CN116310145A - Three-dimensional space model reconstruction method and device based on orthogonal basis functions - Google Patents
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Abstract
The disclosure provides a three-dimensional space model reconstruction method and device based on orthogonal basis functions, wherein the method comprises the following steps: obtaining a first Laplace operator matrix of the initial three-dimensional space model, carrying out feature decomposition on the first Laplace operator matrix to generate a plurality of feature equations, carrying out orthogonalization processing on the plurality of feature equations to obtain a plurality of orthogonal basis functions, determining a target three-dimensional coordinate based on the plurality of orthogonal basis functions, and constructing the target three-dimensional space model based on the plurality of target three-dimensional coordinates. By implementing the method disclosed by the invention, the calculation cost and the storage cost of the model reconstruction process can be reduced to a large extent based on the orthogonal basis function, and the model reconstruction effect is effectively improved.
Description
Technical Field
The disclosure relates to the technical field of computer vision, in particular to a three-dimensional space model reconstruction method and device based on orthogonal basis functions.
Background
Three-dimensional reconstruction refers to the establishment of a mathematical model suitable for computer representation and processing of a three-dimensional object, is the basis for processing, operating and analyzing the properties of the three-dimensional object in a computer environment, and is also a key technology for establishing virtual reality expressing an objective world in a computer.
In the related art, when the model reconstruction is performed on the three-dimensional space model, higher calculation cost and storage cost are required, and the model reconstruction effect is poor.
Disclosure of Invention
The present disclosure aims to solve, at least to some extent, one of the technical problems in the related art.
Therefore, the purpose of the present disclosure is to provide a three-dimensional space model reconstruction method, device, computer equipment and storage medium based on orthogonal basis functions, which can reduce the calculation cost and storage cost of the model reconstruction process to a greater extent based on the orthogonal basis functions, and effectively improve the model reconstruction effect.
The three-dimensional space model reconstruction method based on the orthogonal basis functions provided by the embodiment of the first aspect of the disclosure comprises the following steps:
acquiring a first Laplace operator matrix of an initial three-dimensional space model;
performing feature decomposition on the first Laplace operator matrix to generate a plurality of feature equations;
orthogonalizing the plurality of characteristic equations to obtain a plurality of orthogonal basis functions;
determining a target three-dimensional coordinate based on the plurality of orthogonal basis functions;
and constructing a target three-dimensional space model based on a plurality of target three-dimensional coordinates.
According to the three-dimensional space model reconstruction method based on the orthogonal basis functions, which is provided by the embodiment of the first aspect of the disclosure, through obtaining a first Laplacian matrix of an initial three-dimensional space model, carrying out feature decomposition on the first Laplacian matrix to generate a plurality of feature equations, carrying out orthogonalization processing on the plurality of feature equations to obtain a plurality of orthogonal basis functions, determining target three-dimensional coordinates based on the plurality of orthogonal basis functions, and constructing the target three-dimensional space model based on the plurality of target three-dimensional coordinates. By implementing the method disclosed by the invention, the calculation cost and the storage cost of the model reconstruction process can be reduced to a large extent based on the orthogonal basis function, and the model reconstruction effect is effectively improved.
An embodiment of the second aspect of the present disclosure provides a three-dimensional space model reconstruction device based on an orthogonal basis function, including:
the acquisition module is used for acquiring a first Laplacian matrix of the initial three-dimensional space model;
the first processing module is used for carrying out feature decomposition on the first Laplacian matrix so as to generate a plurality of feature equations;
the second processing module is used for orthogonalizing the plurality of characteristic equations to obtain a plurality of orthogonal basis functions;
a determining module, configured to determine a three-dimensional coordinate of the target based on the plurality of orthogonal basis functions;
and the model construction module is used for constructing a target three-dimensional space model based on a plurality of target three-dimensional coordinates.
According to the three-dimensional space model reconstruction device based on the orthogonal basis functions, which is provided by the embodiment of the second aspect of the disclosure, through obtaining the first Laplacian matrix of the initial three-dimensional space model, carrying out feature decomposition on the first Laplacian matrix to generate a plurality of feature equations, carrying out orthogonalization processing on the plurality of feature equations to obtain a plurality of orthogonal basis functions, determining target three-dimensional coordinates based on the plurality of orthogonal basis functions, and constructing the target three-dimensional space model based on the plurality of target three-dimensional coordinates. By implementing the method disclosed by the invention, the calculation cost and the storage cost of the model reconstruction process can be reduced to a large extent based on the orthogonal basis function, and the model reconstruction effect is effectively improved.
