WO2018072081A1 - 花朵开放过程的重建方法、计算机可读存储介质及设备 - Google Patents

花朵开放过程的重建方法、计算机可读存储介质及设备 Download PDF

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WO2018072081A1
WO2018072081A1 PCT/CN2016/102360 CN2016102360W WO2018072081A1 WO 2018072081 A1 WO2018072081 A1 WO 2018072081A1 CN 2016102360 W CN2016102360 W CN 2016102360W WO 2018072081 A1 WO2018072081 A1 WO 2018072081A1
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point cloud
cloud data
flower
grid template
petal
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PCT/CN2016/102360
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English (en)
French (fr)
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黄惠
郑倩
范晓晨
多伊森奥利夫·马丁
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中国科学院深圳先进技术研究院
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Priority to PCT/CN2016/102360 priority Critical patent/WO2018072081A1/zh
Publication of WO2018072081A1 publication Critical patent/WO2018072081A1/zh

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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects

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  • the present invention relates to the field of simulation modeling technologies, and in particular, to a method for reconstructing a flower opening process, a computer readable storage medium, and a device.
  • 3D scanning is mainly used to scan the object's spatial shape, structure and color to obtain the spatial coordinates of the surface of the object.
  • the important significance of 3D scanning is that it can convert the stereo information of the real object into a digital signal that can be directly processed by the computer, which provides a convenient and quick means for physical digitization.
  • the data collected during the scan is generally a point cloud that creates the geometric surface of the object. These points can be used to interpolate the surface shape of the object. The denser the point cloud can create a more accurate model. This process is called 3D reconstruction.
  • the raw output of the 3D scanner will have various defects, including noise, missing data and outliers, if it is affected by the external environment.
  • image-based modeling methods based on the image-based modeling method, an optimization equation is established from a large number of images of different objects from different perspectives, and the camera position and the three-dimensional coordinates of the object are directly and simultaneously solved. This method is called Structure From Motion.
  • the point cloud-based reconstruction method reconstructs the high-quality mesh model directly from the acquired point cloud.
  • the well-known Poisson reconstruction method uses an implicit surface to express the reconstructed mesh, and divides the space into three parts: The position of the mesh is obtained by solving the implicit equations on the surface, outside the surface, and inside the surface.
  • these methods are based on the assumption that the scanned object is static, and the complete reconstruction model is obtained by decomposing the motion of the camera and combining the data of multiple views.
  • the data obtained by scanning a dynamic object is a point cloud sequence that records the deformation information of the object and can be used to generate a complete mesh deformation sequence.
  • This process is called four-dimensional (4D) reconstruction.
  • a common method is to represent the shape of the object with a predefined shape template that is consistent with the geometric properties of the scanned object. Since the scanning interval is generally small and the object has only a small amount of deformation, sufficient feature matching can be established between successive frames to obtain a complete template deformation. sequence.
  • flowers are objects with complex geometric features and strong self-occlusion.
  • the existing 3D scanning technology cannot obtain complete object data of flowers.
  • the flower deformation is more complicated during the flower opening process, and it is impossible to establish an effective feature matching relationship.
  • a more accurate and realistic 4D reconstruction technique has not yet been proposed.
  • the existing modeling method is based on the physical simulation method, using the physical model, especially the mechanical principle, to apply a virtual force to the existing petal model, to promote the change of the petals, so that the whole flower reaches an open status.
  • this method based on physical simulation does not truly reflect the actual flowering process, and the movement of the petals is too simple and regular.
  • the invention provides a method for reconstructing a flower opening process, a computer readable storage medium and a device.
  • the flower opening process obtained by the method is more realistic and accurate than the flower opening process obtained in the prior art.
  • a method for reconstructing a flower opening process includes: collecting four-dimensional point cloud data of an entire flower opening process; and selecting a frame of point cloud data including all petal information from the point cloud data, And creating a flower grid template according to the selected point cloud data, wherein the flower grid template includes a plurality of petal grid templates; and driving the flower net based on a correspondence between the flower grid template and the point cloud data
  • the grid template performs mesh deformation to track the point cloud data, and respectively obtains a flower grid template corresponding to each frame point cloud data, wherein shape constraint, collision constraint and each petal grid template are performed in the mesh deformation process.
  • Fixed root constraint; all the flower grid templates obtained are arranged in the order in which the flowers are opened, and the dynamic process of opening the flowers is obtained.
  • a computer readable storage medium comprising computer readable instructions, when executed, causes a processor to perform at least a reconstruction method of the flower opening process described above.
  • an apparatus comprising: a processor; and a memory including computer readable instructions that, when executed, cause the processor to perform reconstruction of the flower opening process described above method.
  • the flower grid template is implemented in a data-driven manner by the reconstructed method of the flower opening process, the computer readable storage medium and the device of the present invention, based on the collected real flower opening process point cloud data and the created flower grid template.
  • Effective mesh deformation, updating the position of the mesh vertices can ensure the authenticity of the template deformation, but also A sufficient degree of freedom can be ensured so that the deformed template is maximally consistent with the geometry exhibited by the actual point cloud data.
  • the petal mesh template is constrained to ensure that the shape of the template does not undergo abnormal distortion and structural changes and that there is no cross collision between the petal meshes, so that the motion between the petals is not interfered with each other.
  • the flower opening process thus reconstructed can reflect the flower opening process more accurately and realistically, and even achieve the same visual effect as the actual flower opening process.
  • FIG. 1 is a flow chart of a method for reconstructing a flower opening process according to an embodiment of the present invention
  • FIG. 2 is a schematic diagram of comparison of point cloud data and reconstruction open process of water lily according to an embodiment of the present invention
  • FIG. 3 is a structural block diagram of a reconstruction apparatus for a flower opening process according to an embodiment of the present invention.
  • FIG. 4 is a schematic diagram showing a comparison of the point cloud data and the open process of reconstruction of the golden lily of the embodiment of the present invention
  • FIG. 5 is a schematic diagram showing a comparison of point cloud data and reconstruction opening process of a single piece of flower petals according to an embodiment of the present invention
  • FIG. 6 is a schematic diagram of a reconstruction process of a flower opening process according to an embodiment of the present invention.
  • FIG. 7 is an apparatus according to an embodiment of the present invention.
  • the animation of flower opening based on physical simulation can not truly reflect the actual flowering process; however, the existing four-dimensional reconstruction method can not be directly used for flower reconstruction flower opening process due to the complex geometric features of flowers and self-occlusion.
  • the reconstruction of the flower opening process can be seen as a tracking problem of multiple objects in the case of mutual occlusion. This is different from the reconstruction of human motion and facial expressions (the template and the tracking object are often only one during the reconstruction of human motion and facial expression, and there is no occlusion relationship between objects).
  • the problem solved by the present invention is how to effectively track the template when a plurality of objects have a significant occlusion relationship, thereby reconstructing the entire motion process.
  • FIG. 1 is a flowchart of a method for reconstructing a flower opening process according to an embodiment of the present invention. As shown in FIG. 1, the method includes the following steps S101 to S104.
  • Step S101 collecting four-dimensional point cloud data of the entire flower opening process.
  • the existing 3D scanning technology can be used to collect the four-dimensional (4D) point cloud data of the flower opening process.
  • 4D point cloud data adds time information, that is, the collected point cloud data is frame by frame, and is displayed according to the time course of the flower from the flower state to the completely open state.
  • Step S102 Select a frame of point cloud data including all petal information from the point cloud data, and create a flower grid template according to the selected point cloud data, wherein the flower grid template includes a plurality of petal grid templates.
  • the present invention selects a frame of point cloud data containing complete petal information from the collected point cloud data, and creates a flower grid template based on the selected point cloud data.
  • the flower grid template may be manually created according to the selected point cloud data and the flower object, or the flower grid template may be created according to the selected point cloud data by using the pre-edited software, thereby obtaining a more realistic flower grid. template.
  • the present invention divides the flower geometrically.
  • the flower grid template is divided into a plurality of petal grid templates, and the petals are used as a basic unit.
  • Step S103 based on the correspondence between the flower grid template and the point cloud data, driving the flower grid template to perform mesh deformation to track the point cloud data, respectively obtaining a flower grid template corresponding to each frame point cloud data, wherein, in the network Shape constraint, collision constraint and fixed root constraint are applied to each petal grid template during lattice deformation.
  • the collected point cloud data is a real point cloud sequence of the flower opening process, and there are slight movement changes between successive frames.
  • the flower grid template is created according to a certain frame point cloud data, and the entire flower is reconstructed in order to drive the template deformation.
  • the collected point cloud data needs to be segmented according to the geometric features of the flower grid template, and the corresponding relationship (or matching relationship) between the template and the real point cloud data is obtained, and the template and point cloud data are at the petal level.
  • One-to-one correspondence Therefore, on the basis of the above corresponding relationship, according to the deformation of the real point cloud data frame by frame, the flower grid template can also be correctly and effectively deformed to achieve the geometric shape exhibited by the point cloud data.
  • step S104 all the obtained flower grid templates are arranged in the order in which the flowers are opened, and a dynamic process of opening the flowers is obtained.
  • the effective mesh deformation of the flower grid template is performed in a data-driven manner, and the position of the grid vertex is updated to ensure the template.
  • the authenticity of the deformation, while also ensuring sufficient freedom, so that the deformed template is maximized The geometry of the actual point cloud data is consistent.
  • the petal mesh template is constrained to ensure that the shape of the template does not undergo abnormal distortion and structural changes and that there is no cross collision between the petal meshes, so that the motion between the petals is not interfered with each other.
