CN110223392B - Region selection method easy to interact - Google Patents
Region selection method easy to interact Download PDFInfo
- Publication number
- CN110223392B CN110223392B CN201910345442.2A CN201910345442A CN110223392B CN 110223392 B CN110223392 B CN 110223392B CN 201910345442 A CN201910345442 A CN 201910345442A CN 110223392 B CN110223392 B CN 110223392B
- Authority
- CN
- China
- Prior art keywords
- grid
- thermonuclear
- vertex
- model
- boundary
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T15/00—3D [Three Dimensional] image rendering
- G06T15/10—Geometric effects
-
- 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
- G06T17/30—Polynomial surface description
Landscapes
- Physics & Mathematics (AREA)
- Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Geometry (AREA)
- Computer Graphics (AREA)
- Mathematical Analysis (AREA)
- Pure & Applied Mathematics (AREA)
- Mathematical Physics (AREA)
- Mathematical Optimization (AREA)
- Software Systems (AREA)
- Algebra (AREA)
- Image Analysis (AREA)
Abstract
The invention discloses an area selection method easy to interact, which comprises the following steps: constructing a feature vector of grid vertexes of the three-dimensional grid model surface; establishing a characteristic measurement distance equation between corresponding grid vertexes; performing region selection on the surface of the three-dimensional grid model according to the characteristic tolerance value specified by user interaction to form an initialization region selection boundary segmentation ring formed by the edge sequences; and carrying out optical smoothing on the initial region selection boundary segmentation ring by a geometric optimization method to obtain a final region boundary ring. The method provided by the invention allows the user to input the characteristic tolerance value for region selection, improves the degree of freedom of user interaction, can dynamically realize model surface region selection, effectively improves the region selection efficiency and the practicability, and has higher accuracy without being interfered by noise.
Description
Technical Field
The invention relates to the technical field of data acquisition and reconstruction, in particular to an easy-to-interact region selection method
Background
Three-dimensional model segmentation is one of the hot research subjects in computer graphics and computer aided design, and has gained more attention in research, and analysis and research methods of three-dimensional grid models have established a very reliable mathematical basis in graphics and geometric modeling. Compared with the characteristics such as color, texture and the like, the shape characteristics describe the shape information of an object from the geometric perspective, and are widely applied to fields such as target recognition, character recognition, robot navigation and the like, the segmentation method of the interactive three-dimensional model can be mainly divided into two types of boundary-based methods and area-based methods, wherein the boundary-based methods require a user to specify points or strokes on the boundary required to be segmented, and the area-based methods allow the user to freely draw strokes in foreground and background areas to mark the areas required to be segmented.
The method is mainly used for grid segmentation, the type of the common method is boundary-based region selection, a user is required to input some prompt information near the edge of a region to be selected or segmented, a part of scholars put forward the method of region selection or segmentation by forming a boundary by a user specified point sequence, the boundary is formed by the connection point sequence, a part of scholars apply an improved Dijkstra algorithm to search for segmented boundary contours, a graph cutting algorithm is also an effective method for calculating the boundary contours of the region, a part of scholars form a shortest closed path through calculating geodesic lines on a grid to segment the boundary of the region, and in the research of geodesic lines or geodesic rings, xin and the like sequentially put forward two methods for calculating geodesic rings, but the method is difficult to apply to real-time interaction because the calculation cost is too high. Boundary-based methods often require the user to pay attention to the direction of the stroke, and often require multiple strokes to obtain the desired result; the region-based method can be divided into a region growing algorithm, a random walk algorithm, a graph dividing method and a hierarchical clustering method from the aspect of a calculation method, and the dividing boundary or region information input by a user lacks accuracy, so that the obtained final dividing ring cannot meet the requirements of the user. Meng Min proposes a mesh model slicing algorithm based on the harmonic field and graph cut technique on the mesh and is applicable to mesh models with single or complex features. Further, some scholars propose a method for implementing grid segmentation by inducing optimal contours with a user input trajectory as a scalar field, allowing a user to specify a region of interest on a grid by way of a scribe line. The interactive process performed by the region-based method is static and does not meet the user's expectations of dynamically changing the selected region through interaction.
In fact, typically, by a user specifying a boundary or region on the mesh surface for model segmentation, the resulting segmented region is either not smooth enough in boundary or requires the user to specify more refinement operations to complete the interaction based on the hints. It is therefore particularly necessary to propose a region selection method which is easy to interact with the user.