Embodiments of the third aspect of the present disclosure provide a computer device, including: the system comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein the processor realizes the three-dimensional space model reconstruction method based on the orthogonal basis functions as provided by the embodiment of the first aspect of the disclosure when the processor executes the program.
An embodiment of a fourth aspect of the present disclosure proposes a non-transitory computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements a three-dimensional spatial model reconstruction method based on orthogonal basis functions as proposed by an embodiment of the first aspect of the present disclosure.
An embodiment of a fifth aspect of the present disclosure proposes a computer program product which, when executed by a processor, performs a three-dimensional spatial model reconstruction method based on orthogonal basis functions as proposed by an embodiment of the first aspect of the present disclosure.
Additional aspects and advantages of the disclosure will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the disclosure.
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The foregoing and/or additional aspects and advantages of the present disclosure will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings, in which:
FIG. 1 is a flow chart of a three-dimensional model reconstruction method based on orthogonal basis functions according to an embodiment of the present disclosure;
FIG. 2 is a flow chart of a three-dimensional model reconstruction method based on orthogonal basis functions according to another embodiment of the present disclosure;
FIG. 3 is a schematic diagram of a polygonal patch model reconstruction flow proposed in accordance with the present disclosure;
FIG. 4 is a schematic diagram of a model reconstruction effect proposed in accordance with the present disclosure;
FIG. 5 is a schematic structural diagram of a three-dimensional model reconstruction device based on orthogonal basis functions according to an embodiment of the present disclosure;
FIG. 6 illustrates a block diagram of an exemplary computer device suitable for use in implementing embodiments of the present disclosure.
Detailed Description
Embodiments of the present disclosure are described in detail below, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to like or similar elements or elements having like or similar functions throughout. The embodiments described below by referring to the drawings are exemplary only for explaining the present disclosure and are not to be construed as limiting the present disclosure. On the contrary, the embodiments of the disclosure include all alternatives, modifications, and equivalents as may be included within the spirit and scope of the appended claims.
Fig. 1 is a flow chart of a three-dimensional model reconstruction method based on orthogonal basis functions according to an embodiment of the disclosure.
It should be noted that, the execution body of the three-dimensional space model reconstruction method based on the orthogonal basis functions in this embodiment is a three-dimensional space model reconstruction device based on the orthogonal basis functions, and the device may be implemented in a software and/or hardware manner, and the device may be configured in a computer device, where the computer device may include, but is not limited to, a terminal, a server, and the like, and the terminal may be a mobile phone, a palm computer, and the like.
As shown in fig. 1, the three-dimensional space model reconstruction method based on the orthogonal basis functions includes:
s101: a first laplacian matrix of the initial three-dimensional spatial model is obtained.
The initial three-dimensional space model refers to an unprocessed three-dimensional space model obtained in the embodiment of the disclosure, for example, may be a three-dimensional space model of an area (such as a coal mine) or a three-dimensional space model of an object (such as a vehicle), which is not limited.
Wherein the first Laplace matrix, which is the Laplace calculated from the initial three-dimensional model by the pointer (Laplacian Operator), may be used to describe the "degree of curvature" or "rate of change" of the function on the manifold.
That is, in the embodiment of the present disclosure, when model reconstruction is performed, the first laplacian matrix of the initial three-dimensional space model may be calculated, so as to provide reliable data support for the calculation process of the subsequent model reconstruction.
S102: the first laplacian matrix is eigen-decomposed to generate a plurality of eigen equations.
The feature decomposition, also called spectral decomposition, is a method of decomposing a matrix into products of the matrix represented by its feature values and feature vectors.
That is, in the embodiment of the present disclosure, after the first laplacian matrix of the initial three-dimensional space model is acquired, the first laplacian matrix may be subjected to feature decomposition to generate a plurality of feature equations, so that the obtained plurality of feature equations may accurately describe feature information of different frequencies of the initial three-dimensional space model.
S103: orthogonalizing the plurality of characteristic equations to obtain a plurality of orthogonal basis functions.
