Subdivision wavelet method and device combining CB spline and progressive interpolation

Abstract

The present invention discloses an image processing method, specifically, a subdivision wavelet method and device combining C-B spline and progressive interpolation. The method comprises: obtaining an initial three-dimensional model, which is a 3D grid including face points, edge points and vertices, and is used to present the three-dimensional shape, spatial structure and surface details of an object; constructing a reversible harmonic Catmull-Clark subdivision rule based on C-B spline and progressive interpolation, and the harmonic Catmull-Clark subdivision rule can be applied to forward subdivision and reverse subdivision; converting the harmonic Catmull-Clark subdivision rule into a set of reversible local operators; based on the reversible local operators, converting the forward subdivision and reverse subdivision into wavelet transform, and using the decomposition algorithm and reconstruction algorithm of the wavelet transform to realize the transformation of the initial three-dimensional model. The method can improve the accuracy and stability of the three-dimensional model in the process of medical image processing.

Description

Technical Field

[0001] The invention belongs to an image processing method, and specifically relates to a subdivision wavelet method and device combining CB spline and progressive interpolation. Background Art

[0002] In medical image processing, three-dimensional reconstruction is a technology in medical imaging that can convert two-dimensional images into three-dimensional images through computers in order to more accurately observe and evaluate the condition. For example, 3D reconstruction of bone and joint images in medical images helps in the stereoscopic positioning of fracture fragments and the correct classification of bone and joint injuries, and supplements new fracture classifications in three-dimensional space to facilitate doctors' judgment. Finite element analysis is a method that divides complex structures into a finite number of units through numerical approximation, thereby calculating the force characteristics of each unit and obtaining the overall mechanical characteristics. It is widely used in medical disciplines such as orthopedics and dentistry, and is an important research method in biomechanics. In the processing of femoral finite element analysis, the model results can be verified through physical experiments, and then the new structure can be expanded and analyzed. It is an important tool for studying the force characteristics of the human body.

[0003] Whether it is 3D reconstruction of bone joints in medical images or finite element analysis of femur, the 3D mesh multi-resolution transformation method is required to not only represent regular surfaces such as spheres and ellipsoids with high precision, but also retain the shape characteristics of 3D geometric bodies and have good data compression performance, so as to ensure the accuracy of the analysis results and the stability of the model.

[0004] At present, the known subdivision wavelet methods are mostly aimed at surface modeling of conventional shapes, and cannot accurately represent circles, spheres, ellipsoids, etc., and cannot perform multi-resolution transformation processing. The patent application with publication number CN117541747A introduces CB spline technology into Catmull-Clark subdivision, that is, the edge point subdivision formula is modified to contain the control parameter angle value, so that the CB spline subdivision wavelet transform based on CB spline not only has the conventional Catmull-Clark subdivision function, but also can accurately represent surfaces such as spheres and rotating ellipsoids, and can further increase the degree of freedom of surface modeling by adjusting parameters. Although this method can greatly change the surface shape and accurately represent the surface shapes of spheres, ellipsoids, etc., it cannot stably maintain the shape characteristics of 3D geometric bodies.

[0005] In medical image processing, the shape characteristics of 3D geometric bodies have a crucial impact on medical image analysis. Existing methods cannot stably maintain the shape characteristics of 3D geometric bodies during the multi-resolution transformation of 3D models, which leads to the reduction of the accuracy and stability of the 3D models during medical image processing. Summary of the invention

[0006] The technical problem to be solved by the present invention is that the existing methods cannot stably maintain the shape characteristics of 3D geometric bodies during the multi-resolution transformation of 3D models, which leads to the reduction of the accuracy and stability of the 3D models during medical image processing. In order to solve the above problem, the present invention provides a subdivision wavelet method and device combining CB spline and progressive interpolation.

[0007] The content of the present invention includes: In a first aspect, an embodiment of the present invention provides a subdivision wavelet method combining CB spline and progressive interpolation, comprising: Acquire an initial three-dimensional model, wherein the initial three-dimensional model is a 3D mesh including face points, edge points and vertices, and is used to present the three-dimensional shape, spatial structure and surface details of the object; Based on CB spline and progressive interpolation, a reversible harmonic Catmull-Clark subdivision rule is constructed, wherein the harmonic Catmull-Clark subdivision rule can be applied to forward subdivision and reverse subdivision, and the harmonic Catmull-Clark subdivision rule includes the subdivision rule of the face point, the subdivision rule of the edge point and the subdivision rule of the vertex; converting the harmonic Catmull-Clark subdivision rule into a set of reversible local operators; Based on the reversible local operator, the forward subdivision and the reverse subdivision are converted into wavelet transform, and the decomposition algorithm and reconstruction algorithm of wavelet transform are used to realize the transformation of the initial three-dimensional model.