Disclosure of Invention
The invention aims at overcoming the defects of the prior art, and provides an easy-to-interact region selection method which is based on different regions of a three-dimensional grid model and is convenient for a user to carry out tolerance interaction selection, so that the region selection of the surface of the model can be dynamically realized, and the efficiency and the practicability of the region selection are greatly improved.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
an easy-to-interact region selection method, comprising the steps of:
constructing a feature vector of grid vertexes of the three-dimensional grid model surface;
establishing a characteristic measurement distance equation between corresponding grid vertexes;
performing region selection on the surface of the three-dimensional grid model according to the characteristic tolerance value specified by user interaction to form an initialization region selection boundary segmentation ring formed by the edge sequences;
and carrying out optical smoothing on the initial region selection boundary segmentation ring by a geometric optimization method to obtain a final region boundary ring.
Preferably, the feature vectors of the mesh vertices constructing the three-dimensional mesh model surface are specifically:
and constructing the feature vector of the grid vertex of the three-dimensional model surface by utilizing the thermonuclear feature and the average curvature of the three-dimensional grid model.
Preferably, the method further comprises the steps of:
combining the thermonuclear features and the average curvature of the three-dimensional mesh model into a new feature vector f (x) = (α·p) x ,β·K x ),P x Is the thermonuclear eigenvector at vertex x, K x The average curvature at the vertex x is shown, and alpha and beta are constant coefficients;
and calculating the similarity between the vertexes by combining the thermonuclear characteristics and the average curvature of the three-dimensional grid model.
Preferably, the method further comprises the steps of:
preprocessing and extracting thermonuclear characteristics of the three-dimensional grid model: extracting thermonuclear feature vectors of grid vertices according to Riemann popularity and thermonuclear feature theory, wherein the thermal diffusion method on Riemann manifold comprises the following steps:
wherein delta is M The Laplace-Beltrami operator on the manifold is represented, the function u (x, t) represents the heat condition of the vertex x on the three-dimensional model at the moment t, and the solution of the equation is a thermonuclear;
limiting thermonuclear to the time domain according to the thermonuclear feature theory HKS for
The thermonuclear descriptors of the three-dimensional model are a list of vectors:
P X ＝(p 1 (x),p 2 (x),…,p n (x)) T (2)
wherein the component p i (x) For different times t i The lower part of the HKS,
wherein lambda is k 、
Is the kth eigenvalue and eigenvector of Laplace-Beltrami operator;
preprocessing to calculate the average curvature of the three-dimensional grid model: the curvature value of smooth change is calculated by adopting a least square method, and the calculation formula is as follows:
wherein L (·) represents the discrete Laplace operator, k i ' and k i The method respectively represents the current curvature and the updated curvature, wherein the first term ensures that the curvature value of the adjacent point changes smoothly, and the second term requires that the curvature value of each vertex after updating is close to the current value. In the first iteration, the Laplacian values of the points are set to the average curvature of the points on the boundary curve.
Preferably, the establishing a characteristic metric distance equation between the corresponding grid vertices is specifically:
calculating the characteristic measurement distance between grid vertexes by using a Euclidean distance formula, wherein the formula specifically comprises the following steps:
dp(x,y)＝||f(x)-f(y)|| 2 (5)
wherein f (X) and f (Y) are feature vectors of two vertexes X, Y on the model respectively.
Preferably, the method further comprises the steps of:
the characteristic tolerance value appointed by the user is obtained, the characteristic tolerance between grid vertexes is calculated, and the calculation formula is as follows:
d(x 0 ,x i )＝||f(x 0 )-f(x i )|| 2 <Tε (6)
wherein x is 0 Grid vertex selected by user interaction as source point, x i Grid vertices, f (x) 0 ) And f (x) i ) Respectively the source points x 0 And vertex x i T is a tolerance value specified by the user and is an integer, epsilon is a constant value.
And selecting the grid vertexes which are obtained through calculation and accord with a preset tolerance range between the source point characteristics as the boundary vertexes of the initialization area.
Preferably, the optical smoothing of the initial region selection boundary segmentation ring by a geometric optimization method specifically comprises the following steps:
taking a path formed by edge sequences in the boundary of the initialization area as an initial path;
taking the length of the geodesic distance as an objective function;
and carrying out iterative computation through a geometric optimization method to obtain a final region boundary ring.
Preferably, the method further comprises the steps of:
setting a density value ρ (x i ) =a, a is constant in order to optimize the objective function for localization:
the partial derivative equation of equation (7) is:
wherein p is i Is on the path and the ith edge
Crossing of (1) at the same time->
By scalar coefficient lambda i And edge vertex->
Establishing corresponding relation, and marking the T-shaped face sequence of the partition ring as (s, p) 1 ,p 2 ,…,p k S), s is a fixed vertex in the partition ring Γ.