The orthogonal basis functions are mutually orthogonal basis functions obtained by orthogonalizing a plurality of characteristic equations.
It will be appreciated that since the laplace matrix is a symmetric semi-positive definite matrix, an n-order matrix must have n linearly independent eigenvectors. n linearly independent vectors in an n-dimensional linear space may all form a set of bases. Thus, the n eigenvectors of the laplace matrix are linearly independent, being a set of bases in n-dimensional space. Meanwhile, feature vectors corresponding to different feature values of the symmetric matrix are mutually orthogonal, and a matrix formed by the orthogonal feature vectors is an orthogonal matrix. Thus, the n eigenvectors of the laplace matrix are a set of orthonormal basis in n-dimensional space. However, due to possible heavy root and numerical calculation accuracy influence, the plurality of characteristic equations may not be orthogonal, so that in the embodiment of the disclosure, the plurality of characteristic equations may be orthogonalized to obtain a plurality of orthogonal basis functions, and thus, the robustness of the model reconstruction process may be effectively improved.
S104: the three-dimensional coordinates of the target are determined based on a plurality of orthogonal basis functions.
The three-dimensional coordinates of the target may be vertex reconstruction coordinates obtained based on a plurality of orthogonal basis functions.
For example, in the embodiments of the present disclosure, the coordinates of the vertex on each axis may be regarded as a scalar field acting on the three-dimensional model, and the calculation process of the scalar field may be based on the following steps:
1. determining a set of basis functions: a set of basis functions with good properties, such as trigonometric functions, polynomial functions, etc., is selected.
2. Determining the number of basis functions: the number of basis functions used is determined according to the requirements of the problem and the complexity of the algorithm.
3. Approximating the scalar field with the selected basis function: representing scalar fields as linear combinations of basis functions, i.e.
Wherein->
Is a scalar field,/->
Is a coefficient of->
Is the kth basis function. Coefficient->
Representing the weight of each basis function in the scalar field.
4. Solving coefficients: optimizing weight coefficients by minimizing errors
Can be calculated by a least square method or the like, and can be adjusted for different optimization targets.
5. Using the approximation expression: the scalar field is calculated and rendered using the above approximation expression, i.e. a linear combination of basis functions of the scalar field.
S105: and constructing a target three-dimensional space model based on the plurality of target three-dimensional coordinates.
In this embodiment, a first laplacian matrix of an initial three-dimensional space model is obtained, a feature decomposition is performed on the first laplacian matrix to generate a plurality of feature equations, orthogonalization processing is performed on the plurality of feature equations to obtain a plurality of orthogonal basis functions, a target three-dimensional coordinate is determined based on the plurality of orthogonal basis functions, and a target three-dimensional space model is constructed based on the plurality of target three-dimensional coordinates. By implementing the method disclosed by the invention, the calculation cost and the storage cost of the model reconstruction process can be reduced to a large extent based on the orthogonal basis function, and the model reconstruction effect is effectively improved.
Fig. 2 is a flow chart of a three-dimensional model reconstruction method based on orthogonal basis functions according to another embodiment of the present disclosure.
As shown in fig. 2, the three-dimensional space model reconstruction method based on the orthogonal basis functions includes:
s201: the model type of the initial three-dimensional space model is determined.
The model type may refer to the type of the initial three-dimensional space model.
It will be appreciated that there may be differences in the laplacian matrix calculation process for different types of three-dimensional space models, and thus, in embodiments of the present disclosure, when determining the model type of the initial three-dimensional space model, reliable reference information may be provided for the calculation process of the subsequent first laplacian matrix.
S202: based on the model type, a first laplacian matrix is acquired.
That is, in the embodiment of the present disclosure, the model type of the initial three-dimensional space model may be determined, and the first laplacian matrix may be acquired based on the model type, so that suitability of the first laplacian matrix acquiring process and the model type of the initial three-dimensional space model may be effectively improved.
Alternatively, in some embodiments, when the first laplacian matrix is acquired based on the model type, the laplacian matrix of the initial three-dimensional space model may be calculated as the first laplacian matrix when the model type indicates that the initial three-dimensional space model belongs to the triangle patch model.
The triangular surface patch model refers to a three-dimensional space model which is composed of triangular surface patches.