[0008] Optionally, the constructing of a reversible harmonic Catmull-Clark subdivision rule based on CB splines and progressive interpolation includes: Determine the basic Catmull-Clark segmentation rule; The basic Catmull-Clark subdivision rule is updated according to the principle of progressive difference to obtain a Catmull-Clark subdivision rule based on progressive interpolation and CB spline; A harmonic parameter is introduced into the Catmull-Clark subdivision rule based on progressive interpolation and CB spline to obtain the harmonic Catmull-Clark subdivision rule.

[0009] Optionally, the Catmull-Clark subdivision rule based on progressive interpolation and CB spline is: ; ; ; in, , , , Respectively represent the surface The four vertices around and For the edge point The points of two adjacent faces, is the noodle with serial number i, For the noodle point with serial number (i-2+n)%n, is the edge point with serial number i, is a vertex with serial number 0, a(n), b(n), c(n) are all greater than or equal to 0, and a(n)+nb(n)+nc(n)=1, is a vertex with valence n, There are 2n surrounds The vertex of is the preset parameter, To control the parameter angle, i is the serial number of the vertex, edge point and surface point, i and n are both positive integers, i%n represents the remainder after the integer i is divided by n, (i-2+n)%n represents the remainder after (i-2+n) is divided by n; The Catmull-Clark subdivision rule based on progressive interpolation and CB spline The equivalent form is: .

[0010] Optionally, the harmonized Catmull-Clark subdivision rule is: ; ; , in, , , , Respectively represent the surface The four surrounding vertices, and For the edge point The points of two adjacent faces, is the noodle with serial number i, For the noodle point with serial number (i-2+n)%n, is the edge point with serial number i, is the vertex with sequence number 0, , , are both greater than or equal to 0, and +n +n =1, is a vertex with valence n, There are 2n surrounds The vertex of is the preset parameter, To control the parameter angle, is the harmonic parameter, i is the serial number of the vertex, edge point and surface point, i and n are both positive integers, i%n represents the remainder after the integer i is divided by n, (i-2+n)%n represents the remainder after (i-2+n) is divided by n; The harmonic Catmull-Clark subdivision rule The equivalent form is: .

[0011] Optionally, the blending parameter The value range is [-1, 1].

[0012] Optionally, the blending parameter The value of is related to the shape of the initial three-dimensional model.

[0013] Optionally, before converting the forward subdivision and the reverse subdivision into wavelet transform based on the reversible local operator and implementing the transformation of the initial three-dimensional model using the decomposition algorithm and reconstruction algorithm of the wavelet transform, the method further comprises: Specify the preset parameters The value of Based on the preset parameters The value of is used to calculate the orthogonalization coefficient of the corresponding surface point wavelet and the orthogonalization coefficient of the corresponding edge point wavelet. The orthogonalization coefficient of the surface point wavelet and the orthogonalization coefficient of the edge point wavelet are used to construct the decomposition algorithm and the reconstruction algorithm.

[0014] In a second aspect, an embodiment of the present invention provides a subdivision wavelet device combining CB spline and progressive interpolation, comprising: An acquisition module is used to acquire an initial three-dimensional model, wherein the initial three-dimensional model is a 3D mesh including surface points, edge points and vertices, and is used to present the three-dimensional shape, spatial structure and surface details of the object; A construction module, used for constructing a reversible harmonic Catmull-Clark subdivision rule based on CB spline and progressive interpolation, wherein the harmonic Catmull-Clark subdivision rule can be applied to forward subdivision and reverse subdivision, and the harmonic Catmull-Clark subdivision rule includes the subdivision rule of the face point, the subdivision rule of the edge point and the subdivision rule of the vertex; A conversion module, for converting the harmonic Catmull-Clark subdivision rule into a set of reversible local operators; The transformation module is used to convert the forward subdivision and the reverse subdivision into wavelet transformation based on the reversible local operator, and realize the transformation of the initial three-dimensional model by using the decomposition algorithm and reconstruction algorithm of the wavelet transformation.