Preferably, the method further comprises the steps of:
acquiring parameters such as a triangular mesh curved surface S, an initial path Γ, a fixed point S epsilon S of the initial path Γ, a fault tolerance value epsilon and the like of the three-dimensional mesh model;
traversing all vertices v of initial path Γ i Lowering the apex v i The edges e included in the left/right peripheral angles are added to the initial path ring in sequence;
randomly assigning lambda to each edge e i Obtaining
Using equation (7) and equation(8) Performing continuous iterative calculation to respectively calculate the value and gradient of the objective function L
Updating and obtaining a new path, traversing all vertexes v of the new path i When lambda is i =1 or λ i When=0, p is used i The triangular faces that are not in the face sequence on one side replace triangular faces that are already in the face sequence.
Compared with the prior art, the method provided by the invention allows the user to input the characteristic tolerance value for region selection, improves the degree of freedom of user interaction, can dynamically realize model surface region selection, effectively improves the region selection efficiency and the practicability, is not interfered by noise, and has obvious application effects on a plurality of application effects including model segmentation due to the interaction generation of region boundaries.
Drawings
FIG. 1 is a flow chart of an area selection method for easy interaction according to the first embodiment;
FIG. 2 is a flow chart of edge sequence update according to the present invention;
FIG. 3 is a calculated initial region boundary loop of the present invention.
FIG. 4 is a flow chart of the process from initial grid state to final formation for region selection in accordance with the present invention;
FIG. 5 is a graph showing the variation of tolerance values according to the present invention;
FIG. 6 is a graph showing a comparison of the effect of selecting a region profile according to the present invention;
fig. 7 is a graph comparing noise robustness against noise in accordance with the present invention.
Detailed Description
The following are specific embodiments of the present invention and the technical solutions of the present invention will be further described with reference to the accompanying drawings, but the present invention is not limited to these embodiments.
Example 1
The embodiment provides an easy-to-interact area selection method, as shown in fig. 1, including the steps of:
s100, constructing a feature vector of a grid vertex of the three-dimensional grid model surface;
s200, establishing a characteristic measurement distance equation between corresponding grid vertexes;
s300, performing region selection on the surface of the three-dimensional grid model according to the characteristic tolerance value specified by user interaction to form an initialization region selection boundary segmentation ring formed by an edge sequence;
s400, carrying out optical smoothing on the initial region selection boundary segmentation ring by a geometric optimization method to obtain a final region boundary ring.
Considering that different areas of the three-dimensional model have different features and are convenient for a user to perform tolerance interaction selection, in this embodiment, similarity between grid vertices is conveniently calculated by constructing feature vectors between grid vertices of the model surface in step S100, and preferably, the feature vectors of the grid vertices constructing the three-dimensional grid model surface are specifically:
and constructing the feature vector of the grid vertex of the three-dimensional model surface by utilizing the thermonuclear feature and the average curvature of the three-dimensional grid model.
The relationship between grid vertices can be well reflected through thermonuclear features (heat kernel signature, HKS) and average curvature on the three-dimensional grid model, and the thermonuclear features of the thermal diffusion of the model surface have equidistant invariance and are local and global properties of the grid vertices, so that the method can be used for interactive selection of region division. The thermonuclear can be regarded as a transition probability of brownian motion in the manifold and also as heat flowing from the heat source to other points during time t. The study of thermonuclear begins with heat conduction and diffusion; the mean curvature (mean curvature) is an "extrinsic" curvature measure in digital geometry that describes locally the degree of concave curvature of the mesh model, and the present embodiment uses the least squares method to calculate smoothly varying curvature removal values. Preferably, the method further comprises the steps of:
preprocessing and extracting thermonuclear characteristics of the three-dimensional grid model: extracting thermonuclear feature vectors of grid vertices according to Riemann popularity and thermonuclear feature theory, wherein the thermal diffusion method on Riemann manifold comprises the following steps:
wherein delta is M The Laplace-Beltrami operator on the manifold is represented, the function u (x, t) represents the heat condition of the vertex x on the three-dimensional model at the moment t, and the solution of the equation is a thermonuclear;
limiting thermonuclear to the time domain according to the thermonuclear feature theory HKS for
The thermonuclear descriptors of the three-dimensional model are a list of vectors:
P X ＝(p 1 (x),p 2 (x),…,p n (x)) T (2)
wherein the component p i (x) For different times t i The lower part of the HKS,
wherein lambda is k 、
Is the kth eigenvalue and eigenvector of Laplace-Beltrami operator;
in this embodiment, 100 time nodes are selected to calculate the thermonuclear value, so that a 100-dimensional thermonuclear feature vector can be obtained on each grid vertex of the three-dimensional grid model.
