface control mesh;
Steps A 12: two-layer segmentation also calculates local coordinate: the geometric coordinate of the point obtained after record field of definition grid subdivision twice and these relative coordinates at Local grid;
Steps A 13: constructive geometry coordinate and projection coordinate thereof: utilize relative coordinate to extrapolate these partial projection coordinates with choice refreshments after knowing the projection of coarse grid in the middle of the card of local.
4. a kind ofly as claimed in claim 1 create the method for flow pattern by rarefaction representation, it is characterized in that, described steps A comprises the following steps:
Steps A 21: given wire frame structure: wire-frame model is made up of the line of three-dimensional;
Steps A 22: the structure structure field of definition grid according to steps A 21: the line of the three-dimensional in steps A 21 constructs a field of definition network naturally, extracts this structure;
Steps A 23: calculate the projection coordinate that line is put: the local coordinate of the point on the line of the three-dimensional in steps A 21 is the coordinate on the line on field of definition grid, calculates the coordinate of partial projection with this.
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