  • the precise and realistic flower opening process thus reconstructed can more realistically reflect the flower opening process and even achieve the same visual effect as the actual flower opening process.
  • the problem solved by the present invention is to reconstruct a real flower open mesh sequence from the open 4D point cloud data of the flower.
  • the above problem is abstracted into a problem of maximum a posteriori estimation, and the problem is abstracted from two aspects of probability and geometry, thereby obtaining an energy optimization equation of flower grid deformation.
  • the flower grid template is created based on the point cloud data of a certain frame quality during the flower opening process.
  • the static flower grid template is based on the data forward (flower state) and/or backward (open). State) Deformation of the template to reconstruct the dynamic process of real flower opening.
  • M M 1:T , 1 ⁇ t ⁇ T, where M is a flower grid template, each flower is composed of K petals, and the petals are represented by M k , 1 ⁇ k ⁇ K.
  • the present invention treats each petal grid template as a Gaussian Mixture Models (GMM), that is, each vertex on the template is the center of a Gaussian distribution, and all the vertices on the template constitute a mixed distribution, then
  • GMM Gaussian Mixture Models
  • the corresponding point cloud data collected is the actual observation point set of the GMM, and the deformation of the template is converted into the point cloud data according to the actual observation, and it is inferred that each vertex of the template conforms to the new position of the point cloud data, and at the same time, it is guaranteed The nature of the template itself. So the above problem becomes a problem with the largest a posteriori estimate:
  • M t ) represents a likelihood probability, ie the probability of observing the point cloud Q t under the current template M t
  • p(M t ) represents the prior probability, ie the constraint of the template itself Probability of occurrence.
  • the basic unit of the flower grid template is the petal grid template M k , but the collected point cloud data has no split information, it is necessary to determine the point cloud data set corresponding to each petal grid template before performing the template deformation. That is, the point cloud data is segmented according to the petal information, and the point cloud data corresponding to each petal grid template is obtained. Then for the flower grid template, the Expectation Maximization (EM) iterative algorithm is used to solve the problem of the maximum a posteriori estimation, and the next position of the template, ie the new template, is obtained. .
  • EM Expectation Maximization
  • FIG. 2 is a schematic diagram of a comparison of the point cloud data of the water lily and the open process of the reconstruction according to the embodiment of the present invention.
  • the actually collected water lily data exceeds 100 frames, and FIG. 2 only shows representative 6 frames of data, which are respectively recorded as t1. , t2, t3, t4, t5, t6.
  • step S103 may include: mode (1) and/or mode (2).
  • step A1 and step A2 are performed frame by frame from the back to the front until the flower corresponding to the point cloud data of each frame before the selected point cloud data is obtained.
  • Grid template For the selected point cloud data and the previous point cloud data of each frame, step A1 and step A2 are performed frame by frame from the back to the front until the flower corresponding to the point cloud data of each frame before the selected point cloud data is obtained.
  • Step A1 segmenting the previous frame point cloud data of the current frame point cloud data according to the geometric feature of the flower grid template corresponding to the current frame point cloud data, and obtaining the correspondence between the flower grid template and the previous frame point cloud data.
  • the corresponding relationship is that the collection point in the point cloud data of the previous frame belongs to which petal grid template in the flower grid template corresponding to the current frame point cloud data;
  • Step A2 performing mesh transformation on the flower grid template corresponding to the current frame point cloud data based on the previous frame point cloud data and the corresponding relationship, and obtaining a flower grid template consistent with the geometric shape exhibited by the previous frame point cloud data.
  • step B1 and step B2 are performed frame by frame from the time of going to, until the flower network corresponding to the point cloud data of each frame after the selected point cloud data is obtained.
  • Grid template For the selected point cloud data and the subsequent point cloud data of each frame, step B1 and step B2 are performed frame by frame from the time of going to, until the flower network corresponding to the point cloud data of each frame after the selected point cloud data is obtained.
  • Step B1 segment the next frame point cloud data of the current frame point cloud data according to the geometric feature of the flower grid template corresponding to the current frame point cloud data, and obtain a correspondence between the flower grid template and the next frame point cloud data.
  • the correspondence relationship is which petal grid template in the flower grid template corresponding to the current frame point cloud data belongs to the collection point in the next frame point cloud data;
  • Step B2 Perform mesh transformation on the flower grid template corresponding to the current frame point cloud data based on the next frame point cloud data and the corresponding relationship, and obtain a flower grid template that is consistent with the geometric shape exhibited by the next frame point cloud data. .
  • the fourth frame point cloud data (t4) is selected to create a flower grid template (denoted as M4).
  • the flower grid templates M1, M2, and M3 corresponding to t1, t2, and t3 can be obtained by using the mode (1);
  • the flower grid templates M5 and M6 corresponding to t5 and t6 can be obtained by using the method (2). Thereby, a flower grid template corresponding to each frame point cloud data is obtained.
  • t4 is used as the current frame point cloud data
  • t3 is segmented according to the geometric feature of M4, and the correspondence relationship between each petal grid template and t3 in M4 is obtained, and based on t3 and the obtained correspondence, mesh is performed on M4.
  • Deformation the flower mesh template M3 corresponding to t3 is obtained.
  • the t2 is segmented, and the corresponding relationship between each petal grid template and t2 in M3 is obtained, and the mesh deformation is performed on M3 based on t2 and the obtained correspondence relationship.
  • the flower grid template M2 corresponding to t2 is obtained.
  • t6 is selected to create a flower grid template (denoted as M6).
  • the corresponding flower grid templates M1 to M5 can be obtained using mode (1).
  • t1 is selected to create a flower grid template (denoted as M1).
  • t2 to t6 the corresponding flower grid templates M2 to M6 can be obtained using mode (2).
  • point cloud data segmentation may be based on the distance of point cloud data to each petal grid template.
  • the specific operations of segmenting point cloud data according to the geometric features of the flower grid template are as follows:
  • each petal grid template in the flower grid template corresponding to the current frame point cloud data is calculated respectively.
  • Distance sort the distance values corresponding to the collection points from large to small, select the last two distance values, and calculate the ratio of the two distance values; if the ratio is less than the preset threshold, determine that the collection point belongs to the minimum a petal grid template corresponding to the distance value; if the ratio is greater than or equal to a preset threshold, determining that the collection point does not belong to any petal grid template;
  • the distance from the collection point to each petal grid template in the flower grid template corresponding to the current frame point cloud data is separately calculated. And sorting the distance values corresponding to the collection points from large to small, selecting the last two distance values, and calculating the ratio of the two distance values; if the ratio is less than the preset threshold, determining that the collection point belongs to the minimum distance The petal grid template corresponding to the value; if the ratio is greater than or equal to the preset threshold, it is determined that the collection point does not belong to any petal grid template.
  • calculating, respectively, a distance from the collection point to each petal grid template in the flower grid template corresponding to the current frame point cloud data including: calculating, for each petal grid template, the collection point to the petal grid template The distance of each vertex in the middle, and calculate the closest distance, which is the distance from the collection point to the petal grid template.
  • the confidence level ie, the preset threshold value
  • the collection point is indicated.
  • the probability that the point belongs to the petal grid template corresponding to the minimum distance is high, and the collection point is assigned to the petal grid template; otherwise, the collection point is considered not to belong to any petal. This can eliminate inaccurate data and improve the accuracy of point cloud data segmentation.
  • obtaining a correspondence between the flower grid template and the point cloud data includes: calculating, for each petal grid template, each vertex on the petal grid template and each of the petals belonging to the petal grid template
  • the probability of matching between collection points, the matching probability between the flower grid template and all acquisition points is represented by the correlation matrix Z, the elements Z ij ⁇ [0,1] in the correlation matrix Z, and the elements Z ij in the correlation matrix Z ⁇ [0,1].
  • m i represents the i-th vertex on the flower grid template M
  • m i belongs to the k-th petal grid template
  • the k-th petal grid template is represented by M k
  • Q k represents point cloud data corresponding to M k
  • q j represents the jth collection point in the point cloud data Q
  • m i ) is a likelihood probability, which is represented at the vertex m of the flower grid template M The probability of collecting the point q j of the point cloud data Q under i .
  • the position of the template vertex is updated by solving the energy equation of the maximum a posteriori estimation, so that the template can better match the point cloud data.
  • mesh transformation is performed on the flower grid template corresponding to the current frame point cloud data, including: using an expectation maximization iterative algorithm to solve the energy equation of the maximum a posteriori estimate:
  • Q, Z) is a data item representing the degree of conformity between the flower grid template M and the point cloud data Q; the association matrix Z represents a match between the flower grid template M and all collection points Probability; p(M
  • the energy equation is solved to obtain a new position of each vertex in the flower grid template corresponding to the current frame point cloud data corresponding to the point cloud data of the previous frame; In the case, the energy equation is solved to obtain a new position of each vertex in the flower grid template corresponding to the current frame point cloud data corresponding to the next frame point cloud data.
  • the data item defines the distance relationship between the template vertex and the corresponding point cloud, so the smaller the data item, the closer the template is to the point cloud.
  • the expression for the data item is:
  • w 1 represents the weight of the data item
  • M k represents the kth petal grid template
  • Q k represents the point cloud data corresponding to the kth petal grid template M k
  • D(Q k , M k ) represents the kth
  • m i represents the i-th vertex on the flower grid template M
  • m i belongs to the k-th petal grid template M k
  • q j represents the j-th collection point in the point cloud data Q
  • the collection point belongs to the M
  • Z ij represents the matching probability between the i-th vertex on the flower grid template M and the j-th collection point in the point cloud data Q.