Preprocessing to calculate the average curvature of the three-dimensional grid model: the curvature value of smooth change is calculated by adopting a least square method, and the calculation formula is as follows:
wherein L (·) represents the discrete Laplace operator, k i ' and k i Respectively representing the current curvature and the updated curvature, wherein the first term ensures the smooth change of the curvature value of the adjacent point, and the second term requires the updated curvature value of each vertexNear the current value. In the first iteration, the Laplacian values of the points are set to the average curvature of the points on the boundary curve.
Preferably, the method further comprises the steps of:
combining the thermonuclear features and the average curvature of the three-dimensional mesh model into a new feature vector f (x) = (α·p) x ,β·K x ),P x Is the thermonuclear eigenvector at vertex x, K x The average curvature at the vertex x is shown, and alpha and beta are constant coefficients;
and calculating the similarity between the vertexes by combining the thermonuclear characteristics and the average curvature of the three-dimensional grid model.
For a manifold polyhedral mesh M, the selection of the areas with magic wand properties is realized on the surface, and the range of the selected areas is mainly adjusted according to the characteristic values among the vertexes of the mesh surface and the tolerance range thereof. The present embodiment considers that the region selection follows a certain adjacency and mesh curvature consistency, calculates the similarity between vertices by combining the mesh surface HKS features and the average curvature, and combines the two features into a new feature vector f (x) = (α·p) x ,β·K x ),P x Is the thermonuclear eigenvector at vertex x, K x For the average curvature at vertex x, α, β are constant coefficients, and this embodiment sets α=0.1, β=10. Thus, similarity measures are performed for vertices on the mesh model.
Step S200 establishes a feature metric distance equation between corresponding grid vertices, preferably, the establishing a feature metric distance equation between corresponding grid vertices is specifically:
calculating the characteristic measurement distance between grid vertexes by using a Euclidean distance formula, wherein the formula specifically comprises the following steps:
dp(x,y)＝||f(x)-f(y)|| 2 (5)
wherein f (X) and f (Y) are feature vectors of two vertexes X, Y on the model respectively.
Step S300, realizing the area selection of the magic stick-like on the surface of the three-dimensional model according to the measurement tolerance value specified by the user interaction, and forming an initialization area selection boundary formed by an edge sequence; preferably, the method further comprises the steps of:
the characteristic tolerance value appointed by the user is obtained, the characteristic tolerance between grid vertexes is calculated, and the calculation formula is as follows:
d(x 0 ,x i )＝||f(x 0 )-f(x i )|| 2 <Tε (6)
wherein x is 0 Grid vertex selected by user interaction as source point, x i Grid vertices, f (x) 0 ) And f (x) i ) Respectively the source points x 0 And vertex x i T is a tolerance value specified by a user and is an integer, epsilon is a constant value, and epsilon is 0.3 in the embodiment.
And selecting the grid vertexes which are obtained through calculation and accord with a preset tolerance range between the source point characteristics as the boundary vertexes of the initialization area.
In this embodiment, a user selects an interaction point as a source point on a mesh surface, and allows the user to set a feature tolerance range, and automatically selects vertices close to the source point according to feature distances between vertices, where equation (6) is a calculation equation of feature tolerance between vertices. Based on the formula (6), the characteristic difference value between the vertexes on the three-dimensional model can be calculated, the selection of the region can be realized according to the user input tolerance value, and the initial selected region boundary ring Γ is obtained.
The process of calculating the boundary ring initial path by the characteristic tolerance mode is specifically as follows: vertex x to be selected by user interaction 0 Is set as a source point, and sequentially points towards x from the near to the far 0 The surrounding expansion judges whether the adjacent point is an alternative vertex, a list is newly established at the beginning of the program and is marked as a ring gamma for storing the edge sequence passed by the boundary ring, and x is firstly calculated 0 Opposite edge e 0 ,e 1 ,...,e k Put the list in reverse (clockwise) and then judge the outgoing edges in turn, we need to add the current edge e to be added i The judgment is carried out according to the following cases:
case 1-current decision Point x i Adjacent to the point x' i Component edge e (x i ,x′ i ) After insertion into the list Γ, the edge adjacent to it in the list Γ is in the same triangle f in the mesh, and then another edge of the triangle f is used instead of e (x) i ,x′ i ) And to the process for preparing the sameAdjacent edges, as shown in fig. 2.