[0015] In a third aspect, an embodiment of the present invention provides an electronic device, comprising: a memory, a processor, and a program stored in the memory and executable on the processor; the processor is used to read the program in the memory to implement the steps in the subdivision wavelet method combining CB splines and progressive interpolation as described in the first aspect.

[0016] In a fourth aspect, an embodiment of the present invention provides a readable storage medium for storing a program, which, when executed by a processor, implements the steps in the subdivision wavelet method combining CB spline and progressive interpolation as described in the first aspect.

[0017] The beneficial effect of the present invention is that, in the embodiment of the present application, a reversible harmonic Catmull-Clark subdivision rule is constructed based on CB splines and progressive interpolation, the reversible harmonic Catmull-Clark subdivision rule is converted into a set of reversible local operators embedded in the wavelet transform, and the forward subdivision and reverse subdivision are converted into wavelet transform based on the reversible local operator, and the transformation of the three-dimensional model is realized by using the decomposition algorithm and reconstruction algorithm of the wavelet transform. The harmonic Catmull-Clark subdivision rule in the present application has the characteristics of both CB splines and progressive interpolation, which can not only represent regular surfaces such as spheres and ellipsoids with high precision, but also retain the shape characteristics of 3D geometric bodies, and has good data compression performance, which improves the accuracy and stability of the three-dimensional model in the medical image processing process. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Attached Figure 1 A flowchart of a subdivision wavelet method combining CB spline and progressive interpolation provided by an embodiment of the present invention; Attached Figure 2 A schematic diagram of the basic Catmull-Clark subdivision format; Attached Figure 3 A schematic diagram of a subdivision wavelet device combining CB spline and progressive interpolation provided in an embodiment of the present invention; Attached Figure 4 A schematic diagram of the structure of an electronic device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0019] In the embodiments of the present application, the term "and / or" describes the association relationship of associated objects, indicating that three relationships may exist. For example, A and / or B may represent: A exists alone, A and B exist at the same time, and B exists alone. The character " / " generally indicates that the objects associated before and after are in an "or" relationship. In the embodiments of the present application, the term "multiple" refers to two or more, and other quantifiers are similar. The terms "first", "second", etc. in the specification and claims of the present application are used to distinguish similar objects, and are not used to describe a specific order or sequence. It should be understood that the terms used in this way can be interchangeable under appropriate circumstances, so that the embodiments of the present application can be implemented in an order other than those illustrated or described here, and the objects distinguished by "first" and "second" are generally of the same type, and the number of objects is not limited. For example, the first object can be one or more.

[0020] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0021] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art to which this application belongs. The terms used herein are only for the purpose of describing the embodiments of this application and are not intended to limit this application.

[0022] The embodiments of the present application provide a subdivision wavelet method and device combining CB spline and progressive interpolation, aiming to improve the accuracy and stability of three-dimensional models in the process of medical image processing.

[0023] See also Figure 1 , Figure 1 The present invention provides a flow chart of a subdivision wavelet method combining CB spline and progressive interpolation, wherein the method specifically comprises the following steps: Step 101, obtaining an initial three-dimensional model, wherein the initial three-dimensional model is a 3D mesh including face points, edge points and vertices, and is used to present the three-dimensional shape, spatial structure and surface details of an object.

[0024] Step 102, constructing a reversible harmonic Catmull-Clark subdivision rule based on CB spline and progressive interpolation, wherein the harmonic Catmull-Clark subdivision rule can be applied to forward subdivision and reverse subdivision, and the harmonic Catmull-Clark subdivision rule includes the subdivision rule of the surface points, the subdivision rule of the edge points and the subdivision rule of the vertices.

[0025] Step 103: convert the harmonic Catmull-Clark subdivision rule into a set of reversible local operators.

[0026] Step 104: based on the reversible local operator, convert the forward subdivision and the reverse subdivision into wavelet transform, and use the decomposition algorithm and reconstruction algorithm of wavelet transform to realize the transformation of the initial three-dimensional model.

[0027] In this embodiment, the initial three-dimensional model is usually a 3D mesh formed by mosaicking or splicing basic units such as triangular facets or quadrilateral facets, which contains a large number of points, lines, and faces, and can accurately present the three-dimensional shape, spatial structure, and surface details of the object. It is commonly used in 3D reconstruction of medical images, digital geometric modeling transformation, 3D printing of digital models, and game development, animation production, etc. Preferably, the initial three-dimensional model in this embodiment is a three-dimensional model obtained by three-dimensional reconstruction based on medical images, and is applied in the medical field.