  • the prior terms include: shape constraint E shape , collision constraint E collision and fixed root constraint E root , wherein the shape constraint is used to geometrically constrain the petal mesh template, and the collision constraint is used to ensure each petal mesh template There is no cross collision between the two, and the fixed root constraint is used to ensure that the petal mesh template has a fixed root bottom.
  • the geometric constraint of the flower grid template is required to ensure that the template can maintain the quality and structure of the mesh during the deformation process.
  • the ARAP (as-rigid-as-possible) method can be used to ensure that the local transformation should be as rigid as possible during the mesh deformation process.
  • w 2 represents the weight of the shape constraint
  • N(i) represents the set of vertices adjacent to the i-th vertex on the flower grid template M
  • c ij represents the weight of the edge composed of the i-th vertex and the j-th vertex
  • R i represents the rotation matrix of the ith vertex
  • 2 indicates the Euclidean distance.
  • the flower grid template is composed of K petal grid templates. During the process of tracking point cloud data deformation, cross collision may occur between the petals grid templates. This is impossible in the actual flowering process, so it is necessary to add collision constraints. To ensure that no cross collision occurs.
  • the new vertex position is gradually obtained in an iterative manner. Before each iteration, it is necessary to detect the collision between the petals. If the vertex m i is detected as the collision point, the distance along the surface of the collided mesh is reversed back to obtain a new position to avoid collision. .
  • w 4 represents the weight of the fixed root constraint
  • S R represents the set of root nodes
  • the local optimization method can be used to solve the nonlinear optimization equation shown in equation (2).
  • the rotation matrix R i and the collision in the shape constraint are solved.
  • the energy equation of the maximum a posteriori estimate is transformed into a linear equation to solve the new position of the vertex; the above partial and integral processes are iterated until convergence, and the new position of the petal grid template is obtained.
  • the above process is repeated for each frame point cloud data until the reconstruction of the entire point cloud data sequence is completed.
  • the embodiment of the present invention further provides a reconstruction device for a flower opening process, which can be used to implement the method described in the foregoing embodiments. Since the principle of solving the problem of the device is similar to the above method, the implementation of the device can be referred to the implementation of the above method, and the repeated description is not repeated.
  • the term "unit” or “module” may implement a combination of software and/or hardware of a predetermined function. Although the systems described in the following embodiments are preferably implemented in software, hardware, or a combination of software and hardware, is also possible and contemplated.
  • FIG. 3 is a structural block diagram of a device for reconstructing a flower opening process according to an embodiment of the present invention. As shown in FIG. 3, the device includes: a data collecting unit 31, a template creating unit 32, a driving deformation unit 33, and a display unit 34. This structure will be specifically described.
  • the data collection unit 31 is configured to collect four-dimensional point cloud data of the entire flower opening process
  • the template creating unit 32 is configured to select a frame of point cloud data including all the petal information from the point cloud data, and create a flower grid template according to the selected point cloud data, where the flower grid template includes a plurality of petal grid templates;
  • the driving deformation unit 33 is configured to drive the flower grid template to perform grid deformation to track the point cloud data based on the correspondence between the flower grid template and the point cloud data, and obtain a flower grid template corresponding to each frame point cloud data respectively. Wherein, in the process of mesh deformation, shape constraint, collision constraint and fixed root constraint are applied to each petal mesh template;
  • the display unit 34 is configured to arrange all the flower grid templates obtained in the order in which the flowers are opened, and obtain a dynamic process in which the flowers are open.
  • the effective mesh deformation of the flower grid template is performed in a data-driven manner, and the position of the grid vertex is updated to ensure the template.
  • the authenticity of the deformation can also ensure sufficient freedom, so that the shape of the deformed template is the same as that of the actual point cloud data.
  • the petal mesh template is constrained to ensure that the shape of the template does not abnormal.
  • the distortion and structural changes and the cross-collision between the petals grids make the movement between the petals undisturbed.
  • the precise and realistic flower opening process thus reconstructed can more realistically reflect the flower opening process and even achieve the same visual effect as the actual flower opening process.
  • the drive deformation unit 33 may include: a first drive module, a first split module, a first deformation module, a second drive module, a second split module, and a second deformation module.
  • a first driving module configured to trigger the first segmentation module and the first deformation module frame by frame from the back to the front for the selected point cloud data and the previous frame cloud data thereof until each time before the selected point cloud data is obtained a flower grid template corresponding to one frame of point cloud data;
  • the first segmentation module is configured to segment the previous frame point cloud data of the current frame point cloud data according to the geometric feature of the flower grid template corresponding to the current frame point cloud data, and obtain the flower grid template and the previous frame point cloud. Correspondence relationship of data;
  • the first deformation module is configured to perform mesh transformation on the flower grid template corresponding to the current frame point cloud data based on the point cloud data and the corresponding relationship of the previous frame, and obtain the geometric shape consistent with the point cloud data of the previous frame.
  • Flower grid template corresponding to the current frame point cloud data based on the point cloud data and the corresponding relationship of the previous frame, and obtain the geometric shape consistent with the point cloud data of the previous frame.
  • a second driving module configured to trigger the second segmentation module and the second deformation module from frame to frame for the selected point cloud data and subsequent frame point cloud data, until each of the selected point cloud data is obtained a flower grid template corresponding to the frame point cloud data;
  • the second segmentation module is configured to segment the next frame point cloud data of the current frame point cloud data according to the geometric feature of the flower grid template corresponding to the current frame point cloud data, and obtain a flower grid template and a next frame point cloud. Correspondence relationship of data;
  • a second deformation module configured to calculate a flower corresponding to the current frame point cloud data based on the next frame point cloud data and the correspondence relationship
  • the grid template is mesh deformed to obtain a flower grid template consistent with the geometry exhibited by the next frame point cloud data.
  • the first driving module, the first dividing module, the first deforming module, the second driving module, the second dividing module and the second deforming module may be independent modules, each of which implements its function, or may be an integrated module.
  • the first segmentation module is specifically configured to: calculate, for each collection point in the point cloud data of the previous frame, a distance of each of the petal grid templates in the flower grid template corresponding to the current frame point cloud data; The distance values corresponding to the collection points are sorted from large to small, and the last two distance values are selected, and the ratio of the two distance values is calculated; if the ratio is less than the preset threshold, it is determined that the collection point belongs to the minimum distance value.
  • the petal grid template if the ratio is greater than or equal to the preset threshold, it is determined that the collection point does not belong to any petal grid template.
  • the second segmentation module is specifically configured to calculate, for each collection point in the next frame point cloud data, a distance of each of the petal grid templates in the flower grid template corresponding to the current frame point cloud data;
  • the distance values corresponding to the collection points are sorted from large to small, and the last two distance values are selected, and the ratio of the two distance values is calculated; if the ratio is less than the preset threshold, it is determined that the collection point belongs to the minimum distance value.
  • the petal grid template if the ratio is greater than or equal to the preset threshold, it is determined that the collection point does not belong to any petal grid template.
  • the distance from the collection point to each vertex in the petal grid template may be calculated, and the closest distance is calculated, and the closest distance is used as the distance from the collection point to the petal grid template.
  • the first segmentation module and the second segmentation module each include: a first calculation submodule, configured to calculate, for each petal grid template, each vertex on the petal grid template and belong to the petal net
  • the probability of matching between each collection point of the grid template, the matching probability between the flower grid template and all collection points is represented by the correlation matrix Z, which is the element Z ij ⁇ [0,1] in the matrix Z.
  • m i represents the i-th vertex on the flower grid template M
  • m i belongs to the k-th petal grid template
  • the k-th petal grid template is represented by M k
  • Q k represents point cloud data corresponding to M k
  • q j represents the jth collection point in the point cloud data Q
  • m i ) is a likelihood probability, which is represented at the vertex m of the flower grid template M The probability of collecting the point q j of the point cloud data Q under i .
  • the first deformation module and the second deformation module each include: a second calculation sub-module that uses an expectation maximization iterative algorithm to solve the energy equation of the maximum a posteriori estimate:
  • the energy equation is solved to obtain a new position of each vertex in the flower grid template corresponding to the current frame point cloud data corresponding to the previous frame point cloud data.
  • the energy equation is solved to obtain a new position of each vertex in the flower grid template corresponding to the current frame point cloud data corresponding to the next frame point cloud data.
  • the above a priori items include: a shape constraint E shape , a collision constraint E collision and a fixed root constraint E root , the shape constraint is used for geometrically constraining the petal mesh template, and the collision constraint is used to ensure that each petal mesh template is between No cross collision occurs, and the fixed root constraint is used to ensure that the petal mesh template has a fixed root bottom.
  • the expressions of the data items and the a priori items are as described in the foregoing method embodiments, and are not described herein again.
  • the second calculation sub-module is specifically configured to: for each vertex on the flower grid template, solve the rotation matrix R i in the shape constraint and the new position of the vertex m i in the collision constraint to avoid collision
  • the energy equation of the maximum a posteriori estimate is transformed into a linear equation to solve the new position of the vertex; the above solution process is iterated until convergence, and the new position of the flower grid template is obtained.
  • module division is only a schematic division, and the present invention is not limited thereto. As long as the module division capable of achieving the object of the present invention is within the scope of protection of the present invention.
  • FIG. 4 is a comparative diagram of the point cloud data and the open process of the reconstruction of the golden lily of the embodiment of the present invention
  • FIG. 5 is a single embodiment of the present invention.
  • FIG. 6 is a schematic diagram of a process of reconstructing a flower opening process according to an embodiment of the present invention.
  • a point cloud data is collected, a flower grid template is created, and a flower grid is based on a correspondence between a point cloud data and a flower grid template.
  • the template performs forward and backward mesh deformation to track point cloud data, and finally obtains a grid sequence of flowers, reconstructing the real flower opening process.
  • Embodiments of the present invention also provide a computer readable storage medium comprising computer readable instructions that, when executed, cause a processor to perform at least the reconstruction method of the flower opening process described above.
  • an embodiment of the present invention further provides an apparatus, including a processor 71 and a memory 72 including computer readable instructions that, when executed, cause the processor 71 to perform the reconstruction of the flower opening process described above. method.
  • the method for reconstructing the flower opening process, the computer readable storage medium and the device provided by the present invention adopt a completely different idea from the principle of the existing physical drive-based reconstruction method, and the present invention collects
  • the 4D point cloud data of the real flowering process is based on data driving.
  • the method of forward tracking it gradually traces from the open state to the state of the flower buds from the back to the front, effectively reconstructing the complex form in which the petals of the initial state are completely invisible.
  • the invention can effectively avoid the collision of the petals and the loss of the processing data, and ensure that the petals can be deformed correctly and truly.
  • the invention is capable of generating an animation of a realistic flower opening process, achieving an opening effect that is almost identical to a real flower.
  • each functional unit in each embodiment of the present invention may be integrated into one processing module, or each unit may exist physically separately, or two or more units may be integrated into one module.
  • the above integrated modules can be implemented in the form of hardware or in the form of software functional modules.
  • the integrated modules, if implemented in the form of software functional modules and sold or used as stand-alone products, may also be stored in a computer readable storage medium.
  • the above mentioned storage medium may be a read only memory, a magnetic disk or an optical disk or the like.

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Abstract

本发明公开了一种花朵开放过程的重建方法、计算机可读存储介质及设备，其中，该方法包括：采集整个花朵开放过程的四维点云数据；选择一帧包括所有花瓣信息的点云数据，并根据所选点云数据创建花朵网格模板，花朵网格模板包括多个花瓣网格模板；基于花朵网格模板与点云数据的对应关系，驱动花朵网格模板进行网格形变以跟踪点云数据，分别得到每一帧点云数据对应的花朵网格模板，在网格形变过程中对各花瓣网格模板进行形状约束、碰撞约束和固定根约束；将得到的所有花朵网格模板按照花朵开放顺序排列，得到花朵开放的动态过程。本发明基于采集的真实点云数据及创建的花朵网格模板，以数据驱动的方式进行花朵网格模板的有效形变，能够重建出精确逼真的花朵开放过程。

Description

花朵开放过程的重建方法、计算机可读存储介质及设备 技术领域
本发明涉及仿真建模技术领域，尤其涉及花朵开放过程的重建方法、计算机可读存储介质及设备。
背景技术
在生物科学领域，对于花朵开放过程的研究已经有了很长的历史。传统意义上，这样的研究依赖于手动记录下的过程，或者用相机间隔的拍照，然后在图片上进行测量。这样的工作流程是繁琐并且低效的，容易出现测量偏差。
三维(3D)扫描技术的进步为精确测量花朵开放过程提供了新的机会和方法。3D扫描主要用于对物体空间外形、结构及色彩进行扫描，以获得物体表面的空间坐标。3D扫描的重要意义在于能够将实物的立体信息转换为计算机能直接处理的数字信号，为实物数字化提供了相当方便快捷的手段。扫描过程中采集的数据一般为创建物体几何表面的点云，这些点可用来插补成物体的表面形状，越密集的点云可以创建更精确的模型，这个过程称为三维重建。
三维扫描仪的原始输出如果受到外界环境影响会有各种缺陷，包括噪声、丢失的数据和异常值。现在已经有不少方法用于改善相应的重构模型的质量，例如，基于图片的建模方法以及基于点云的重建方法。其中，基于图片的建模方法，从大量相同物体不同视角下的图片中，建立优化方程，直接并且同时求解出相机位置和物体的三维坐标，这种方法被称为Structure From Motion。基于点云的重建方法直接从采集到的点云重建出高质量网格模型，例如，比较著名的泊松重建方法，用隐式曲面来表达重建的网格，将空间划分为三个部分：在曲面上、在曲面外部以及在曲面内部，通过求解隐式方程得到网格的位置。然而，这些方法都是在假设扫描对象是静态的前提下，通过分解出摄像头的运动以及合并扫描多视角的数据，从而得到完整的重建模型。
随着3D扫描技术的日渐成熟，将扫描技术运用在动态物体捕捉上的应用越来越多，重建技术例如已经广泛用到人体运动、人脸表情以及其它可变形物体的动态捕捉上。扫描动态物体得到的数据是记录了物体变形信息的点云序列，可用于生成完整的网格变形序列。这个过程被称为四维(4D)重建。常用的方法是用一个与扫描物体几何性质一致的、预定义好的形状模板来表示物体形态。由于扫描的间隔一般很小，物体只有少量的形变，所以能够在连续的帧之间建立足够的特征匹配，从而获得完整的模板变形 序列。
但是花朵是自身几何特征复杂、自遮挡严重的物体，现有的3D扫描技术并不能获得花朵完整的物体数据。同时，花朵开放过程中，花朵的变形比较复杂，无法建立有效的特征匹配关系。针对类似于花朵这样的物体(拥有复杂的几何形态，自遮挡严重)，目前尚未提出比较精确逼真的4D重建技术。
植物的建模一直备受计算机图形学的关注。虽然目前可以制作非常逼真的植物，但是我们感兴趣的是实际的植物生长过程的状态情况，并且分析真正的生长数据可以反过来用于重新创建高质量几何形状或动画。
对于花朵开放过程，现有的建模方法是基于物理模拟的方法，利用物理模型，尤其是力学原理，对已有的花瓣模型施加虚拟的力，推动花瓣的变化，从而使整个花朵达到开放的状态。然而这种基于物理模拟的方法，并不能真实地反应实际的开花过程，花瓣的运动显得过于简单和规整。
发明内容
本发明提供了一种花朵开放过程的重建方法、计算机可读存储介质及设备，通过该方法得到的花朵开放过程，相较于现有技术得到的花朵开放过程，结果更加逼真精确。
根据本发明的一个方面，提供了一种花朵开放过程的重建方法，包括：采集整个花朵开放过程的四维点云数据；从所述点云数据中选择一帧包括所有花瓣信息的点云数据，并根据所选点云数据创建花朵网格模板，其中所述花朵网格模板包括多个花瓣网格模板；基于所述花朵网格模板与所述点云数据的对应关系，驱动所述花朵网格模板进行网格形变以跟踪所述点云数据，分别得到每一帧点云数据对应的花朵网格模板，其中，在网格形变过程中对各花瓣网格模板进行形状约束、碰撞约束和固定根约束；将得到的所有花朵网格模板按照花朵开放的顺序排列，得到花朵开放的动态过程。
根据本发明的另一方面，提供了一种包括计算机可读指令的计算机可读存储介质，所述计算机可读指令在被执行时使处理器至少执行上述花朵开放过程的重建方法。
根据本发明的另一个方面，提供了一种设备，包括：处理器；和包括计算机可读指令的存储器，所述计算机可读指令在被执行时使所述处理器执行上述花朵开放过程的重建方法。
通过本发明的花朵开放过程的重建方法、计算机可读存储介质及设备，基于采集到的真实的花朵开放过程点云数据以及创建的花朵网格模板，以数据驱动的方式进行花朵网格模板的有效网格形变，更新网格顶点的位置，能够保证模板形变的真实性，同时也 能够保证足够的自由度，使得形变后的模板最大程度与实际点云数据所展现的几何形态一致。同时，对花瓣网格模板进行约束，保证模板形状不发生非正常的扭曲和结构变化以及花瓣网格之间不发生交叉碰撞，使得花瓣之间的运动不受彼此的干扰。由此而重建出的花朵开放过程，能够更精确更真实地反应花朵开放过程，甚至能与实际花朵开放过程达到一模一样的视觉效果。
附图说明
为了更清楚地说明本发明实施例中的技术方案，下面将对实施例描述中所需要使用的附图作简单地介绍，显而易见地，下面描述中的附图仅仅是本发明的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据这些附图获得其他的附图。在附图中：
图1是本发明实施例的花朵开放过程的重建方法的流程图；
图2是本发明实施例的睡莲的点云数据和重建的开放过程的比较示意图；
图3是本发明实施例的花朵开放过程的重建装置的结构框图；
图4是本发明实施例的金百合的点云数据和重建的开放过程的比较示意图；
图5是本发明实施例的单片花瓣的点云数据和重建的开放过程的比较示意图；
图6是本发明实施例的花朵开放过程的重建流程示意图；
图7是本发明实施例提供的一种设备。
具体实施方式
为使本发明实施例的目的、技术方案和优点更加清楚明白，下面结合附图对本发明实施例做进一步详细说明。在此，本发明的示意性实施例及其说明用于解释本发明，但并不作为对本发明的限定。
基于物理模拟生成花朵开放的动画，并不能真实地反应实际的开花过程；而现有的四维重建方法，由于花朵几何特征复杂且自遮挡严重，不能直接用于花朵重建花朵开放过程。花朵开放过程的重建，可以看成多个物体在相互遮挡情况下的跟踪问题。这不同于人体运动和人脸表情的重建(人体运动和人脸表情的重建过程中模板以及跟踪的对象往往只有一个，物体之间更不会存在遮挡关系)。本发明解决的问题是：当多个物体在有显著遮挡关系时，如何有效进行模板的跟踪，从而重建出整个运动过程。
本发明实施例提供了一种花朵开放过程的重建方法，图1是本发明实施例的花朵开放过程的重建方法的流程图，如图1所示，该方法包括如下的步骤S101至步骤S104。
步骤S101，采集整个花朵开放过程的四维点云数据。
具体的，可以利用现有的3D扫描技术采集花朵开放过程的四维(4D)点云数据。4D点云数据与3D数据相比，加入了时间信息，即所采集的点云数据是一帧一帧的，按照花朵从花苞状态到完全开放状态的时间过程展现。
步骤S102，从点云数据中选择一帧包括所有花瓣信息的点云数据，并根据所选点云数据创建花朵网格模板，其中该花朵网格模板包括多个花瓣网格模板。
花朵自遮挡的存在，使得采集到的点云数据会不完整，无法扫描到每一个花瓣所对应的点云数据，得到的数据只能是花朵表面的点云数据，而内部的结构却无法得到，例如花朵在花苞状态，仅能看到表面的几个花瓣，存在大量的花瓣缺失，导致采集到的对应状态的点云数据严重丢失。为了提高重建的真实效果，本发明从所采集的点云数据中选择一帧包含花瓣信息较为完整的点云数据，在所选点云数据的基础上，创建花朵网格模板。具体的，可以是人工按照所选点云数据和花朵实物创建花朵网格模板，也可以通过预先编辑好的软件按照所选点云数据创建花朵网格模板，从而得到较为真实合理的花朵网格模板。
由于花朵的几何形态比较复杂，不能简单的将花朵作为一个整体进行处理。所以本发明对花朵进行几何意义上的分割，在创建花朵网格模板时，将花朵网格模板分割为多个花瓣网格模板，以花瓣作为基本单元。
步骤S103，基于花朵网格模板与点云数据的对应关系，驱动花朵网格模板进行网格形变以跟踪点云数据，分别得到每一帧点云数据对应的花朵网格模板，其中，在网格形变过程中对各花瓣网格模板进行形状约束、碰撞约束和固定根约束。
所采集的点云数据是花朵开放过程的真实点云序列，连续帧之间会有微小的动作变化，花朵网格模板是根据某一帧点云数据创建的，为了驱动模板形变，重建整个花朵开放过程，需要根据花朵网格模板的几何特征去分割所采集的点云数据，得到模板与真实点云数据的对应关系(或称为匹配关系)，达到模板和点云数据在花瓣层面上的一一对应。从而在上述对应关系的基础上，按照真实点云数据一帧一帧的形变，花朵网格模板也能够进行正确有效的形变，以达到与点云数据所展现的几何形态一致。
步骤S104，将得到的所有花朵网格模板按照花朵开放的顺序排列，得到花朵开放的动态过程。
通过上述方案，基于采集到的真实的花朵开放过程点云数据以及创建的花朵网格模板，以数据驱动的方式进行花朵网格模板的有效网格形变，更新网格顶点的位置，能够保证模板形变的真实性，同时也能够保证足够的自由度，使得形变后的模板最大程度与 实际点云数据所展现的几何形态一致。在此过程中，对花瓣网格模板进行约束，保证模板形状不发生非正常的扭曲和结构变化以及花瓣网格之间不发生交叉碰撞，使得花瓣之间的运动不受彼此的干扰。由此重建出的精确逼真的花朵开放过程，能够更真实地反应花朵开放过程，甚至能与实际花朵开放过程达到一模一样的视觉效果。
本发明所解决的问题是从花朵开放的4D点云数据上，重建出真实的花朵开放的网格序列。在本发明中，把上述问题抽象成了一个最大后验估计的问题，从概率和几何两个方面对问题进行了抽象，从而得到花朵网格形变的能量优化方程。
花朵网格模板是以花朵开放过程中的某一帧质量较好的点云数据为基础创建的，通过这个静态的花朵网格模板，基于数据向前(花苞状态)和/或向后(开放状态)进行模板的形变，重建出真实的花朵开放的动态过程。
问题的输入：Q＝Q1:T，1≤t≤T，其中，t为帧数，Q为点云数据。
问题的输出：M＝M1:T，1≤t≤T，其中，M为花朵网格模板，每一朵花都由K个花瓣构成，花瓣用Mk表示，1≤k≤K。
本发明将每一个花瓣网格模板都看成一个高斯混合分布(Gaussian Mixture Models，GMM)，即模板上的每个顶点是一个高斯分布的中心，模板上的所有顶点构成了一个混合分布，那么采集到的相对应的点云数据即为GMM的实际观测点集，模板的形变就转换成根据实际观测到的点云数据，推断模板每个顶点符合该点云数据的新位置，同时要保证模板本身的性质。因此上述问题就变成了一个最大后验估计的问题：
arg max p(Qt|Mt)p(Mt)
其中，Mt为未知数，p(Qt|Mt)表示似然概率，即在当前模板Mt下观测点云Qt的概率，p(Mt)表示先验概率，即模板自身的约束出现概率。
由于花朵网格模板的基本单元是花瓣网格模板Mk，但是采集的点云数据是没有分割信息的，所以需要在进行模板形变前，确定每一个花瓣网格模板所对应的点云数据集合，即对点云数据根据花瓣信息进行分割，获取每一个花瓣网格模板所对应的点云数据。然后对于花朵网格模板，采用期望最大化(Expectation Maximization，EM)迭代算法求解最大后验估计的问题，得到该模板的下一个位置，即新模板
Figure PCTCN2016102360-appb-000001
。
图2是本发明实施例的睡莲的点云数据和重建的开放过程的比较示意图，实际采集的睡莲数据超过了100帧，图2仅示出了具有代表性的6帧数据，分别记为t1、t2、t3、t4、t5、t6。
下面结合图2说明步骤S103中基于数据驱动花朵网格模板进行网格形变的过程。基于所选点云数据在全部点云数据中的位置，步骤S103可以包括：方式(1)和/或方式(2)。
(1)针对所选点云数据及其之前的各帧点云数据，从后往前逐帧执行步骤A1和步骤A2，直到得到所选点云数据之前的每一帧点云数据对应的花朵网格模板。
步骤A1，根据当前帧点云数据对应的花朵网格模板的几何特征，对当前帧点云数据的上一帧点云数据进行分割，得到花朵网格模板与上一帧点云数据的对应关系，该对应关系即上一帧点云数据中的采集点属于当前帧点云数据对应的花朵网格模板中的哪个花瓣网格模板；
步骤A2，基于上一帧点云数据和对应关系，对当前帧点云数据对应的花朵网格模板进行网格形变，得到与上一帧点云数据所展现的几何形态一致的花朵网格模板。
(2)针对所选点云数据及其之后的各帧点云数据，从前往后逐帧执行步骤B1和步骤B2，直到得到所选点云数据之后的每一帧点云数据对应的花朵网格模板。
步骤B1，根据当前帧点云数据对应的花朵网格模板的几何特征，对当前帧点云数据的下一帧点云数据进行分割，得到花朵网格模板与下一帧点云数据的对应关系，该对应关系即下一帧点云数据中的采集点属于当前帧点云数据对应的花朵网格模板中的哪个花瓣网格模板；
步骤B2，基于下一帧点云数据和对应关系，对当前帧点云数据对应的花朵网格模板进行网格形变，得到与下一帧点云数据所展现的几何形态一致的花朵网格模板。
如图2所示，假设选取第四帧点云数据(t4)创建花朵网格模板(记为M4)。对于第一帧至第三帧点云数据(t1至t3)，可以使用方式(1)得到t1、t2、t3对应的花朵网格模板M1、M2、M3；对于第五帧和第六帧点云数据(t5、t6)，可以使用方式(2)得到t5、t6对应的花朵网格模板M5、M6。由此，得到了每一帧点云数据对应的花朵网格模板。
具体的，以t4作为当前帧点云数据，根据M4的几何特征，对t3进行分割，得到M4中各花瓣网格模板与t3的对应关系，基于t3和得到的对应关系，对M4进行网格形变，得到t3对应的花朵网格模板M3。然后，以t3作为当前帧点云数据，根据M3的几何特征，对t2进行分割，得到M3中各花瓣网格模板与t2的对应关系，基于t2和得到的对应关系，对M3进行网格形变，得到t2对应的花朵网格模板M2。以t2作为当前帧点云数据，根据M2的几何特征，对t1进行分割，得到M2中各花瓣网格模板与t1的对 应关系，基于t1和得到的对应关系，对M2进行网格形变，得到t1对应的花朵网格模板M1。同样的，以t4作为当前帧点云数据，得到M5，以t5作为当前帧点云数据，得到M6。由此得到了全部花朵网格模板M1至M6。
假设选取t6创建花朵网格模板(记为M6)。对于t1至t5，可以使用方式(1)得到其对应的花朵网格模板M1至M5。假设选取t1创建花朵网格模板(记为M1)，对于t2至t6，可以使用方式(2)得到其对应的花朵网格模板M2至M6。选取t1创建花朵网格模板，由于花苞状态点云数据缺失，因此重建结果与选取花瓣信息更为完整的点云数据所得到的重建结果相比，逼真效果差一些。
在一个实施例中，点云数据分割可以基于点云数据到每一个花瓣网格模板的距离所决定。根据花朵网格模板的几何特征对点云数据进行分割的具体操作如下：
对于从后往前逐帧处理的情况，针对上一帧点云数据中的每个采集点，分别计算该采集点到当前帧点云数据对应的花朵网格模板中每个花瓣网格模板的距离；将该采集点对应的距离值由大到小进行排序，选取排在最后的两个距离值，并计算这两个距离值的比值；如果比值小于预设阈值，确定该采集点属于最小距离值对应的花瓣网格模板；如果比值大于或等于预设阈值，确定该采集点不属于任何花瓣网格模板；
对于从前往后逐帧处理的情况，针对下一帧点云数据中的每个采集点，分别计算该采集点到当前帧点云数据对应的花朵网格模板中每个花瓣网格模板的距离；将该采集点对应的距离值由大到小进行排序，选取排在最后的两个距离值，并计算这两个距离值的比值；如果比值小于预设阈值，确定该采集点属于最小距离值对应的花瓣网格模板；如果比值大于或等于预设阈值，确定该采集点不属于任何花瓣网格模板。
具体的，分别计算该采集点到当前帧点云数据对应的花朵网格模板中每个花瓣网格模板的距离，包括：针对每个花瓣网格模板，计算该采集点到该花瓣网格模板中每个顶点的距离，并计算最近距离，将该最近距离作为该采集点到该花瓣网格模板的距离。
本实施例中，考虑到如果直接判定采集点属于最小距离对应的花瓣网格模板，可能会出现误差，因此，加入置信度(即上述预设阈值)，如果比值小于预设阈值，说明该采集点属于最小距离对应的花瓣网格模板的概率很高，将该采集点分配给该花瓣网格模板；否则，认为该采集点不属于任何花瓣。由此可以排除不准确的数据，提高点云数据分割的准确性。
在一个实施例中，得到花朵网格模板与点云数据的对应关系，包括：针对每一个花瓣网格模板，计算该花瓣网格模板上的每一个顶点与属于该花瓣网格模板的每一个采集 点之间的匹配概率，花朵网格模板和所有采集点之间的匹配概率用关联矩阵Z表示，关联矩阵Z中的元素Zij∈[0,1]，关联矩阵Z中的元素Zij∈[0,1]。
Figure PCTCN2016102360-appb-000002
其中，mi表示花朵网格模板M上的第i个顶点，mi属于第k个花瓣网格模板，第k个花瓣网格模板用Mk表示，
Figure PCTCN2016102360-appb-000003
Qk表示与Mk对应的点云数据，qj表示点云数据Q中的第j个采集点，p(qj|mi)为似然概率，表示在花朵网格模板M的顶点mi下观测点云数据Q的采集点qj的概率。
当花朵网格模板与对应点云数据的关联矩阵求出之后，通过求解最大后验估计的能量方程更新模板顶点的位置，使模板能更好地与点云数据相吻合。
在一个实施例中，对当前帧点云数据对应的花朵网格模板进行网格形变，包括：采用期望最大化迭代算法求解最大后验估计的能量方程：
arg min(-log p(M|Q,Z)-log p(M))     (2)
其中，-log p(M|Q,Z)为数据项，表示花朵网格模板M与点云数据Q之间的符合程度；关联矩阵Z表示花朵网格模板M和所有采集点之间的匹配概率；p(M|Q,Z)为似然概率，表示在花朵网格模板M下观测点云数据Q的概率；-logp(M)为花朵网格模板的先验项，表示花朵网格模板M自身的约束；p(M)为先验概率，表示花朵网格模板M自身约束的出现概率。
对于从后往前逐帧处理的情况，求解该能量方程得到当前帧点云数据对应的花朵网格模板中各顶点对应于上一帧点云数据的新位置；对于从前往后逐帧处理的情况，求解该能量方程得到当前帧点云数据对应的花朵网格模板中各顶点对应于下一帧点云数据的新位置。
数据项定义了模板顶点与对应点云之间的距离关系，所以当数据项越小，模板与点云越接近。数据项的表达式为：
-log p(M|Q,Z)＝Σkw1D(Qk,Mk)    (3)
其中，w1表示数据项的权重，Mk表示第k个花瓣网格模板，Qk表示第k个花瓣网格模板Mk对应的点云数据，D(Qk,Mk)表示第k个花瓣网格模板Mk与其对应的点云数 据Qk的距离函数，
Figure PCTCN2016102360-appb-000004
mi表示花朵网格模板M上的第i个顶点，mi属于第k个花瓣网格模板Mk；qj表示点云数据Q中的第j个采集点，且该采集点属于与Mk对应的点云数据Qk；Zij表示花朵网格模板M上的第i个顶点与点云数据Q中的第j个采集点之间的匹配概率。
在模板与点云数据吻合的基础上，为了保证模板自身的形状不发生非正常的扭曲和拓扑结构的改变，需要对模板本身添加先验约束项。先验项包括：形状约束Eshape、碰撞约束Ecollision和固定根约束Eroot，其中，形状约束用于对花瓣网格模板进行几何形状上的约束，碰撞约束用于保证各花瓣网格模板之间不发生交叉碰撞，固定根约束用于保证花瓣网格模板拥有固定根底部。
先验项的表达式为：
-log p(M)＝Eshape+Ecollision+Eroot          (4)
为了保证生成的花朵网格模板像真实的花朵，需要对花朵网格模板进行几何形状上的约束，保证模板在形变的过程中，能够保持网格的质量和结构。可以使用ARAP(as-rigid-as-possible)方法，保证网格形变过程中，局部变换要尽可能保持刚性变换。
形状约束Eshape的表达式为：
Figure PCTCN2016102360-appb-000005
其中，w2表示形状约束的权重，N(i)表示在花朵网格模板M上与第i个顶点相邻的顶点集合，cij表示第i个顶点和第j个顶点组成的边的权重，Ri表示第i个顶点的旋转矩阵，
Figure PCTCN2016102360-appb-000006
表示顶点mi形变前的位置，
Figure PCTCN2016102360-appb-000007
表示顶点mj形变前的位置，||·||2表示欧式距离。
花朵网格模板由K个花瓣网格模板组成，在跟踪点云数据形变的过程中花瓣网格模板之间可能会发生交叉碰撞，这在实际开花过程中是不可能的，所以需要添加碰撞约束，保证不发生交叉碰撞。
碰撞约束Ecollision的表达式为：
Figure PCTCN2016102360-appb-000008
其中，w3表示碰撞约束的权重，SC表示发生碰撞的顶点的集合，
Figure PCTCN2016102360-appb-000009
表示顶点mi避免碰撞的新位置，||·||2表示欧式距离。
在求解能量方程时，采用迭代的方式逐渐得到新的顶点位置。在每次迭代之前，都需要对花瓣之间进行碰撞检测，如果检测到顶点mi是碰撞点，则沿着被碰撞的网格的面反向往回走一段距离，得到避免碰撞的新位置
Figure PCTCN2016102360-appb-000010
。
对于所有花瓣而言，底部在花朵开放过程中都是固定不动的，固定根约束Eroot的表达式为：
Figure PCTCN2016102360-appb-000011
其中，w4表示固定根约束的权重，SR表示根节点的集合，
Figure PCTCN2016102360-appb-000012
表示顶点mi形变前的位置。
在一个实施例中，可以采用局部整体的方法求解式(2)所示的非线性优化方程，在局部上，针对花朵网格模板的每一个顶点，求解形状约束中的旋转矩阵Ri以及碰撞约束中顶点mi避免碰撞的新位置
Figure PCTCN2016102360-appb-000013
；在整体上，将最大后验估计的能量方程转化成线性方程，求解顶点的新位置；迭代上述局部和整体两个过程直至收敛，得到花瓣网格模板的新位置。对每一帧点云数据重复上述过程，直到完成整个点云数据序列的重建。