Case 2 if the current decision point x i Is adjacent to point x' i Is the judged vertex, but edge e (x i ,x′ i ) Not yet added to list Γ, then it is necessary to add edge e (x i ,x′ i ) To divide edges, the list Γ is divided into two sub-lists Γ 1 And Γ 2 Then respectively to Γ 1 And Γ 2 The sequential judgment is performed as shown in fig. 3.
The specific calculation steps of the region tolerance calculation based on the characteristic vector are as follows:
input: source point x 0 And tolerance value T
And (3) outputting: initial selection of region boundary ring Γ
Step1. Set x 0 Is identified as True, a set of points S is initialized, and x will be the same as 0 Adjacent point x' 0 Put into the point set S, set x 0 The identification of the adjacent point is True, and all x are calculated 0 The opposite edges e are joined in a counter-clockwise manner to form a ring Γ.
Step2 taking a point x from the set of points S i If x i Is x 'of the adjacent point of (2)' i Is True, then, if e (x i ,x′ i ) If the judgment is not yet made, the cutting ring Γ needs to be pressed by the edge e (x i ,x′ i ) Divided into two rings Γ 1 And Γ 2 (as shown in figure 3).
Step3 if adjacent point x' i Is identified as False, and is associated with source point x 0 Whether the characteristic distance difference therebetween satisfies the formula (5),
if Step3.1 is satisfied, x 'will be' i Put in the set of points S and in the ring Γ at point x i Edge e (x) i ,x′ i ) Where is arranged x' i Is identified as True. In Γ, if e (x i ,x′ i ) If the same triangle surface f is in the left adjacent side, the other side of the triangle surface f is used to replace e (x) i ,x′ i ) And its left adjacent edge (as shown in fig. 2) if e (x i ,x′ i ) If the right adjacent edge is in the same triangle plane f, then the other edge of the triangle plane f is used instead of e (x i ,x′ i ) A kind of electronic device with high-pressure air-conditioning systemAnd its right adjacent side.
If tep 3.2.3.2 is not satisfied, continuing to judge the next x i Is provided.
Step4, if the point set S is not empty, jumping to Step2, and if the point set S is not empty, jumping to Step4.
Step5. return to the original region boundary ring Γ.
The area boundary ring calculated according to the interaction tolerance algorithm is divided into three-dimensional grid planes along the edges on the molding surface, the obtained division boundary has poor smoothness, and the smooth and flat area boundary ring is gradually valued by researchers and users, in this embodiment, the initial area selection boundary dividing ring is optically smoothed by using a geometric optimization method in step 400 to obtain the final smoother area boundary ring, and preferably, the optical smoothing of the initial area selection boundary dividing ring by using the geometric optimization method is specifically as follows:
taking a path formed by edge sequences in the boundary of the initialization area as an initial path;
taking the length of the geodesic distance as an objective function;
and carrying out iterative computation through a geometric optimization method to obtain a final region boundary ring.
The method for calculating the geodesic line and the geodesic ring by adopting the optimization method mainly comprises the steps of 2 steps, wherein an initial path is given in the first step, and the path formed by the edge sequences in the split ring Γ is used as the initial path in the embodiment; and secondly, taking the length of the geodesic distance as an objective function, and performing iterative calculation in a geometric optimization mode to obtain a final result. In order to make the trend of the area profile point to the outside of the selected area as much as possible in the optimization process, the method preferably further comprises the steps of:
setting a density value ρ (x i ) =a, a is constant in order to optimize the objective function for localization:
the partial derivative equation of equation (7) is:
wherein p is i Is on the path and the ith edge
Crossing of (1) at the same time->
By scalar coefficient lambda i And edge vertex->
Establishing corresponding relation, and marking the T-shaped face sequence of the partition ring as (s, p) 1 ,p 2 ,…,p k S), s is a fixed vertex in the split ring Γ, and may be selected between the split ring Γ and the source point x 0 Is the one most distant from the feature.
Preferably, the method further comprises the steps of:
acquiring parameters such as a triangular mesh curved surface S, an initial path Γ, a fixed point S epsilon S of the initial path Γ, a fault tolerance value epsilon and the like of the three-dimensional mesh model;
traversing all vertices v of initial path Γ i Lowering the apex v i The edges e included in the left/right peripheral angles are added to the initial path ring in sequence;
randomly assigning lambda to each edge e i Obtaining
Continuous iterative calculation is performed by using the formula (7) and the formula (8), and the value of the objective function L and the gradient of L are calculated respectively
Until the difference of the lengths of the paths calculated in the two continuous iterative calculation processes is larger than the fault tolerance value epsilon.