[0028] Exemplarily, in some embodiments, the initial three-dimensional model in step 101 can be obtained based on the 3D model of bone joints in medical images. In some embodiments, after obtaining the three-dimensional model in the medical field, the model can be preprocessed so that the model format is suitable for multi-resolution transformation, and then multi-resolution transformation is performed. The specific process is not repeated here.

[0029] In the embodiment of the present application, a reversible harmonic Catmull-Clark subdivision rule is constructed based on CB splines and progressive interpolation, and the reversible harmonic Catmull-Clark subdivision rule is converted into a set of reversible local operators embedded in the wavelet transform. Based on the reversible local operators, the forward subdivision and the reverse subdivision are converted into the wavelet transform, and the decomposition algorithm and reconstruction algorithm of the wavelet transform are used to realize the transformation of the three-dimensional model. The harmonic Catmull-Clark subdivision rule in the present application has the characteristics of both CB splines and progressive interpolation, which can not only represent regular surfaces such as spheres and ellipsoids with high precision, but also retain the shape characteristics of 3D geometric bodies, and has good data compression performance, which improves the accuracy and stability of the three-dimensional model in the process of medical image processing.

[0030] The following is an introduction to the construction process of reconciling the Catmull-Clark segmentation rules. Optionally, in some embodiments, step 102 includes: Determine the basic Catmull-Clark segmentation rule; The basic Catmull-Clark subdivision rule is updated according to the principle of progressive difference to obtain a Catmull-Clark subdivision rule based on progressive interpolation and CB spline; Introducing a harmonic parameter into the Catmull-Clark subdivision rule based on progressive interpolation and CB splines , and obtain the harmonic Catmull-Clark subdivision rule.

[0031] First, the basic Catmull-Clark subdivision rule is introduced. In the subdivision process, at each subdivision step, each face and each edge of the mesh in the three-dimensional curve model generates a new face point and a new edge point, and at the same time, each vertex point will also be updated. Figure 2 As shown in the figure, after a Catmull-Clark subdivision, each face of the mesh is a quadrilateral. is a vertex with valence n, There are 2n surrounds The vertex.

[0032] The basic Catmull-Clark subdivision rules include the subdivision rules for face points, edge points, and vertices, as follows: Basic Catmull-Clark segmentation rule The segmentation rule for the following points: (1); Basic Catmull-Clark subdivision rule Subdivision rules for the following points: (2); (3); Vertex subdivision rules under the basic Catmull-Clark subdivision rule: (4).

[0033] is the preset parameter, To control the parameter angle. According to the principle of gradual difference, the above basic Catmull-Clark subdivision rule is updated to obtain the Catmull-Clark subdivision rule based on gradual interpolation and CB spline (referred to as CBSW1). The specific process is as follows: According to the principle of gradual interpolation, the limit vertex can be obtained as: (5); Substituting the above formulas (1) and (2) into the above formula (5), we can get: (6); Introducing variables a(n), b(n), c(n), then: (7); Obviously, a(n), b(n), c(n) are all ≥ 0 and a(n)+nb(n)+nc(n)=1.

[0034] Will get Assign to , we can get the Catmull-Clark subdivision rule based on progressive interpolation and CB spline (CBSW1 for short). Similarly, CBSW1 also includes the subdivision rules of face points, edge points and vertices, as follows: (8); To export the CBSW1 reversible subdivision format, Transformed into an equivalent form, we get: (9); According to the principle of progressive interpolation, progressive interpolation can make the subdivision result of 3D geometric bodies better maintain the shape characteristics of the initial model, and Catmull-Clark subdivision based on CB splines can perform high-precision geometric modeling on quadratic curve surfaces such as circles and spheres. In the embodiment of the present application, the Catmull-Clark subdivision rule based on progressive interpolation and CB splines has the characteristics of both progressive interpolation and CB splines, and can obtain better subdivision effects in maintaining the stability and smoothness of the 3D model.

[0035] Furthermore, a harmonic parameter is introduced into the Catmull-Clark subdivision rule based on progressive interpolation and CB spline. , we can get the Harmonic Catmull-Clark Segmentation Rule (HBSW for short): (10); (11); Likewise, , , are both greater than or equal to 0, and +n +n = 1. To export the HBSW reversible subdivision format, Transformed into an equivalent form, we get: (12).