Optionally, in some embodiments, when the first laplace operator matrix is acquired based on the model type, when the model type indicates that the initial three-dimensional space model belongs to the polygon patch model, performing model conversion on the initial three-dimensional space model to obtain a target three-dimensional space model, acquiring a second laplace operator matrix of the target three-dimensional space model, and performing matrix conversion on the second laplace operator matrix to obtain the first laplace operator matrix, where the target three-dimensional space model belongs to the triangle patch model, thereby realizing calculation of the laplace operator matrix for the polygon patch model and effectively improving practicality of a calculation process of the laplace operator matrix.
The polygonal surface patch model may be a three-dimensional model composed of any polygonal surface patch.
That is, in the embodiment of the present disclosure, when the initial three-dimensional space model belongs to the triangular patch model, the first laplacian matrix may be directly obtained by calculation, and when the initial three-dimensional space model belongs to the polygonal patch model, the initial three-dimensional space model may be subjected to model conversion to obtain the target three-dimensional space model, the second laplacian matrix of the target three-dimensional space model is obtained, and the second laplacian matrix is subjected to matrix conversion to obtain the first laplacian matrix, so as to effectively improve flexibility of a model reconstruction process.
S203: the number of vertices contained in the initial three-dimensional spatial model is determined.
In an embodiment of the present disclosure, the initial three-dimensional space model may be formed by stitching a plurality of polygonal patches, and the number of vertices may refer to the number of vertices of the plurality of polygonal patches.
S204: and obtaining model reconstruction requirement information of the initial three-dimensional space model.
The model reconstruction requirement information may be used to describe a model reconstruction requirement of a user on an initial three-dimensional space model, for example, a simulation degree requirement of the user on a model obtained after reconstruction.
S205: and determining the number of feature roots to be calculated based on the number of vertexes and the model reconstruction requirement information.
The number of feature roots to be calculated may refer to the number of feature equations that need to be calculated when performing feature decomposition on the first laplacian matrix.
In the embodiment of the disclosure, the number of one or more feature roots to be calculated can be determined according to the model reconstruction requirement information and used for the subsequent model reconstruction process respectively, which is not limited.
S206: and carrying out feature decomposition on the first Laplacian matrix based on the number of the feature roots to be calculated so as to generate a plurality of feature equations.
That is, in the embodiment of the present disclosure, after the first laplace operator matrix is acquired based on the model type, the number of vertices included in the initial three-dimensional space model may be determined, model reconstruction requirement information of the initial three-dimensional space model may be acquired, the number of feature roots to be calculated may be determined based on the number of vertices and the model reconstruction requirement information, and feature decomposition may be performed on the first laplace operator matrix based on the number of feature roots to be calculated, so as to generate a plurality of feature equations, thereby effectively fusing the number of vertices and the model reconstruction requirement information in a feature decomposition process of the first laplace operator matrix, and effectively improving practicability of the obtained plurality of feature equations.
S207: orthogonalizing the plurality of characteristic equations to obtain a plurality of orthogonal basis functions.
For example, in the embodiment of the present disclosure, the minimum number of feature roots (i.e. the number of feature roots to be calculated) may be set to K, and the feature equation may be calculated by decomposition
To obtain an orthogonal basis function, the present invention can use Schmidt orthogonalization to obtain an orthogonal basis functionThe number is calculated by the following steps:
then aggregate
Is the desired orthogonal basis function.
S208: based on the orthogonal basis function and the number of vertices, a reference coordinate equation is determined, wherein the reference coordinate equation contains an orthogonal projection coefficient corresponding to the orthogonal basis function, the reference coordinate equation indicating a scalar field of the first coordinate value, or the second coordinate value, or the third coordinate value.
Wherein the orthogonal projection coefficients may be used to indicate the weights of the corresponding orthogonal basis functions in the scalar field.
The first coordinate value, the second coordinate value and the third coordinate value may be coordinate values corresponding to X, Y and Z axes of the vertex in a three-dimensional cartesian coordinate system.
S209: based on the characteristic information of the orthogonal basis function, an expression of the orthogonal projection coefficient is calculated.
For example, considering the coordinates of each axis as a scalar field acting on a three-dimensional model, the orthogonal basis functions can be expressed as:
wherein,,
representing the number of vertices, +.>
Is a scalar representing the orthogonal projection coefficients, < >>
Representing orthogonal basis functions. Due to the orthogonal basis functions satisfying->
We can therefore calculate arbitrary coefficients from the orthogonal relationship: />
The expression that is to say the orthogonal projection coefficients can be expressed as
。
S210: the first coordinate value, or the second coordinate value, or the third coordinate value is calculated based on the orthogonal basis function, the number of feature roots to be calculated, and the expression.
S211: the target three-dimensional coordinate is determined based on the first coordinate value, the second coordinate value, and the third coordinate value.
For example, in the embodiment of the present disclosure, when the number of feature roots to be calculated is K, the original coordinate equation may be written as
Which is a kind of
I.e. the position of the reconstructed coordinate point, the subscript indicates +.>
Coordinates, replace it with +.>
And obtaining the three-dimensional coordinates of each reconstruction vertex by the coordinates.
That is, in the embodiment of the present disclosure, after orthogonalization processing is performed on a plurality of feature equations to obtain a plurality of orthogonal base functions, a reference coordinate equation may be determined based on the orthogonal base functions and the number of vertices, where the reference coordinate equation includes an orthographic projection coefficient corresponding to the orthogonal base functions, the reference coordinate equation is used to indicate a scalar field of a first coordinate value, or a second coordinate value, or a third coordinate value, based on feature information of the orthogonal base functions, an expression of the orthographic projection coefficient is calculated, based on the orthogonal base functions, the number of feature roots to be calculated, and the expression, a first coordinate value, or a second coordinate value, or a third coordinate value is calculated, and a target three-dimensional coordinate is determined based on the first coordinate value, the second coordinate value, and the third coordinate value, thereby, reliability of a calculation process of the target three-dimensional coordinate may be effectively improved, and accuracy of the obtained target three-dimensional coordinate may be ensured.
S212: and constructing a target three-dimensional space model based on the plurality of target three-dimensional coordinates.
The description of S212 may be specifically referred to the above embodiments, and will not be repeated here.
In this embodiment, the model type of the initial three-dimensional space model is determined, and the first laplace operator matrix is acquired based on the model type, so that suitability of the first laplace operator matrix acquisition process and the model type of the initial three-dimensional space model can be effectively improved. When the model type indicates that the initial three-dimensional space model belongs to the polygonal patch model, performing model conversion on the initial three-dimensional space model to obtain a target three-dimensional space model, obtaining a second Laplace operator matrix of the target three-dimensional space model, and performing matrix conversion on the second Laplace operator matrix to obtain a first Laplace operator matrix, wherein the target three-dimensional space model belongs to the triangular patch model, so that Laplace operator matrix calculation on the polygonal patch model can be realized, and the practicability of the Laplace operator matrix calculation process can be effectively improved. The method comprises the steps of determining the number of vertexes contained in an initial three-dimensional space model, obtaining model reconstruction requirement information of the initial three-dimensional space model, determining the number of feature roots to be calculated based on the number of vertexes and the model reconstruction requirement information, and carrying out feature decomposition on a first Laplace operator matrix based on the number of feature roots to be calculated to generate a plurality of feature equations, so that the number of vertexes and the model reconstruction requirement information can be effectively fused in the feature decomposition process of the first Laplace operator matrix, and the practicability of the obtained plurality of feature equations is effectively improved. And determining a reference coordinate equation based on the orthogonal basis function and the number of vertexes, wherein the reference coordinate equation comprises an orthogonal projection coefficient corresponding to the orthogonal basis function, the reference coordinate equation is used for indicating a scalar field of a first coordinate value, a second coordinate value or a third coordinate value, an expression of the orthogonal projection coefficient is calculated based on characteristic information of the orthogonal basis function, the number of characteristic roots to be calculated and the expression, the first coordinate value, the second coordinate value or the third coordinate value are calculated based on the orthogonal basis function, the number of characteristic roots to be calculated and the expression, and the target three-dimensional coordinate is determined based on the first coordinate value, the second coordinate value and the third coordinate value, so that reliability of a calculation process of the target three-dimensional coordinate can be effectively improved, and accuracy of the obtained target three-dimensional coordinate is guaranteed.
For example, as shown in fig. 3, fig. 3 is a schematic diagram of a polygonal patch model reconstruction flow according to the present disclosure, which includes two stages: (1) computing a laplacian matrix of any polygon; (2) And carrying out feature decomposition and orthogonalization of a feature equation based on the Laplace operator matrix, and carrying out model three-dimensional reconstruction by utilizing the orthogonalization equation. The Laplacian matrix of the three-dimensional model of any polygon is calculated by inserting virtual vertexes on each polygonal surface sheet, calculating the Laplacian matrix of the triangular mesh model formed after the virtual vertexes are inserted, and converting the model Laplacian matrix of the triangular mesh back to the original polygonal model by using a Galerkin method on the basis. After the Laplacian matrix of any polygon is obtained through calculation, the first K characteristic equations and characteristic values are obtained through characteristic decomposition of the Laplacian matrix, at the moment, the characteristic equations may not be orthogonal, schmidt orthogonalization and normalization processing are adopted to obtain an orthogonalization unit vector as an orthogonalization basis function, orthogonalization coefficients of the coordinate equations are calculated, and then space reconstruction is carried out.
For example, as shown in fig. 4, fig. 4 is a schematic diagram of the model reconstruction effect according to the present disclosure, in which an initial three-dimensional space model (original model) is developed, and the number of feature roots K to be calculated is taken as 20, 30, 40, and 50, and the resulting model is reconstructed according to the present invention.
Fig. 5 is a schematic structural diagram of a three-dimensional model reconstruction device based on orthogonal basis functions according to an embodiment of the present disclosure.
As shown in fig. 5, the three-dimensional space model reconstruction device 50 based on the orthogonal basis functions includes:
an obtaining module 501, configured to obtain a first laplacian matrix of an initial three-dimensional space model;
a first processing module 502, configured to perform feature decomposition on the first laplacian matrix to generate a plurality of feature equations;
a second processing module 503, configured to orthogonalize a plurality of feature equations to obtain a plurality of orthogonal basis functions;
a determining module 504, configured to determine a three-dimensional coordinate of the target based on a plurality of orthogonal basis functions;
the model building module 505 is configured to build a three-dimensional space model of the target based on the plurality of three-dimensional coordinates of the target.
It should be noted that the foregoing explanation of the three-dimensional model reconstruction method based on the orthogonal basis functions is also applicable to the three-dimensional model reconstruction device based on the orthogonal basis functions in this embodiment, and will not be repeated here.
In this embodiment, a first laplacian matrix of an initial three-dimensional space model is obtained, a feature decomposition is performed on the first laplacian matrix to generate a plurality of feature equations, orthogonalization processing is performed on the plurality of feature equations to obtain a plurality of orthogonal basis functions, a target three-dimensional coordinate is determined based on the plurality of orthogonal basis functions, and a target three-dimensional space model is constructed based on the plurality of target three-dimensional coordinates. By implementing the method disclosed by the invention, the calculation cost and the storage cost of the model reconstruction process can be reduced to a large extent based on the orthogonal basis function, and the model reconstruction effect is effectively improved.
FIG. 6 illustrates a block diagram of an exemplary computer device suitable for use in implementing embodiments of the present disclosure. The computer device 12 shown in fig. 6 is merely an example and should not be construed as limiting the functionality and scope of use of the disclosed embodiments.
As shown in FIG. 6, the computer device 12 is in the form of a general purpose computing device. Components of computer device 12 may include, but are not limited to: one or more processors or processing units 16, a system memory 28, a bus 18 that connects the various system components, including the system memory 28 and the processing units 16.
Although not shown in fig. 6, a magnetic disk drive for reading from and writing to a removable non-volatile magnetic disk (e.g., a "floppy disk"), and an optical disk drive for reading from or writing to a removable non-volatile optical disk (e.g., a compact disk read only memory (Compact Disc Read Only Memory; hereinafter CD-ROM), digital versatile read only optical disk (Digital Video Disc Read Only Memory; hereinafter DVD-ROM), or other optical media) may be provided. In such cases, each drive may be coupled to bus 18 through one or more data medium interfaces. Memory 28 may include at least one program product having a set (e.g., at least one) of program modules configured to carry out the functions of the various embodiments of the disclosure.
A program/utility 40 having a set (at least one) of program modules 42 may be stored in, for example, memory 28, such program modules 42 including, but not limited to, an operating system, one or more application programs, other program modules, and program data, each or some combination of which may include an implementation of a network environment. Program modules 42 generally perform the functions and/or methods in the embodiments described in this disclosure.
The computer device 12 may also communicate with one or more external devices 14 (e.g., keyboard, pointing device, display 24, etc.), one or more devices that enable a person to interact with the computer device 12, and/or any devices (e.g., network card, modem, etc.) that enable the computer device 12 to communicate with one or more other computing devices. Such communication may occur through an input/output (I/O) interface 22. Moreover, the computer device 12 may also communicate with one or more networks such as a local area network (Local Area Network; hereinafter LAN), a wide area network (Wide Area Network; hereinafter WAN) and/or a public network such as the Internet via the network adapter 20. As shown, network adapter 20 communicates with other modules of computer device 12 via bus 18. It should be appreciated that although not shown, other hardware and/or software modules may be used in connection with computer device 12, including, but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, data backup storage systems, and the like.
The processing unit 16 executes various functional applications and data processing by running a program stored in the system memory 28, for example, implementing the three-dimensional space model reconstruction method based on orthogonal basis functions mentioned in the foregoing embodiment.
To achieve the above-described embodiments, the present disclosure also proposes a non-transitory computer-readable storage medium having stored thereon a computer program which, when executed by a processor, implements a three-dimensional spatial model reconstruction method based on orthogonal basis functions as proposed in the foregoing embodiments of the present disclosure.
To achieve the above embodiments, the present disclosure also proposes a computer program product which, when executed by an instruction processor in the computer program product, performs a three-dimensional spatial model reconstruction method based on orthogonal basis functions as proposed in the foregoing embodiments of the present disclosure.
Other embodiments of the disclosure will be apparent to those skilled in the art from consideration of the specification and practice of the disclosure disclosed herein. This disclosure is intended to cover any adaptations, uses, or adaptations of the disclosure following the general principles of the disclosure and including such departures from the present disclosure as come within known or customary practice within the art to which the disclosure pertains. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the disclosure being indicated by the following claims.
It is to be understood that the present disclosure is not limited to the precise arrangements and instrumentalities shown in the drawings, and that various modifications and changes may be effected without departing from the scope thereof. The scope of the present disclosure is limited only by the appended claims.
It should be noted that in the description of the present disclosure, the terms "first," "second," and the like are used for descriptive purposes only and are not to be construed as indicating or implying relative importance. Furthermore, in the description of the present disclosure, unless otherwise indicated, the meaning of "a plurality" is two or more.
Any process or method descriptions in flow charts or otherwise described herein may be understood as representing modules, segments, or portions of code which include one or more executable instructions for implementing specific logical functions or steps of the process, and further implementations are included within the scope of the preferred embodiment of the present disclosure in which functions may be executed out of order from that shown or discussed, including substantially concurrently or in reverse order, depending on the functionality involved, as would be understood by those reasonably skilled in the art of the embodiments of the present disclosure.
It should be understood that portions of the present disclosure may be implemented in hardware, software, firmware, or a combination thereof. In the above-described embodiments, the various steps or methods may be implemented in software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, may be implemented using any one or combination of the following techniques, as is well known in the art: discrete logic circuits having logic gates for implementing logic functions on data signals, application specific integrated circuits having suitable combinational logic gates, programmable Gate Arrays (PGAs), field Programmable Gate Arrays (FPGAs), and the like.
Those of ordinary skill in the art will appreciate that all or a portion of the steps carried out in the method of the above-described embodiments may be implemented by a program to instruct related hardware, where the program may be stored in a computer readable storage medium, and where the program, when executed, includes one or a combination of the steps of the method embodiments.
Furthermore, each functional unit in the embodiments of the present disclosure may be integrated in one processing module, or each unit may exist alone physically, or two or more units may be integrated in one module. The integrated modules may be implemented in hardware or in software functional modules. The integrated modules may also be stored in a computer readable storage medium if implemented in the form of software functional modules and sold or used as a stand-alone product.
The above-mentioned storage medium may be a read-only memory, a magnetic disk or an optical disk, or the like.
In the description of the present specification, a description referring to terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present disclosure. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiments or examples. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
Although embodiments of the present disclosure have been shown and described above, it will be understood that the above embodiments are illustrative and not to be construed as limiting the present disclosure, and that variations, modifications, alternatives, and variations may be made to the above embodiments by one of ordinary skill in the art within the scope of the present disclosure.
Claims (10)
1. The three-dimensional space model reconstruction method based on the orthogonal basis functions is characterized by comprising the following steps of:
acquiring a first Laplace operator matrix of an initial three-dimensional space model;
performing feature decomposition on the first Laplace operator matrix to generate a plurality of feature equations;
orthogonalizing the plurality of characteristic equations to obtain a plurality of orthogonal basis functions;
determining a target three-dimensional coordinate based on the plurality of orthogonal basis functions;
and constructing a target three-dimensional space model based on a plurality of target three-dimensional coordinates.
2. The method of claim 1, wherein the performing feature decomposition on the first laplacian matrix to generate a plurality of feature equations comprises:
determining the number of vertices contained in the initial three-dimensional space model;
obtaining model reconstruction requirement information of the initial three-dimensional space model;
determining the number of feature roots to be calculated based on the number of vertexes and the model reconstruction demand information;
and carrying out feature decomposition on the first Laplacian matrix based on the number of the feature roots to be calculated so as to generate the plurality of feature equations.
3. The method of claim 2, wherein the target three-dimensional coordinates comprise: a first coordinate value, a second coordinate value, and a third coordinate value;
wherein the determining the three-dimensional coordinates of the target based on the plurality of orthogonal basis functions includes:
determining a reference coordinate equation based on the orthogonal basis function and the number of vertices, wherein the reference coordinate equation comprises an orthogonal projection coefficient corresponding to the orthogonal basis function, and the reference coordinate equation is used for indicating a scalar field of the first coordinate value, the second coordinate value or the third coordinate value;
calculating an expression of the orthogonal projection coefficient based on the characteristic information of the orthogonal basis function;
calculating the first coordinate value, the second coordinate value or the third coordinate value based on the orthogonal basis function, the feature root number to be calculated and the expression;
the target three-dimensional coordinate is determined based on the first coordinate value, the second coordinate value, and the third coordinate value.
4. The method of claim 1, wherein the obtaining a first laplacian matrix of an initial three-dimensional spatial model comprises:
determining a model type of the initial three-dimensional space model;
and acquiring the first Laplacian matrix based on the model type.
5. The method of claim 4, wherein the obtaining the first laplacian matrix based on the model type comprises:
and when the model type indicates that the initial three-dimensional space model belongs to a triangle patch model, calculating a Laplacian matrix of the initial three-dimensional space model as the first Laplacian matrix.
6. The method of claim 4, wherein the obtaining the first laplacian matrix based on the model type comprises:
when the model type indicates that the initial three-dimensional space model belongs to a polygonal patch model, performing model conversion on the initial three-dimensional space model to obtain a target three-dimensional space model, obtaining a second Laplacian matrix of the target three-dimensional space model, and performing matrix conversion on the second Laplacian matrix to obtain the first Laplacian matrix, wherein the target three-dimensional space model belongs to a triangular patch model.
7. A three-dimensional spatial model reconstruction device based on orthogonal basis functions, comprising:
the acquisition module is used for acquiring a first Laplacian matrix of the initial three-dimensional space model;
the first processing module is used for carrying out feature decomposition on the first Laplacian matrix so as to generate a plurality of feature equations;
the second processing module is used for orthogonalizing the plurality of characteristic equations to obtain a plurality of orthogonal basis functions;
a determining module, configured to determine a three-dimensional coordinate of the target based on the plurality of orthogonal basis functions;
and the model construction module is used for constructing a target three-dimensional space model based on a plurality of target three-dimensional coordinates.
8. A computer device, comprising:
at least one processor; and
a memory communicatively coupled to the at least one processor; wherein,,
the memory stores instructions executable by the at least one processor to enable the at least one processor to perform the method of any one of claims 1-6.
9. A non-transitory computer readable storage medium storing computer instructions, wherein the computer instructions are for causing the computer to perform the method of any one of claims 1-6.
10. A computer program product comprising a computer program which, when executed by a processor, implements the steps of the method according to any of claims 1-6.
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| 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 |
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| CN110415339A (en) * | 2019-07-19 | 2019-11-05 | 清华大学 | The method and apparatus for calculating the matching relationship between input three-dimensional body |
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