Updating and obtaining a new path, traversing all vertexes v of the new path i When lambda is i =1 or λ i When=0, p is used i The triangular faces that are not in the face sequence on one side replace triangular faces that are already in the face sequence.
After the light smoothing is carried out on the initial region selection boundary region, the output division boundary of the selection region is smoother, the practicability is stronger, and the process from the initial grid state of region selection to the final formation is shown in fig. 4.
In order to test the effectiveness and practicality of the algorithm, the embodiment randomly samples 10K vertices for the test model to calculate. Meanwhile, regions near the vertices are selected by setting the tolerance values t=20, t=50, t=100, t=200, respectively, and the density ρ (x) of the vertices of the selected regions is set o ) =10, the average calculation time was counted during the calculation. As shown in table 1, when the tolerance value t=20, the average time of calculating the tolerance allowable range region and the corresponding region contour ring is about 0.05 seconds for the model with about 10 ten thousand top points, and when the tolerance value t=200 is set, the average calculation time is also about 0.1 seconds, so as to completely satisfy the real-time interaction requirement of the user. Meanwhile, the region selection algorithm of the present embodiment was experimentally counted for average calculation time on the kitten model having different accuracies of 5 ten thousand vertices, 10 ten thousand vertices, 50 ten thousand vertices, and the like. The algorithm of the embodiment can also select the region on models with different precision. As can be seen from table 2, even in the model of 50 ten thousand points, the average calculation time of the region selection is only 0.12 seconds, and the real-time interaction operation of the user can be satisfied.
Table 1 time statistics of different models under intolerance values
TABLE 2 comparison of average calculation times in Kitten models of different accuracies
The algorithm of the embodiment is carried out by using a magic stick-like methodThe three-dimensional grid area is interactively selected, the setting of the tolerance value is allowed to be carried out by a user, and the process of carrying out area selection on the setting of the tolerance value is compared with a scribing interactive method in the prior art. A set of comparisons as shown in fig. 5, where a, b, c are the same vertex x on the Hand model 0 And d is a calculation result of drawing a track on the Hand model in the prior art by setting the region selection result obtained by the interactive calculation of the tolerance t=10, t=13 and t=15. As can be seen from fig. 5, by this being a certain tolerance value, by selecting the grid region in a magic wand-like manner through single-point interaction, region selection and grid segmentation similar to the conventional method can be achieved. And the method herein may also be implemented by this of tolerance values. Meanwhile, in this embodiment, the method of interactively calculating the selected area is compared with a geodetic algorithm proposed by a learner, as shown in fig. 6, where a and c are the results of this embodiment, and fig. 6b and d are the results of calculating the selected area by using the existing geodetic method, and it can be seen from fig. 6 that the results obtained by the model area ring obtained by the algorithm of this embodiment in the specific area of the mesh surface better meet the needs of the user. On a triangle mesh with 10 ten thousand vertices, the time consumption of the algorithm of the embodiment is basically less than 0.07 seconds, and meanwhile, the algorithm of the embodiment can calculate more areas for user interaction selection according to the tolerance value input of the user. Thus having wider application range. The robustness of the algorithm of this example was tested in fig. 7 using a bird model and a rabbit model as examples: fig. 7a and c are region contour boundaries obtained by setting tolerance values to allow user interaction with region selection after noise addition, and are substantially similar in shape to the results calculated on the model without noise (as shown in fig. 7b and 7 d). As can be seen from fig. 7, this illustrates that the algorithm herein is insensitive to noise, while the user can interactively select the surface mesh area as desired by the application.
The method provided by the embodiment allows the user to input the characteristic tolerance value for region selection, improves the degree of freedom of user interaction, can dynamically realize model surface region selection, effectively improves the region selection efficiency and the practicability, is not interfered by noise, and has obvious application effects on the interaction generation of region boundaries including model segmentation.
The specific embodiments described herein are offered by way of example only to illustrate the spirit of the invention. Those skilled in the art may make various modifications or additions to the described embodiments or substitutions thereof without departing from the spirit of the invention or exceeding the scope of the invention as defined in the accompanying claims.