[0036] Analyzing the above formula, we can see that in the harmonic parameter When the value of is different, the specific expression method of HBSW is also different. Optionally, in some embodiments, the harmonization parameter The value range is [-1, 1]. In practical applications, HBSW can be used to perform surface subdivision, step-by-step decomposition and other multi-resolution transformations and data compression on 3D models. In specific implementation, appropriate harmonic parameter values ​​can be selected according to the specific structure of the 3D model to obtain the best subdivision rule.

[0037] Optionally, in some embodiments, the blending parameter The value of is related to the shape of the initial three-dimensional model. By controlling the parameter angle value, you can easily adjust the shape of the HBSW subdivision geometry to better suit your specific application needs.

[0038] According to the multi-resolution decomposition and reconstruction theory, a high-resolution subdivision surface model is defined as (where M is the control mesh and V is the control vertex set), which can be decomposed into a low-resolution subdivision surface model by wavelet and some wavelet coefficients , which can be expressed as: (13).

[0039] Wavelet reconstruction is the inverse process of wavelet decomposition. A high-resolution model can be reconstructed from a low-resolution model and wavelet coefficients, as shown below: (14).

[0040] Among them, A and B are called decomposition filters, and P and Q are called reconstruction filters.

[0041] In an embodiment of the present application, the harmonic Catmull-Clark subdivision rule is first converted into a set of simple, reversible local operators, and then the forward subdivision and reverse subdivision are converted into wavelet calculations using the lifting technique, thereby achieving multi-resolution transformation of the subdivided three-dimensional model based on the decomposition algorithm and reconstruction algorithm of the wavelet transform.

[0042] It should be understood that since the Catmull-Clark subdivision rule contains preset parameters , so you need to specify Value, and then the orthogonalization coefficient of the corresponding surface point wavelet can be calculated and , and the orthogonalization coefficients of the edge point wavelet and .

[0043] Optionally, in some embodiments, before step 104, the method further includes: Specify the preset parameters The value of Based on the preset parameters The value of is used to calculate the orthogonalization coefficient of the corresponding surface point wavelet and the orthogonalization coefficient of the corresponding edge point wavelet. The orthogonalization coefficient of the surface point wavelet and the orthogonalization coefficient of the edge point wavelet are used to construct the decomposition algorithm and the reconstruction algorithm.

[0044] As a specific embodiment, the specific conditions of the orthogonalization coefficients of the surface point wavelet and the orthogonalization coefficients of the edge point wavelet under different conditions are given below (u is a free parameter used to fine-tune the coordinate values ​​of the surface points in the 3D Mesh).

[0045] Table 1 = 1 when the pre-calculated orthogonalization coefficients of the surface wavelet are =45 degrees, u=1) Table 2 =1, the pre-calculated orthogonalization coefficients of the edge point wavelet Table 3 = -1 when the pre-calculated orthogonalization coefficients of the surface wavelet ( =45 degrees, u=1) Table 4 =-1 when the pre-calculated orthogonalization coefficients of the edge point wavelet

[0046] As a specific embodiment, for geometric modeling requirements such as smooth surfaces and sharp features, the lifting technology and the orthogonalization coefficients of the above-mentioned surface point wavelet and edge point wavelet can be used to construct a wavelet reconstruction algorithm as follows: Step 1: ; Step 2: ; (smooth edge) ; (sharp edge) Step 3: ; Step 4: ; Step 5: ; Step 6: ; Step 7: ; (smooth edge) ; (sharp edge) ;(corner point) Step 8: .

[0047] Among them, operation It is expressed as the arithmetic average of the x-type vertices that are immediately adjacent to vertex y. represents the weighted average of the wavelet coefficients of the two vertices of a sharp edge, Represents the average value of two sharp edge points adjacent to a vertex.

[0048] After reverse sorting, the wavelet decomposition algorithm is as follows: Step 1: ; Step 2: ; (smooth edge) ; (sharp edge) ;(corner point) Step 3: ; Step 4: ; Step 5: ; Step 6: ; Step 7: ; (smooth edge) ; (sharp edge) Step 8: .

[0049] According to the above content, the wavelet decomposition algorithm and wavelet reconstruction algorithm provided in the embodiment of the present application have the following characteristics: When dealing with irregular free-form surfaces, both the wavelet decomposition algorithm and the wavelet reconstruction algorithm will be used. = 1, and when dealing with quadratic surfaces such as spheres and ellipsoids, both the wavelet decomposition algorithm and the wavelet reconstruction algorithm will use =-1, so that high-precision multi-scale geometric transformation can be performed on complex 3D models that contain both irregular free-form surfaces and quadratic surfaces such as spheres and ellipsoids.

[0050] The method provided in the embodiment of the present application can further improve the processing of the geometric features of the three-dimensional model by distinguishing smooth edges / sharp edges, normal points / corner points, etc. in the 3D Mesh, so that the processed 3D Mesh can well maintain the model geometric features and improve the shape stability of the low-resolution model.

[0051] Through experimental tests and verification, it can be seen that in terms of high-precision transformation of 3D surfaces such as spheres and ellipsoids, 3D data compression performance, low-resolution model stability, sharp geometric feature representation, and real-time wavelet transformation, the subdivision wavelet method combined with CB splines and progressive interpolation provided in this application has better performance than the subdivision wavelet method in the prior art.

[0052] See also Figure 3 The embodiment of the present invention provides a subdivision wavelet device 300 combining CB spline and progressive interpolation, comprising: An acquisition module 301 is used to acquire an initial three-dimensional model, where the initial three-dimensional model is a 3D mesh including surface points, edge points and vertices, and is used to present the three-dimensional shape, spatial structure and surface details of an object; A construction module 302 is used to construct a reversible harmonic Catmull-Clark subdivision rule based on CB splines and progressive interpolation, wherein the harmonic Catmull-Clark subdivision rule can be applied to forward subdivision and reverse subdivision, and the harmonic Catmull-Clark subdivision rule includes the subdivision rule of the face points, the subdivision rule of the edge points, and the subdivision rule of the vertices; A conversion module 303, used to convert the harmonic Catmull-Clark subdivision rule into a set of reversible local operators; The transformation module 304 is used to convert the forward subdivision and the reverse subdivision into wavelet transformation based on the reversible local operator, and realize the transformation of the initial three-dimensional model by using the decomposition algorithm and reconstruction algorithm of the wavelet transformation.

[0053] Optionally, the construction module 302 includes: Determine the unit, used to determine the basic Catmull-Clark subdivision rule; An updating unit, used for updating the basic Catmull-Clark subdivision rule according to the principle of progressive difference to obtain a Catmull-Clark subdivision rule based on progressive interpolation and CB spline; A harmonic unit for introducing harmonic parameters into the Catmull-Clark subdivision rule based on progressive interpolation and CB splines , and obtain the harmonic Catmull-Clark subdivision rule.

[0054] Optionally, the Catmull-Clark subdivision rule based on progressive interpolation and CB spline is: ; ; ; in, , , , Respectively represent the surface The four surrounding vertices, and For the edge point The points of two adjacent faces, is the noodle with serial number i, For the noodle point with serial number (i-2+n)%n, is the edge point with serial number i, is a vertex with serial number 0, a(n), b(n), c(n) are all greater than or equal to 0, and a(n)+nb(n)+nc(n)=1, is a vertex with valence n, There are 2n surrounds The vertex of is the preset parameter, To control the parameter angle, i is the serial number of the vertex, edge point and surface point, i and n are both positive integers, i%n represents the remainder after the integer i is divided by n, (i-2+n)%n represents the remainder after (i-2+n) is divided by n; The Catmull-Clark subdivision rule based on progressive interpolation and CB spline The equivalent form is: .

[0055] Optionally, the harmonized Catmull-Clark subdivision rule is: ; ; ; in, , , , Respectively represent the surface The four surrounding vertices, and For the edge point The points of two adjacent faces, is the noodle with serial number i, For the noodle point with serial number (i-2+n)%n, is the edge point with serial number i, is the vertex with sequence number 0, , , are both greater than or equal to 0, and +n +n =1, is a vertex with valence n, There are 2n surrounds The vertex of is the preset parameter, To control the parameter angle, is the harmonic parameter, i is the serial number of the vertex, edge point and surface point, i and n are both positive integers, i%n represents the remainder after the integer i is divided by n, (i-2+n)%n represents the remainder after (i-2+n) is divided by n; The harmonic Catmull-Clark subdivision rule The equivalent form is: .

[0056] Optionally, the blending parameter The value range is [-1, 1].

[0057] Optionally, the blending parameter The value of is related to the shape of the initial three-dimensional model.

[0058] Optionally, the subdivided wavelet device 300 combining CB spline and progressive interpolation further includes: A specified module is used to specify the preset parameters The value of A calculation module is used to calculate the The value of is used to calculate the orthogonalization coefficient of the corresponding surface point wavelet and the orthogonalization coefficient of the corresponding edge point wavelet. The orthogonalization coefficient of the surface point wavelet and the orthogonalization coefficient of the edge point wavelet are used to construct the decomposition algorithm and the reconstruction algorithm.

[0059] The subdivision wavelet device 300 combining CB spline and progressive interpolation provided in the embodiment of the present application can execute the above method embodiment, and its implementation principle and technical effect are similar, which will not be repeated in this embodiment.

[0060] It should be noted that the division of units in the embodiments of the present application is schematic and is only a logical function division. There may be other division methods in actual implementation. In addition, each functional unit in each embodiment of the present application may be integrated into a processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware or in the form of software functional units.

[0061] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a processor-readable storage medium. Based on this understanding, the technical solution of the present application is essentially or the part that contributes to the prior art or all or part of the technical solution can be embodied in the form of a software product. The computer software product is stored in a storage medium, including several instructions to enable a computer device (which can be a personal computer, server, or network device, etc.) or a processor (processor) to execute all or part of the steps of the method described in each embodiment of the present application. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (Read-Only Memory, ROM), random access memory (Random Access Memory, RAM), disk or optical disk and other media that can store program codes.

[0062] like Figure 4 As shown, an embodiment of the present application provides an electronic device 400, including: a memory 402, a processor 401, and a program stored in the memory 402 and executable on the processor 401; the processor 401 is used to read the program in the memory 402 to implement the steps in the subdivision wavelet method combining CB splines and progressive interpolation as described above.

[0063] The embodiment of the present application also provides a readable storage medium, on which a program is stored. When the program is executed by a processor, each process of the above-mentioned subdivision wavelet method embodiment combining CB spline and progressive interpolation is implemented, and the same technical effect can be achieved. To avoid repetition, it will not be repeated here. Among them, the readable storage medium can be any available medium or data storage device that can be accessed by the processor, including but not limited to magnetic storage (such as floppy disk, hard disk, magnetic tape, magneto-optical disk (MO), etc.), optical storage (such as compact disk (CD), digital video disc (DVD), Blu-ray Disc (BD), high-definition versatile disc (HVD), etc.), and semiconductor storage (such as read-only memory (ROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read only memory (EEPROM), non-volatile memory (NAND FLASH), solid-state drive (Solid State Disk or Solid State Drive, SSD)), etc.

[0064] It should be noted that, in this article, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, an element defined by the sentence "comprises a ..." does not exclude the existence of other identical elements in the process, method, article or device including the element.

[0065] Through the description of the above implementation methods, those skilled in the art can clearly understand that the above-mentioned embodiment methods can be implemented by means of software plus a necessary general hardware platform, and of course by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art, can be embodied in the form of a software product, which is stored in a storage medium (such as ROM / RAM, disk, CD), and includes a number of instructions for a terminal (which can be a mobile phone, computer, server, air conditioner, or network equipment, etc.) to execute the methods described in each embodiment of the present application.

[0066] The embodiments of the present application are described above in conjunction with the accompanying drawings, but the present application is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the guidance of the present application, ordinary technicians in this field can also make many forms without departing from the purpose of the present application and the scope of protection of the claims, all of which are within the protection of the present application.

Claims

1. A subdivision wavelet method combining CB spline and progressive interpolation, characterized in that: include: Acquire an initial three-dimensional model, wherein the initial three-dimensional model is a 3D mesh including face points, edge points and vertices, and is used to present the three-dimensional shape, spatial structure and surface details of the object; Based on CB spline and progressive interpolation, a reversible harmonic Catmull-Clark subdivision rule is constructed, wherein the harmonic Catmull-Clark subdivision rule can be applied to forward subdivision and reverse subdivision, and the harmonic Catmull-Clark subdivision rule includes the subdivision rule of the face point, the subdivision rule of the edge point and the subdivision rule of the vertex; converting the harmonic Catmull-Clark subdivision rule into a set of reversible local operators; Based on the reversible local operator, the forward subdivision and the reverse subdivision are converted into wavelet transform, and the decomposition algorithm and reconstruction algorithm of wavelet transform are used to realize the transformation of the initial three-dimensional model.

2. The method according to claim 1, characterized in that: The reversible harmonic Catmull-Clark subdivision rule based on CB spline and progressive interpolation is constructed, including: Determine the basic Catmull-Clark segmentation rule; The basic Catmull-Clark subdivision rule is updated according to the principle of progressive difference to obtain a Catmull-Clark subdivision rule based on progressive interpolation and CB spline; Introducing a harmonic parameter into the Catmull-Clark subdivision rule based on progressive interpolation and CB splines , and obtain the harmonic Catmull-Clark subdivision rule.

3. The method according to claim 2, characterized in that: The Catmull-Clark subdivision rule based on progressive interpolation and CB spline is: ； ； ； in, , , , Respectively represent the surface The four vertices around and For the edge point The points of two adjacent faces, is the noodle with serial number i, For the noodle point with serial number (i-2+n)%n, is the edge point with serial number i, is a vertex with serial number 0, a(n), b(n), c(n) are all greater than or equal to 0, and a(n)+nb(n)+nc(n)=1, is a vertex with valence n, There are 2n surrounds The vertex of is the preset parameter, To control the parameter angle, i is the serial number of the vertex, edge point and surface point, i and n are both positive integers, i%n represents the remainder after the integer i is divided by n, (i-2+n)%n represents the remainder after (i-2+n) is divided by n; The Catmull-Clark subdivision rule based on progressive interpolation and CB spline The equivalent form is: 。 4. The method according to claim 2, characterized in that: The harmonic Catmull-Clark segmentation rule is: ； ； ； in, , , , Respectively represent the surface The four vertices around and For the edge point The points of two adjacent faces, is the noodle with serial number i, For the noodle point with serial number (i-2+n)%n, is the edge point with serial number i, is the vertex with sequence number 0, , , are both greater than or equal to 0, and +n +n =1, is a vertex with valence n, There are 2n surrounds The vertex of is the preset parameter, To control the parameter angle, is the harmonic parameter, i is the serial number of the vertex, edge point and surface point, i and n are both positive integers, i%n represents the remainder after the integer i is divided by n, (i-2+n)%n represents the remainder after (i-2+n) is divided by n; The harmonic Catmull-Clark subdivision rule The equivalent form is: 。 5. The method according to any one of claims 2 to 4, characterized in that: The value range of the harmonization parameter is [-1, 1].

6. The method according to claim 5, characterized in that: The value of the blending parameter is related to the shape of the initial three-dimensional model.

7. The method according to claim 3 or 4, characterized in that: Before converting the forward subdivision and the reverse subdivision into wavelet transform based on the reversible local operator and realizing the transformation of the initial three-dimensional model by using the decomposition algorithm and reconstruction algorithm of the wavelet transform, the method further comprises: Specify the preset parameters The value of Based on the preset parameters The value of is used to calculate the orthogonalization coefficient of the corresponding surface point wavelet and the orthogonalization coefficient of the corresponding edge point wavelet. The orthogonalization coefficient of the surface point wavelet and the orthogonalization coefficient of the edge point wavelet are used to construct the decomposition algorithm and the reconstruction algorithm.

8. A subdivision wavelet device combining CB spline and progressive interpolation, characterized in that: include: An acquisition module is used to acquire an initial three-dimensional model, wherein the initial three-dimensional model is a 3D mesh including surface points, edge points and vertices, and is used to present the three-dimensional shape, spatial structure and surface details of the object; A construction module, used for constructing a reversible harmonic Catmull-Clark subdivision rule based on CB spline and progressive interpolation, wherein the harmonic Catmull-Clark subdivision rule can be applied to forward subdivision and reverse subdivision, and the harmonic Catmull-Clark subdivision rule includes the subdivision rule of the face point, the subdivision rule of the edge point and the subdivision rule of the vertex; A conversion module, for converting the harmonic Catmull-Clark subdivision rule into a set of reversible local operators; The transformation module is used to convert the forward subdivision and the reverse subdivision into wavelet transformation based on the reversible local operator, and realize the transformation of the initial three-dimensional model by using the decomposition algorithm and reconstruction algorithm of the wavelet transformation.

9. An electronic device, comprising: A memory, a processor and a program stored in the memory and executable on the processor; wherein the processor is used to read the program in the memory to implement the steps in the subdivision wavelet method combining CB spline and progressive interpolation as described in any one of claims 1 to 7.

10. A readable storage medium for storing a program, characterized in that: When the program is executed by a processor, the steps in the subdivision wavelet method combining CB spline and progressive interpolation are implemented as claimed in any one of claims 1 to 7.

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