基于同一发明构思，本发明实施例还提供了一种花朵开放过程的重建装置，可以用于实现上述实施例所描述的方法。由于该装置解决问题的原理与上述方法相似，因此该装置的实施可以参见上述方法的实施，重复之处不再赘述。以下所使用的，术语“单元”或者“模块”可以实现预定功能的软件和/或硬件的组合。尽管以下实施例所描述的系统较佳地以软件来实现，但是硬件，或者软件和硬件的组合的实现也是可能并被构想的。例如，可用本领域公知的下列技术中的任一项或他们的组合来实现：具有用于对数据信号实现逻辑功能的逻辑门电路的离散逻辑电路，具有合适的组合逻辑门电路的专用集成电路，可编程门阵列(PGA)，现场可编程门阵列(FPGA)等。
图3是本发明实施例的花朵开放过程的重建装置的结构框图，如图3所示，该装置包括：数据采集单元31、模板创建单元32、驱动形变单元33和展示单元34，下面对该结构进行具体说明。
数据采集单元31，用于采集整个花朵开放过程的四维点云数据；
模板创建单元32，用于从点云数据中选择一帧包括所有花瓣信息的点云数据，并根据所选点云数据创建花朵网格模板，其中花朵网格模板包括多个花瓣网格模板；
驱动形变单元33，用于基于花朵网格模板与点云数据的对应关系，驱动花朵网格模板进行网格形变以跟踪点云数据，分别得到每一帧点云数据对应的花朵网格模板，其中，在网格形变过程中对各花瓣网格模板进行形状约束、碰撞约束和固定根约束；
展示单元34，用于将得到的所有花朵网格模板按照花朵开放的顺序排列，得到花朵开放的动态过程。
通过上述方案，基于采集到的真实的花朵开放过程点云数据以及创建的花朵网格模板，以数据驱动的方式进行花朵网格模板的有效网格形变，更新网格顶点的位置，能够保证模板形变的真实性，同时也能够保证足够的自由度，使得形变后的模板最大程度与实际点云数据所展现的几何形态一致；同时，对花瓣网格模板进行约束，保证模板形状不发生非正常的扭曲和结构变化以及花瓣网格之间不发生交叉碰撞，使得花瓣之间的运动不受彼此的干扰。由此重建出的精确逼真的花朵开放过程，能够更真实地反应花朵开放过程，甚至能与实际花朵开放过程达到一模一样的视觉效果。
驱动形变单元33可以包括：第一驱动模块、第一分割模块、第一形变模块、第二驱动模块、第二分割模块和第二形变模块。
第一驱动模块，用于针对所选点云数据及其之前的各帧点云数据，从后往前逐帧触发第一分割模块和第一形变模块，直到得到所选点云数据之前的每一帧点云数据对应的花朵网格模板；
第一分割模块，用于根据当前帧点云数据对应的花朵网格模板的几何特征，对当前帧点云数据的上一帧点云数据进行分割，得到花朵网格模板与上一帧点云数据的对应关系；
第一形变模块，用于基于上一帧点云数据和对应关系，对当前帧点云数据对应的花朵网格模板进行网格形变，得到与上一帧点云数据所展现的几何形态一致的花朵网格模板；
第二驱动模块，用于针对所选点云数据及其之后的各帧点云数据，从前往后逐帧触发第二分割模块和第二形变模块，直到得到所选点云数据之后的每一帧点云数据对应的花朵网格模板；
第二分割模块，用于根据当前帧点云数据对应的花朵网格模板的几何特征，对当前帧点云数据的下一帧点云数据进行分割，得到花朵网格模板与下一帧点云数据的对应关系；
第二形变模块，用于基于下一帧点云数据和对应关系，对当前帧点云数据对应的花 朵网格模板进行网格形变，得到与下一帧点云数据所展现的几何形态一致的花朵网格模板。
上述第一驱动模块、第一分割模块、第一形变模块、第二驱动模块、第二分割模块和第二形变模块可以是独立的模块，各自实现其功能，也可以是集成在一起的模块。
第一分割模块具体用于：针对上一帧点云数据中的每个采集点，分别计算该采集点到当前帧点云数据对应的花朵网格模板中每个花瓣网格模板的距离；将该采集点对应的距离值由大到小进行排序，选取排在最后的两个距离值，并计算这两个距离值的比值；如果比值小于预设阈值，确定该采集点属于最小距离值对应的花瓣网格模板；如果比值大于或等于预设阈值，确定该采集点不属于任何花瓣网格模板。
第二分割模块具体用于：针对下一帧点云数据中的每个采集点，分别计算该采集点到当前帧点云数据对应的花朵网格模板中每个花瓣网格模板的距离；将该采集点对应的距离值由大到小进行排序，选取排在最后的两个距离值，并计算这两个距离值的比值；如果比值小于预设阈值，确定该采集点属于最小距离值对应的花瓣网格模板；如果比值大于或等于预设阈值，确定该采集点不属于任何花瓣网格模板。
具体的，针对每个花瓣网格模板，可以计算该采集点到该花瓣网格模板中每个顶点的距离，并计算最近距离，将该最近距离作为该采集点到该花瓣网格模板的距离。
在一个实施例中，第一分割模块和第二分割模块均包括：第一计算子模块，用于针对每一个花瓣网格模板，计算该花瓣网格模板上的每一个顶点与属于该花瓣网格模板的每一个采集点之间的匹配概率，花朵网格模板和所有采集点之间的匹配概率用关联矩阵Z表示，关联矩阵Z中的元素Zij∈[0,1]。
Figure PCTCN2016102360-appb-000014
其中，mi表示花朵网格模板M上的第i个顶点，mi属于第k个花瓣网格模板，第k个花瓣网格模板用Mk表示，
Figure PCTCN2016102360-appb-000015
Qk表示与Mk对应的点云数据，qj表示点云数据Q中的第j个采集点，p(qj|mi)为似然概率，表示在花朵网格模板M的顶点mi下观测点云数据Q的采集点qj的概率。
第一形变模块和第二形变模块均包括：第二计算子模块，采用期望最大化迭代算法求解最大后验估计的能量方程：
arg min(-log p(M|Q,Z)-log p(M))，其中，-log p(M|Q,Z)为数据项，表示花朵网格模板M与点云数据Q之间的符合程度；关联矩阵Z表示花朵网格模板M和所有采 集点之间的匹配概率；p(M|Q,Z)为似然概率，表示在花朵网格模板M下观测点云数据Q的概率；-log p(M)为花朵网格模板的先验项，表示花朵网格模板M自身的约束；p(M)为先验概率，表示花朵网格模板M自身约束的出现概率。
对于从后往前逐帧处理的情况，求解该能量方程得到当前帧点云数据对应的花朵网格模板中各顶点对应于上一帧点云数据的新位置。对于从前往后逐帧处理的情况，求解该能量方程得到当前帧点云数据对应的花朵网格模板中各顶点对应于下一帧点云数据的新位置。
上述先验项包括：形状约束Eshape、碰撞约束Ecollision和固定根约束Eroot，形状约束用于对花瓣网格模板进行几何形状上的约束，碰撞约束用于保证各花瓣网格模板之间不发生交叉碰撞，固定根约束用于保证花瓣网格模板拥有固定根底部。数据项和先验项的表达式如上述方法实施例所述，此处不再赘述。
第二计算子模块具体用于：针对花朵网格模板上的每一个顶点，求解形状约束中的旋转矩阵Ri以及碰撞约束中顶点mi避免碰撞的新位置
Figure PCTCN2016102360-appb-000016
，将最大后验估计的能量方程转化成线性方程，求解顶点的新位置；迭代上述求解过程直至收敛，得到花朵网格模板的新位置。
当然，上述模块划分只是一种示意划分，本发明并不局限于此。只要能实现本发明的目的的模块划分，均应属于本发明的保护范围。
利用本发明的方法，得到金百合和单片花瓣的实际开放过程，图4是本发明实施例的金百合的点云数据和重建的开放过程的比较示意图，图5是本发明实施例的单片花瓣的点云数据和重建的开放过程的比较示意图，如图4和图5所示，经过在数据上的测试，本发明能够有效真实地重建出实际开花的过程。
图6是本发明实施例的花朵开放过程的重建流程示意图，如图6所示，采集点云数据，创建花朵网格模板，基于点云数据与花朵网格模板的对应关系，对花朵网格模板进行向前和向后的网格形变，以跟踪点云数据，最终得到花朵的网格序列，重建了真实的花朵开放过程。
本发明实施例还提供了一种包括计算机可读指令的计算机可读存储介质，该计算机可读指令在被执行时使处理器至少执行上述花朵开放过程的重建方法。
如图7所示，本发明实施例还提供了一种设备，包括处理器71和包括计算机可读指令的存储器72，计算机可读指令在被执行时使处理器71执行上述花朵开放过程的重建 方法。
综上所述，本发明提供的花朵开放过程的重建方法、计算机可读存储介质及设备，与现有的基于物理驱动的重建方法相比，从原理上采用了完全不同的思想，本发明采集真实花开过程的4D点云数据，基于数据驱动，通过向前跟踪的方法，从后往前逐渐从开放状态跟踪到花苞状态，有效重建出初始状态部分花瓣完全不可见等的复杂形态，能够准确地从高度不完整的数据中重建出花朵开放的真实过程。同时，本发明能够有效避免花瓣之间的碰撞交叉以及处理数据缺失等情况，保证花瓣能正确真实地进行形变。本发明能够生成具有真实感的花朵开放过程的动画，达到几乎与真实花朵一模一样的开放效果。
流程图中或在此以其他方式描述的任何过程或方法描述可以被理解为，表示包括一个或更多个用于实现特定逻辑功能或过程的步骤的可执行指令的代码的模块、片段或部分，并且本发明的优选实施方式的范围包括另外的实现，其中可以不按所示出或讨论的顺序，包括根据所涉及的功能按基本同时的方式或按相反的顺序，来执行功能，这应被本发明的实施例所属技术领域的技术人员所理解。
此外，在本发明各个实施例中的各功能单元可以集成在一个处理模块中，也可以是各个单元单独物理存在，也可以两个或两个以上单元集成在一个模块中。上述集成的模块既可以采用硬件的形式实现，也可以采用软件功能模块的形式实现。所述集成的模块如果以软件功能模块的形式实现并作为独立的产品销售或使用时，也可以存储在一个计算机可读取存储介质中。上述提到的存储介质可以是只读存储器，磁盘或光盘等。
在本说明书的描述中，参考术语“一个实施例”、“一些实施例”、“示例”、“具体示例”、或“一些示例”等的描述意指结合该实施例或示例描述的具体特征、结构、材料或者特点包含于本发明的至少一个实施例或示例中。在本说明书中，对上述术语的示意性表述不一定指的是相同的实施例或示例。而且，描述的具体特征、结构、材料或者特点可以在任何的一个或多个实施例或示例中以合适的方式结合。
以上所述的具体实施例，对本发明的目的、技术方案和有益效果进行了进一步详细说明，所应理解的是，以上所述仅为本发明的具体实施例而已，并不用于限定本发明的保护范围，凡在本发明的精神和原则之内，所做的任何修改、等同替换、改进等，均应包含在本发明的保护范围之内。

Claims (14)

  1. 一种花朵开放过程的重建方法，其中，包括：
    采集整个花朵开放过程的四维点云数据；
    从所述点云数据中选择一帧包括所有花瓣信息的点云数据，并根据所选点云数据创建花朵网格模板，其中所述花朵网格模板包括多个花瓣网格模板；
    基于所述花朵网格模板与所述点云数据的对应关系，驱动所述花朵网格模板进行网格形变以跟踪所述点云数据，分别得到每一帧点云数据对应的花朵网格模板，其中，在网格形变过程中对各花瓣网格模板进行形状约束、碰撞约束和固定根约束；
    将得到的所有花朵网格模板按照花朵开放的顺序排列，得到花朵开放的动态过程。
  2. 根据权利要求1所述的方法，其中，基于所述花朵网格模板与所述点云数据的对应关系，驱动所述花朵网格模板进行网格形变以跟踪所述点云数据，分别得到每一帧点云数据对应的花朵网格模板，包括：
    针对所选点云数据及其之前的各帧点云数据，从后往前逐帧执行步骤A1和步骤A2，直到得到所选点云数据之前的每一帧点云数据对应的花朵网格模板；
    步骤A1，根据当前帧点云数据对应的花朵网格模板的几何特征，对所述当前帧点云数据的上一帧点云数据进行分割，得到花朵网格模板与所述上一帧点云数据的对应关系；
    步骤A2，基于所述上一帧点云数据和所述对应关系，对所述当前帧点云数据对应的花朵网格模板进行网格形变，得到与所述上一帧点云数据所展现的几何形态一致的花朵网格模板；
    和/或，
    针对所选点云数据及其之后的各帧点云数据，从前往后逐帧执行步骤B1和步骤B2，直到得到所选点云数据之后的每一帧点云数据对应的花朵网格模板；
    步骤B1，根据当前帧点云数据对应的花朵网格模板的几何特征，对所述当前帧点云数据的下一帧点云数据进行分割，得到花朵网格模板与所述下一帧点云数据的对应关系；
    步骤B2，基于所述下一帧点云数据和所述对应关系，对所述当前帧点云数据对应的花朵网格模板进行网格形变，得到与所述下一帧点云数据所展现的几何形态一致的花朵网格模板。
  3. 根据权利要求2所述的方法，其中，
    对于从后往前逐帧处理的情况，根据当前帧点云数据对应的花朵网格模板的几何特征，对所述当前帧点云数据的上一帧点云数据进行分割，包括：
    针对所述上一帧点云数据中的每个采集点，分别计算该采集点到所述当前帧点云数据对应的花朵网格模板中每个花瓣网格模板的距离；
    将该采集点对应的距离值由大到小进行排序，选取排在最后的两个距离值，并计算这两个距离值的比值；
    如果比值小于预设阈值，确定该采集点属于最小距离值对应的花瓣网格模板；
    如果比值大于或等于所述预设阈值，确定该采集点不属于任何花瓣网格模板；
    对于从前往后逐帧处理的情况，根据当前帧点云数据对应的花朵网格模板的几何特征，对所述当前帧点云数据的下一帧点云数据进行分割，包括：
    针对所述下一帧点云数据中的每个采集点，分别计算该采集点到所述当前帧点云数据对应的花朵网格模板中每个花瓣网格模板的距离；
    将该采集点对应的距离值由大到小进行排序，选取排在最后的两个距离值，并计算这两个距离值的比值；
    如果比值小于预设阈值，确定该采集点属于最小距离值对应的花瓣网格模板；
    如果比值大于或等于所述预设阈值，确定该采集点不属于任何花瓣网格模板。
  4. 根据权利要求3所述的方法，其中，分别计算该采集点到所述当前帧点云数据对应的花朵网格模板中每个花瓣网格模板的距离，包括：
    针对每个花瓣网格模板，计算该采集点到该花瓣网格模板中每个顶点的距离，并计算最近距离，将该最近距离作为该采集点到该花瓣网格模板的距离。
  5. 根据权利要求2所述的方法，其中，得到花朵网格模板与点云数据的对应关系，包括：
    针对每一个花瓣网格模板，计算该花瓣网格模板上的每一个顶点与属于该花瓣网格模板的每一个采集点之间的匹配概率，花朵网格模板和所有采集点之间的匹配概率用关联矩阵Z表示，关联矩阵Z中的元素Zij∈[0,1]；
    Figure PCTCN2016102360-appb-100001
    其中，mi表示花朵网格模板M上的第i个顶点，mi属于第k个花瓣网格模板，第k个花瓣网格模板用Mk表示，
    Figure PCTCN2016102360-appb-100002
    Qk表示与Mk对应的点云数据，qj表示点云数据Q中的第j个采集点，p(qj|mi)为似然概率，表 示在花朵网格模板M的顶点mi下观测点云数据Q的采集点qj的概率。
  6. 根据权利要求2所述的方法，其中，对所述当前帧点云数据对应的花朵网格模板进行网格形变，包括：
    采用期望最大化迭代算法求解最大后验估计的能量方程：
    arg min(-log p(M|Q,Z)-log p(M))；
    对于从后往前逐帧处理的情况，求解该能量方程得到所述当前帧点云数据对应的花朵网格模板中各顶点对应于上一帧点云数据的新位置；
    对于从前往后逐帧处理的情况，求解该能量方程得到所述当前帧点云数据对应的花朵网格模板中各顶点对应于下一帧点云数据的新位置；
    其中，-log p(M|Q,Z)为数据项，表示花朵网格模板M与点云数据Q之间的符合程度；关联矩阵Z表示花朵网格模板M和所有采集点之间的匹配概率；p(M|Q,Z)为似然概率，表示在花朵网格模板M下观测点云数据Q的概率；-log p(M)为花朵网格模板的先验项，表示花朵网格模板M自身的约束；p(M)为先验概率，表示花朵网格模板M自身约束的出现概率。
  7. 根据权利要求6所述的方法，其中，所述数据项的表达式为：
    Figure PCTCN2016102360-appb-100003
    其中，w1表示数据项的权重，Mk表示第k个花瓣网格模板，Qk表示第k个花瓣网格模板Mk对应的点云数据，D(Qk,Mk)表示第k个花瓣网格模板Mk与其对应的点云数据Qk的距离函数，
    Figure PCTCN2016102360-appb-100004
    mi表示花朵网格模板M上的第i个顶点，且该顶点属于第k个花瓣网格模板Mk；qj表示点云数据Q中的第j个采集点，且该采集点属于Qk；Zij表示花朵网格模板M上的第i个顶点与点云数据Q中的第j个采集点之间的匹配概率。
  8. 根据权利要求6所述的方法，其中，所述先验项包括：形状约束Eshape、碰撞约束Ecollision和固定根约束Eroot，其中，所述形状约束用于对所述花瓣网格模板进行几何形状上的约束，所述碰撞约束用于保证各花瓣网格模板之间不发生交叉碰撞，所述固定根约束用于保证花瓣网格模板拥有固定根底部；
    所述先验项的表达式为：-log p(M)＝Eshape+Ecollision+Eroot。
  9. 根据权利要求8所述的方法，其中，所述形状约束Eshape的表达式为：
    Figure PCTCN2016102360-appb-100005
    其中，w2表示形状约束的权重，N(i)表示在花朵网格模板M上与第i个顶点相邻的顶点集合，cij表示第i个顶点和第j个顶点组成的边的权重，Ri表示第i个顶点的旋转矩阵，
    Figure PCTCN2016102360-appb-100006
    表示顶点mi形变前的位置，
    Figure PCTCN2016102360-appb-100007
    表示顶点mj形变前的位置，||·||2表示欧式距离。
  10. 根据权利要求8所述的方法，其中，所述碰撞约束Ecollision的表达式为：
    Figure PCTCN2016102360-appb-100008
    其中，w3表示碰撞约束的权重，SC表示发生碰撞的顶点的集合，
    Figure PCTCN2016102360-appb-100009
    表示顶点mi避免碰撞的新位置，||·||2表示欧式距离。
  11. 根据权利要求8所述的方法，其中，所述固定根约束Eroot的表达式为：
    Figure PCTCN2016102360-appb-100010
    其中，w4表示固定根约束的权重，SR表示根节点的集合，
    Figure PCTCN2016102360-appb-100011
    表示顶点mi形变前的位置。
  12. 根据权利要求6所述的方法，其中，针对每一个花瓣网格模板，采用期望最大化迭代算法求解最大后验估计的能量方程，包括：
    针对花朵网格模板的每一个顶点，求解形状约束中的旋转矩阵Ri以及碰撞约束中顶点mi避免碰撞的新位置
    Figure PCTCN2016102360-appb-100012
    将最大后验估计的能量方程转化成线性方程，求解顶点的新位置；
    迭代上述求解过程直至收敛，得到花朵网格模板的新位置。
  13. 一种包括计算机可读指令的计算机可读存储介质，其中，所述计算机可读指令在被执行时使处理器至少执行权利要求1-12中任一项所述的方法。
  14. 一种设备，其中，包括：
    处理器；和
    包括计算机可读指令的存储器，所述计算机可读指令在被执行时使所述处理器执行如权利要求1-12中任一项所述的方法。
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CN110363804A (zh) * 2019-07-23 2019-10-22 西北农林科技大学 一种基于形变模型的花朵浅浮雕浮雕生成方法
CN110363804B (zh) * 2019-07-23 2022-10-11 西北农林科技大学 一种基于形变模型的花朵浅浮雕浮雕生成方法

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