Claims (7)
1. An easy-to-interact region selection method, comprising the steps of: constructing a feature vector of grid vertexes of the three-dimensional grid model surface;
establishing a characteristic measurement distance equation between corresponding grid vertexes;
performing region selection on the surface of the three-dimensional grid model according to the characteristic tolerance value specified by user interaction to form an initialization region selection boundary segmentation ring formed by the edge sequences;
carrying out optical smoothing on the initial region selection boundary segmentation ring by a geometric optimization method to obtain a final region boundary ring;
the characteristic vector of the grid vertex constructing the three-dimensional grid model surface is specifically as follows:
constructing a feature vector of a grid vertex on the surface of the three-dimensional model by utilizing the thermonuclear feature and the average curvature of the three-dimensional grid model;
the method also comprises the steps of:
combining the thermonuclear features and the average curvature of the three-dimensional mesh model into a new feature vector f (x) = (α·p) x ，β·K x ),P x Is the thermonuclear eigenvector at vertex x, K x The average curvature at the vertex x is shown, and alpha and beta are constant coefficients;
and calculating the similarity between the vertexes by combining the thermonuclear characteristics and the average curvature of the three-dimensional grid model.
2. An easy-to-interact area selection method as recited in claim 1, further comprising the step of:
extracting thermonuclear characteristics of a three-dimensional grid model by preprocessing, namely extracting thermonuclear characteristic vectors of grid vertices according to Riemann fashion and thermonuclear characteristic theory, wherein a thermal diffusion method on Riemann manifold comprises the following steps:
wherein delta is M The Laplace-Beltrami operator on the manifold is represented, the function u (x, t) represents the heat condition of the vertex x on the three-dimensional model at the moment t, and the solution of the equation is a thermonuclear;
limiting thermonuclear to the time domain according to the thermonuclear feature theory HKS for
The thermonuclear descriptors of the three-dimensional model are a list of vectors:
P x ＝(p 1 (x)，p 2 (x)，…，p n (x)) T (2)
wherein the component p i (x) For different times t i The lower part of the HKS,
therein, go into k 、
Is the kth eigenvalue and eigenvector of Laplace-Beltrami operator;
preprocessing to calculate the average curvature of the three-dimensional grid model: the curvature value of smooth change is calculated by adopting a least square method, and the calculation formula is as follows:
wherein L (·) represents the discrete Laplace operator, k i ' and k i The method comprises the steps of respectively representing the current curvature and the updated curvature, wherein a first term ensures smooth change of the curvature value of the adjacent point, a second term requires that the curvature value of each vertex after updating is close to the current value, and the Laplacian value of each point is set as the average curvature of each point on the boundary curve in the first iteration.
3. The method for easily interacted with according to claim 1, wherein the establishing a characteristic metric distance equation between corresponding mesh vertices is specifically:
calculating the characteristic measurement distance between grid vertexes by using a Euclidean distance formula, wherein the formula specifically comprises the following steps:
dp(x，y)＝||f(x)-f(y)|| 2 (5)
wherein f (X) and f (Y) are feature vectors of two vertexes X, Y on the model respectively.
4. An easy-to-interact area selection method as recited in claim 1, further comprising the step of:
the characteristic tolerance value appointed by the user is obtained, the characteristic tolerance between grid vertexes is calculated, and the calculation formula is as follows:
d(x o ,x i )＝||f(x o )-f(x i )|| 2 ＜Tε (6)
wherein x is 0 Grid vertex selected by user interaction as source point, x i Grid vertices, f (x) 0 ) And f (x) i ) Respectively the source points x 0 And vertex x i T is a tolerance value specified by a user, is an integer, and epsilon is a constant value;
and selecting the grid vertexes which are obtained through calculation and accord with a preset tolerance range between the source point characteristics as the boundary vertexes of the initialization area.
5. An easy-to-interact region selection method as claimed in claim 1, characterized in that the optical smoothing of the initial region selection boundary segmentation loop by means of a geometric optimization method is in particular:
taking a path formed by edge sequences in the boundary of the initialization area as an initial path;
taking the length of the geodesic distance as an objective function;
and carrying out iterative computation through a geometric optimization method to obtain a final region boundary ring.
6. An easy-to-interact area selection method as recited in claim 5, further comprising the step of:
setting a density value ρ (x i ) =a, a is constant in order to optimize the objective function for localization:
the partial derivative equation of equation (7) is:
wherein p is i Is on the path and the ith edge
Crossing of (1) at the same time->
By scalar coefficient lambda i And edge vertex->
Establishing corresponding relation, and marking the T-shaped face sequence of the partition ring as (s, p) 1 ，p 2 ，…，p k S), s is a fixed vertex in the partition ring Γ.
