CN110223378B - Quadric surface element extraction method, system and device based on hierarchical clustering - Google Patents
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Abstract
The invention belongs to the field of computer graphic processing, and particularly relates to a quadric surface element extraction method, system and device based on hierarchical clustering, aiming at solving the problem that simple quadric surface element detection is not suitable. The method comprises the steps of obtaining triangular grids of a three-dimensional model, and taking each triangle as a clustering area to obtain a clustering area set; respectively taking the clustering areas adjacent to two sides as an ordered pair, and respectively calculating the fitting cost of each ordered pair; selecting a group of ordered pairs with the minimum fitting cost, fitting the corresponding clustering regions to serve as a new clustering region updating clustering region set; iteratively calculating the fitting cost of each clustering region according to preset iteration times based on the new clustering region set and fitting to obtain the fitting result of each type of clustering region; and extracting the quadric surface element based on the obtained fitting result. The invention provides a high-efficiency quadric surface element detection method, which extracts high-quality simple quadric surface elements.
Description
Technical Field
The invention belongs to the field of computer graphic processing, and particularly relates to a quadric surface element extraction method, system and device based on hierarchical clustering.
Background
Triangular meshes are the most common form of three-dimensional graphical representation in computer graphics and three-dimensional vision. In recent years, with the rapid development of three-dimensional data acquisition technology in hardware and software, it becomes easier to acquire high-precision geometric data. However, the obtained raw data is often large in scale, lacks meaningful information, and is difficult to directly apply to various practical applications. For example, in industrial design and manufacturing applications, the three-dimensional model of the original design may be damaged or otherwise not processed in other software for various reasons, and only the triangular mesh may still be acquired and used. Even if only minor modifications are desired, this is difficult to achieve by simply adjusting the shape parameters. Therefore, in many digital technologies such as three-dimensional scenes and 3D printing, it is necessary to detect and identify high-quality primitives from complex three-dimensional data.
Primitive extraction can be viewed as a grid segmentation problem that has been extensively studied over the past few decades. Different criteria are proposed for different tasks, e.g. approximate fidelity and region smoothness are the main concerns for reverse engineering and shape approximation, 3D printing requires printability and size constraints for each part, shape analysis by splitting shapes along the ridge-valley lines, and scene understanding semantically labels high-level primitives. Correspondingly, there are also a number of grid segmentation algorithms and primitive Extraction algorithms, such as convex decomposition algorithm (j. -m.lien, n.m.amato, applied texture consistent optimization of polymeric and associated applications, complex.air texture in.des.25 (7) (2008) 503. 522.), parametric Extraction algorithm with respect to planar (c. -s.david, a.pierce, d.material, volumetric shape adaptation, ac.graph. (SIGGRAPH)23 (2004) 905. trace 914.), spherical and cylindrical (l.k.wu, joint hua, structural virtual texture in.168. texture, texture in respect of spherical and cylindrical (r.k.wu, texture in.g. 31. 12. ellipsoid, general texture in.24. weigh. 51. 12. texture, texture in.24. texture, texture in.51. 12. ellipsoid, general texture in (r. 12. d.3. 12. ellipsoid, 2. g.3. texture in.51. 12. contour, 2. ellipsoid, 2. 12. ellipsoid, 2. 12. f. And indoor/outdoor scene semantic object recognition algorithms (y.m.kim, n.j.mitra, D. -m.yan, l.j.guibas, Acquiring 3D index definitions with variability and repetition, ACM trans.graph. (sigraph 435 ASIA)31 (2012)138: 1-138: 11.).
However, the detection of simple primitives remains an ill-defined problem, and these methods are not easily generalized for other types of primitives. Of all these existing methods, hierarchical clustering is the simplest and most efficient algorithm for primitive detection. Particularly, for the three-dimensional model, pairwise clustering of adjacent categories is performed from bottom to top through some well-designed fitting standards, so that a high-quality fitting result can be obtained.
Disclosure of Invention
In order to solve the above-mentioned problems in the prior art, that is, to solve the problem that simple quadric surface primitive detection is not suitable, in a first aspect of the present invention, a method for extracting quadric surface primitives based on hierarchical clustering is provided, the method comprising:
step S10, acquiring triangular meshes of the three-dimensional model, and taking each triangle as a clustering area to obtain a clustering area set;
step S20, respectively taking the adjacent clustering areas on two sides as an ordered pair, and respectively calculating the fitting cost of each ordered pair; the fitting cost is obtained based on fitting approximation errors and boundary constraint errors;
step S30, selecting a group of ordered pairs with the minimum fitting cost, fitting the corresponding clustering regions of the ordered pairs to serve as a new clustering region updating clustering region set;
step S40, iteratively executing step S20 and step S30 until reaching preset iteration times based on the new clustering region set, and obtaining the fitting result of each type of clustering region;
in step S50, the quadric surface primitive is extracted based on the fitting result obtained in step S40.
In some preferred embodiments, the "calculating the fitting cost of each ordered pair" in step S20 is performed by:
Eclustering＝Epri+β·Esmth
wherein E isclusteringTo a fitting cost, EpriFor fitting approximation error, EsmthFor boundary constraint errors, β is a weight coefficient.
In some preferred embodiments, the fitting approximation error is calculated by:
wherein,
as a basis of fitThe type of the element is a type of the element,
for the error based on the least-squares distance,
control parameters for fidelity and priority.
In some preferred embodiments, the boundary constraint error is calculated by:
wherein,
is the outer angle formed by the first edge and the first +1 edge of the outer boundary of the class (·), i.e. the turning angle of the two edges.
In some preferred embodiments, the weight coefficient β is
In some preferred embodiments, the setting method of the control parameter of the priority is: when the fitting primitive type is a plane, the control parameter of the priority is 0.8; when the fitting primitive type is a cylindrical surface, the control parameter of the priority is 0.9; when the fitting element type is a spherical surface or a conical surface, the control parameter of the priority is 1; when the fitting element type is not any one of a plane, a cylindrical surface, a spherical surface and a conical surface, the control parameter of the priority is infinite.
The second aspect of the invention provides a system for extracting quadric surface elements based on hierarchical clustering, which comprises an acquisition module, a calculation module, a fitting updating module, an iteration module and an extraction module;
the acquisition module is configured to acquire triangular meshes of the three-dimensional model, and each triangle is used as a clustering area to obtain a clustering area set;
the computing module is configured to respectively take the clustering regions adjacent to the two sides as an ordered pair, and respectively compute the fitting cost of each ordered pair; the fitting cost is obtained based on fitting approximation errors and boundary constraint errors;
the fitting updating module is configured to select a group of ordered pairs with the minimum fitting cost, and fit the corresponding clustering regions of the ordered pairs to serve as a new clustering region updating clustering region set;
the iteration module is configured to iterate the execution calculation module and the fitting update module based on the new clustering region set until a preset iteration number is reached, and obtain a fitting result of each type of clustering region;
and the extraction module is configured to extract the quadric surface element based on the fitting result obtained by the iteration module.
In a third aspect of the present invention, a storage device is provided, in which a plurality of programs are stored, the programs being loaded and executed by a processor to implement the above-mentioned hierarchical clustering-based quadratic primitive extraction method.
In a fourth aspect of the invention, a processing arrangement is provided, comprising a processor, a storage device; a processor adapted to execute various programs; a storage device adapted to store a plurality of programs; the program is adapted to be loaded and executed by a processor to implement the hierarchical clustering based quadric surface primitive extraction method described above.
The invention has the beneficial effects that:
the invention provides a high-efficiency quadric surface element detection method, which extracts high-quality simple quadric surface elements. The invention adopts a hierarchical clustering idea from bottom to top, takes priority and fidelity into consideration simultaneously in clustering by designing two new error metrics, and uses an optimization means of a minimum cost function in an iterative clustering process by adding constraint on boundary smoothness, thereby extracting a high-quality simple quadric surface element result, and having good application value in the fields of reverse engineering, 3D printing and the like.
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Other features, objects and advantages of the present application will become more apparent upon reading of the following detailed description of non-limiting embodiments thereof, made with reference to the accompanying drawings.
FIG. 1 is a schematic flow chart of a hierarchical clustering-based method for extracting quadric surface primitives according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a framework of a hierarchical clustering-based quadric surface primitive extraction method according to an embodiment of the present invention;
FIG. 3 is a diagram illustrating an example of a fitting process of a hierarchical clustering-based method for extracting quadric surface primitives according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is apparent that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The present application will be described in further detail with reference to the following drawings and examples. It is to be understood that the specific embodiments described herein are merely illustrative of the relevant invention and not restrictive of the invention. It should be noted that, for convenience of description, only the portions related to the related invention are shown in the drawings.
It should be noted that the embodiments and features of the embodiments in the present application may be combined with each other without conflict.
The invention relates to a quadric surface element extraction method based on hierarchical clustering, which comprises the following steps:
step S10, acquiring triangular meshes of the three-dimensional model, and taking each triangle as a clustering area to obtain a clustering area set;
step S20, respectively taking the adjacent clustering areas on two sides as an ordered pair, and respectively calculating the fitting cost of each ordered pair; the fitting cost is obtained based on fitting approximation errors and boundary constraint errors;
step S30, selecting a group of ordered pairs with the minimum fitting cost, fitting the corresponding clustering regions of the ordered pairs to serve as a new clustering region updating clustering region set;
step S40, iteratively executing step S20 and step S30 until reaching preset iteration times based on the new clustering region set, and obtaining the fitting result of each type of clustering region;
in step S50, the quadric surface primitive is extracted based on the fitting result obtained in step S40.
In order to more clearly explain the hierarchical clustering-based quadric surface primitive extraction method of the present invention, the following will discuss the steps in an embodiment of the method of the present invention in detail with reference to fig. 1.
And step S10, acquiring triangular meshes of the three-dimensional model, and taking each triangle as a clustering area to obtain a clustering area set.
Triangular meshes are polygonal meshes composed of triangles, are used for establishing a data structure of models for various irregular objects, and are widely used in graphics and modeling. The surface of an object in the real world is visually formed by a curved surface, and in the computer world, because only discrete structures can be used for simulating continuous objects in reality, the curved surface in the real world is actually formed by numerous small polygonal patches in the computer. First, based on a three-dimensional model to be processed, a triangular network of models is obtained.
Step S20, respectively taking the adjacent clustering areas on two sides as an ordered pair, and respectively calculating the fitting cost of each ordered pair; the fitting cost is obtained based on fitting approximation errors and boundary constraint errors.
In this embodiment, each triangle in the triangular mesh is initialized to a clustering region, which is marked as the index number of the triangle. By measuring the fitting error of two clustered regions, a fitting cost function can be defined for all the ordered pairs of adjacent clustered regions, as shown in equation (1):
Eclustering＝Epri+β·Esmth (1)
wherein E isclusteringTo a fitting cost, EpriFor fitting approximation error, EsmthFor the boundary constraint error, β is a weight coefficient, and is set as
The fitting approximation error is established on the basis of a traditional distance-based least square method, and a fitting type scheme with the minimum fitting error is selected from four primitive types to be selected by considering the fidelity of a fitting result and the influence of the priority of the fitting type. The fitting approximation error is defined as shown in equation (2):
wherein,
is the type of the primitive that is fitted,
to fit the primitive types for the present invention,
is a common error based on the least squares distance,
is a newly introduced control parameter of fidelity and priority of the invention, which can determine the best type of fit.
Solving the control parameters of fidelity and priority is shown as equation (3):
wherein,
is a priority parameter, the primitive type of the fitting result can be made as simple as possible, for example, because the priority of the plane is higher than that of the rest of the curved surfaces, the plane is not mistaken for a cylinder with a larger radius,
are parameters of fidelity, which can make the primitive type of the fitting result more accurate (e.g. the chamfer face can be accurately identified), in the invention, they are respectively shown in formulas (4) and (5):
wherein, Area (.) is the Area of the region, i and j are the category representing parameters, and has no practical significance.
The boundary constraint error is the smoothness of the boundary of the newly generated clustering region after fitting is considered. Three-dimensional models tend to require smooth segmentation boundaries, but existing work always deals with irregular boundaries in post-processing steps. Here, we achieve the requirement of boundary smoothness in the merging process by introducing a new boundary constraint term, and the boundary constraint error solution is shown in equation (6):
wherein,
the outer angle formed by the first edge and the first +1 edge of the outer boundary of the class (·), namely the steering angle of the two edges, and the values of k, l and n which are edges represent parameters, have no practical significance.
The sum of the steering angles approximately reflects the degree of tortuosity or smoothness of the outer boundary, which is a term that measures the change in smoothness of the overall boundary before and after fitting by calculating the change in the sum of the steering angles before and after fitting. The smaller the value of this term, the smoother the boundary of the existing clustering region is made by the fitting operation.
And step S30, selecting a group of ordered pairs with the minimum fitting cost, fitting the corresponding clustering regions of the ordered pairs to serve as a new clustering region updating clustering region set.
Clustering analysis is a very important field of unsupervised learning. The unsupervised learning means that data is not labeled by categories, and an algorithm extracts a certain rule from the exploration of original data. Clustering analysis, in turn, attempts to partition the samples in a data set into disjoint subsets, each of which is referred to as a "cluster". Hierarchical clustering is a generic term of a class of algorithms, and is to form nested clusters, i.e., merging and splitting, by continuously merging clusters from bottom to top or continuously separating clusters from top to bottom. This hierarchical class is represented by a "tree diagram".
In this embodiment, the clustering region sets obtained in step S10 are sorted according to the fitting cost from small to large, and the clustering regions are fitted in the order arranged at the forefront, that is, the order with the smallest fitting cost, and the clustering regions after fitting are used as new clustering regions, and the sets of the clustering regions are updated.
And step S40, iteratively executing the step S20 and the step S30 until reaching the preset iteration times based on the new clustering region set, and obtaining the fitting result of each type of clustering region.
The invention uses a merging algorithm in hierarchical clustering, and the principle of the algorithm is that all data points are taken as clusters at the beginning, then two clusters with the closest distance are found out and combined into one cluster, and the steps are repeated continuously until the number of the preset clusters is reached.
And based on the new cluster region set obtained in the step S30, calculating the fitting cost of each cluster region in the set, and selecting the cluster region with the minimum fitting cost again for fitting until a preset number of iterations is reached, thereby obtaining the fitting result of each type of cluster region.
In step S50, the quadric surface primitive is extracted based on the fitting result obtained in step S40.
In this embodiment, the fitting result of each type of clustering region obtained in step S40 is used as a basic segmentation part, the total number of segmentation parts of the three-dimensional model is verified with a preset value, if the number of segmentation parts is satisfied, a quadric surface parameter equation corresponding to each fitting element type of the three-dimensional model is extracted, the segmentation results, that is, all quadric surface elements, are output, and otherwise, fitting is performed again.
Fig. 3 illustrates the fitting process of the present invention. FIG. 3 (a) is an input initial model; fig. 3 (b) the first set of ordered pairs of triangles (dark) with the smallest cost function; fig. 3 (c) preferentially extracts a planar-type quadric surface; after all the plane-type curved surfaces are extracted in fig. 3 (d), the cylindrical surface-type quadric surfaces are extracted; in fig. 3, (e) the regularity of the boundaries of the clustering regions is maintained during the extraction process; fig. 3 (f) final extraction result.
A second embodiment of the present invention provides a hierarchical clustering-based quadric surface primitive extraction system, as shown in fig. 2, including: the system comprises an acquisition module 100, a calculation module 200, a fitting update module 300, an iteration module 400 and an extraction module 500;
the acquisition module 100 is configured to acquire triangular meshes of the three-dimensional model, and each triangle is used as a clustering region to obtain a clustering region set;
the calculating module 200 is configured to respectively take the clustering regions with two adjacent sides as an ordered pair, and respectively calculate the fitting cost of each ordered pair; the fitting cost is obtained based on fitting approximation errors and boundary constraint errors;
the fitting updating module 300 is configured to select a group of ordered pairs with the minimum fitting cost, fit the corresponding clustering regions of the ordered pairs, and serve as a new clustering region updating clustering region set;
the iteration module 400 is configured to iteratively execute the calculation module 200 and the fitting update module 300 until a preset iteration number is reached based on the new clustering region set, and obtain a fitting result of each type of clustering region;
an extraction module 500 configured to extract the quadric surface primitive based on the fitting result obtained by the iteration module 400.
It is clear to those skilled in the art that, for convenience and brevity of description, the specific working process and related description of the system described above may refer to the corresponding process in the embodiment of the signature method, and will not be described herein again.
It should be noted that, the hierarchical clustering-based quadric surface primitive extraction system provided in the foregoing embodiment is only illustrated by the division of the foregoing functional modules, and in practical applications, the functions may be distributed by different functional modules according to needs, that is, the modules or steps in the embodiment of the present invention are further decomposed or combined, for example, the modules in the foregoing embodiment may be combined into one module, or may be further split into a plurality of sub-modules, so as to complete all or part of the functions described above. The names of the modules and steps involved in the embodiments of the present invention are only for distinguishing the modules or steps, and are not to be construed as unduly limiting the present invention.
A storage device according to a third embodiment of the present invention stores therein a plurality of programs adapted to be loaded by a processor and to implement the hierarchical clustering-based method for extracting a quadratic primitive described above.
A processing apparatus according to a fourth embodiment of the present invention includes a processor, a storage device; a processor adapted to execute various programs; a storage device adapted to store a plurality of programs; the program is adapted to be loaded and executed by a processor to implement the hierarchical clustering based quadric surface primitive extraction method described above.
It is clear to those skilled in the art that, for convenience and brevity, the specific working processes and descriptions of the storage device and the processing device described above may refer to the corresponding processes in the example of the signing method, and are not described herein again.
Those of skill in the art would appreciate that the various illustrative modules, method steps, and modules described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both, and that programs corresponding to the software modules, method steps may be located in Random Access Memory (RAM), memory, Read Only Memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art. To clearly illustrate this interchangeability of electronic hardware and software, various illustrative components and steps have been described above generally in terms of their functionality. Whether such functionality is implemented as electronic hardware or software depends upon the particular application and design constraints imposed on the solution. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention.
The terms "first," "second," and the like are used for distinguishing between similar elements and not necessarily for describing or implying a particular order or sequence.
The terms "comprises," "comprising," or any other similar term are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus.
So far, the technical solutions of the present invention have been described in connection with the preferred embodiments shown in the drawings, but it is easily understood by those skilled in the art that the scope of the present invention is obviously not limited to these specific embodiments. Equivalent changes or substitutions of related technical features can be made by those skilled in the art without departing from the principle of the invention, and the technical scheme after the changes or substitutions can fall into the protection scope of the invention.
Claims (7)
1. A quadric surface element extraction method based on hierarchical clustering is characterized by comprising the following steps:
step S10, acquiring triangular meshes of the three-dimensional model, and taking each triangle as a clustering area to obtain a clustering area set;
step S20, respectively taking the adjacent clustering areas on two sides as an ordered pair, and respectively calculating the fitting cost of each ordered pair; the fitting cost is obtained based on fitting approximation errors and boundary constraint errors; the fitting approximation error is obtained based on a least square distance error, a fidelity parameter and a priority control parameter;
wherein E ispriIn order to fit the approximation error,
in order to fit the primitive types,
for the error based on the least-squares distance,
for control parameters of fidelity and priority,
is a control parameter of the priority level,
is a safeguardThe fidelity parameter, Area (.) is the Area of the region, i and j are category representative parameters, and no practical significance is achieved;
step S30, selecting a group of ordered pairs with the minimum fitting cost, fitting the corresponding clustering regions of the ordered pairs to serve as a new clustering region updating clustering region set;
step S40, iteratively executing step S20 and step S30 until reaching preset iteration times based on the new clustering region set, and obtaining the fitting result of each type of clustering region;
in step S50, the quadric surface primitive is extracted based on the fitting result obtained in step S40.
2. The method for extracting quadric surface primitive based on hierarchical clustering as claimed in claim 1, wherein in step S20, "calculating the fitting cost of each ordered pair respectively" includes:
Eclustering＝Epri+β·Esmth
wherein E isclusteringTo a fitting cost, EpriFor fitting approximation error, EsmthFor boundary constraint errors, β is a weight coefficient.
3. The hierarchical clustering-based quadric surface primitive extraction method as claimed in claim 2, wherein the boundary constraint error is calculated by:
wherein,
is the outer angle formed by the first edge and the first +1 edge of the outer boundary of the class (·), i.e. the turning angle of the two edges.
4. The method of claim 2, wherein the weight coefficients are weighted according to the hierarchical clustering-based quadric surface primitive extraction methodBeta is
5. A quadric surface element extraction system based on hierarchical clustering is characterized by comprising an acquisition module, a calculation module, a fitting updating module, an iteration module and an extraction module;
the acquisition module is configured to acquire triangular meshes of the three-dimensional model, and each triangle is used as a clustering area to obtain a clustering area set;
the computing module is configured to respectively take the clustering regions adjacent to the two sides as an ordered pair, and respectively compute the fitting cost of each ordered pair; the fitting cost is obtained based on fitting approximation errors and boundary constraint errors; the fitting approximation error is obtained based on a least square distance error, a fidelity parameter and a priority control parameter;
wherein E ispriIn order to fit the approximation error,
in order to fit the primitive types,
for the error based on the least-squares distance,
for control parameters of fidelity and priority,
is a control parameter of the priority level,
the fidelity parameter is, Area (Area) is the Area of the region, i and j are category representative parameters, and no practical significance is realized;
the fitting updating module is configured to select a group of ordered pairs with the minimum fitting cost, and fit the corresponding clustering regions of the ordered pairs to serve as a new clustering region updating clustering region set;
the iteration module is configured to iterate the execution calculation module and the fitting update module based on the new clustering region set until a preset iteration number is reached, and obtain a fitting result of each type of clustering region;
and the extraction module is configured to extract the quadric surface element based on the fitting result obtained by the iteration module.
6. A storage device having stored therein a plurality of programs, wherein said program applications are loaded and executed by a processor to implement the hierarchical clustering based quadric surface primitive extraction method of any one of claims 1-4.
7. A processing device comprising a processor, a storage device; a processor adapted to execute various programs; a storage device adapted to store a plurality of programs; characterized in that said program is adapted to be loaded and executed by a processor to implement the hierarchical clustering based quadric surface primitive extraction method of any one of claims 1-4.
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| CN104361578A (en) * | 2014-10-20 | 2015-02-18 | 北京大学 | Hierarchical grid partition method under multi-scale precision control |
| CN109801299A (en) * | 2019-01-22 | 2019-05-24 | 中国科学院大学 | Interactive segmentation method, system, the device of model based on Quadratic Surface Fitting |
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