7. The easy-to-interact area selection method of claim 6, further comprising the steps of:
acquiring parameters of a triangular mesh curved surface S, an initial path Γ, a fixed point S epsilon S of the initial path Γ and a fault tolerance value epsilon of a three-dimensional mesh model;
traversing all vertices v of initial path Γ i Vertex v i The edges e included in the left/right peripheral angles are added to the initial path ring in sequence;
randomly assigning lambda to each edge e i Obtaining
Continuous iterative calculation is performed by using the formula (7) and the formula (8), and the value of the objective function L and the gradient of L are calculated respectively
Updating and obtaining new paths, traversing all tops v of the new paths i When lambda is i =1 or λ i When=0, p is used i The triangular faces that are not in the face sequence on one side replace triangular faces that are already in the face sequence.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910345442.2A CN110223392B (en) | 2019-04-26 | 2019-04-26 | Region selection method easy to interact |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910345442.2A CN110223392B (en) | 2019-04-26 | 2019-04-26 | Region selection method easy to interact |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN110223392A CN110223392A (en) | 2019-09-10 |
| CN110223392B true CN110223392B (en) | 2023-04-28 |
Family
ID=67819983
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201910345442.2A Active CN110223392B (en) | 2019-04-26 | 2019-04-26 | Region selection method easy to interact |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN110223392B (en) |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102708591A (en) * | 2012-04-28 | 2012-10-03 | 浙江大学 | Hole repairing method for digital tooth grid model |
| CN105046750A (en) * | 2015-08-24 | 2015-11-11 | 杭州美齐科技有限公司 | Method for automatically segmenting whole dental triangular mesh model |
-
2019
- 2019-04-26 CN CN201910345442.2A patent/CN110223392B/en active Active
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102708591A (en) * | 2012-04-28 | 2012-10-03 | 浙江大学 | Hole repairing method for digital tooth grid model |
| CN105046750A (en) * | 2015-08-24 | 2015-11-11 | 杭州美齐科技有限公司 | Method for automatically segmenting whole dental triangular mesh model |
Non-Patent Citations (3)
| Title |
|---|
| An optimization-driven approach for computing geodesic paths on triangle meshes;Bangquan Liu 等;《Computer-Aided Design》;20170930;第105-112页 * |
| 轻松交互式网格曲面建模方法的研究;计忠平;《中国博士学位论文全文数据库 信息科技辑》;20090315;第25、36-38、40、46-48页 * |
| 轻松交互式网格曲面建模方法的研究;计忠平;《中国博士学位论文全文数据库信息科技辑》;20090315;第25、36-38、40、46-48页 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN110223392A (en) | 2019-09-10 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN107123164B (en) | Three-dimensional reconstruction method and system for keeping sharp features | |
| Lee et al. | Mesh scissoring with minima rule and part salience | |
| CN108010116B (en) | Point cloud feature point detection method and point cloud feature extraction method | |
| Ke et al. | Feature-based reverse modeling strategies | |
| CN106023298B (en) | Point cloud Rigid Registration method based on local Poisson curve reestablishing | |
| Mehra et al. | Abstraction of man-made shapes | |
| Ji et al. | A novel simplification method for 3D geometric point cloud based on the importance of point | |
| CN108711194B (en) | Three-dimensional grid model splicing method based on cubic B spline interpolation | |
| CN109360272B (en) | Grid curved surface curve design method based on distance constraint | |
| CN107610061B (en) | Edge-preserving point cloud hole repairing method based on two-dimensional projection | |
| CN106780458B (en) | Point cloud framework extraction method and device | |
| CN110599506B (en) | Point cloud segmentation method for three-dimensional measurement of complex special-shaped curved surface robot | |
| US20120013617A1 (en) | Method for global parameterization and quad meshing on point cloud | |
| CN108230452B (en) | Model hole filling method based on texture synthesis | |
| CN110458764A (en) | A kind of point cloud data smoothing method based on morphology graphics process | |
| Zeng et al. | Interactive shape from shading | |
| Hu et al. | Geometric feature enhanced line segment extraction from large-scale point clouds with hierarchical topological optimization | |
| CN110223392B (en) | Region selection method easy to interact | |
| Boukhayma et al. | Video based animation synthesis with the essential graph | |
| Zhang et al. | Model reconstruction from cloud data | |
| Quadros et al. | 3 D discrete skeleton generation by wave propagation on PR-octree for finite element mesh sizing | |
| Yao et al. | Region-based line field design using harmonic functions | |
| CN109102565A (en) | A method of automatically generating Virtual Terrain | |
| CN110163973A (en) | A kind of zone boundary ring method for fairing | |
| Qun et al. | Research and implementation of 3D reconstruction technique based on images |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |