CN107909099A - A kind of threedimensional model identification and search method based on thermonuclear - Google Patents

Abstract

The invention discloses a method for identifying and retrieving a three-dimensional model based on a thermonucleus, which comprises the steps of extracting thermonuclear features irrelevant to the size of the three-dimensional model; improving the thermonuclear features so that the thermonuclear features have scale transformation invariance, and obtaining The improved thermonuclear feature NSI-HKS(x); select the amplitude of the second to sixth low-frequency components of NSI-HKS(x) as a local feature for sampling; perform K-means clustering on the sampled thermonuclear features , to obtain the cluster to which each data object belongs; to measure the similarity of the 3D model, and to identify and retrieve the 3D model. The beneficial effect of the present invention is: use thermonuclear features to improve the invariance of scale transformation, then improve the selection of data samples, then perform k-means processing, so that the features between different models can be compared, and finally adopt the The distance comparison method of Skid distance improves the efficiency and accuracy of recognition and retrieval.

Description

A Thermokernel-Based 3D Model Recognition and Retrieval Method

technical field

The invention relates to the field of computer technology, in particular to a thermonuclear-based three-dimensional model identification and retrieval method.

Background technique

With the development of computer technology and the improvement of computer hardware technology, the acquisition technology of 3D model develops rapidly. Not only has the number of 3D models increased by leaps and bounds, but the application of 3D models has become more and more extensive. The main application areas include industrial product design, virtual reality, 3D games, building design, film and television animation, medical diagnosis and molecular biology research and so on. It is precisely because of the rapid growth of 3D model application requirements that more and more 3D model libraries have emerged, such as industrial solid model libraries, 3D game model libraries, architectural model libraries, vehicle model libraries, and protein molecular model libraries. 3D models are heavily used in many industries, as creating a high-fidelity 3D model takes a lot of time and effort. Sometimes it is only necessary to partially modify the existing 3D model to use it. According to statistics, more than 85% of new products are updated and modified on the basis of the original products. It is very important to effectively manage these massive model information to facilitate retrieval, query and reuse. Therefore, rapid identification and retrieval of 3D models has become an urgent problem to be solved.

Contents of the invention

In order to solve the above problems, the present invention provides a thermonuclear-based three-dimensional model recognition and retrieval method, comprising steps:

S100) extracting the size-independent thermonuclear features of the 3D model, and expressing the thermonuclear features of the 3D model as a function HKS(x) in the time domain:

Where λ _i and φ _i (x) are the i-th eigenvalue and eigenfunction of the Laplace-Beltrami operator of the shape;

S200) Improving the thermonuclear feature, so that the thermonuclear feature has scale transformation invariance, and obtains the improved thermonuclear feature NSI-HKS(x);

S300) Select the amplitudes of the second to sixth low-frequency components of NSI-HKS(x) as local features for sampling;

S400) Perform K-means clustering processing on the sampled thermonuclear features to obtain the cluster to which each data object belongs;

S500) Measure the similarity of the 3D model, and identify and retrieve the 3D model.

Preferably, the step of extracting the size-independent thermonuclear feature of the three-dimensional model comprises:

S110) Calculate Laplace-beltrami operator Δ _X =A ^-1 W according to the formula, wherein A and W are area normalization matrix and cosine weight matrix respectively;

S120) Eigendecomposing the Laplace-beltrami operator to obtain λ _i where φ _i is the i-th eigenvalue and eigenvector respectively.

Preferably, the step of improving thermonuclear features includes:

S210) For each point x on the model, use time t=α ^τ to sample thermal characteristics, and the discrete function is as shown in formula (1):

h _τ ＝h(x,α ^τ ) (1)

The scaling ratio β of the S220 model will be converted into a time shift s=2log _α β and an amplitude scaling β ² , as shown in formula (2):

h′ _τ = β ² h _τ+s (2);

S230) h takes the logarithmic form, and then seeks the derivative of the discrete form to eliminate the constant β ² , as shown in formula (3):

in,

which is

S240) to Perform discrete-time Fourier transform, as shown in formula (4):

H'(ω)＝H(ω)e ^2πωs (4)

Among them, H and H' are respectively and The Fourier transform of , ω∈[0,2π]

S250) Then, e ^2πωs is eliminated by taking the modulus, that is, |H'(ω)|=|H(ω)|, and |H(ω)| is recorded as NSI-HKS(x).

Preferably, the selection of τ in the characteristic function NSI-HKS(x) is τ∈[τ _min ,τ _max ], and the amplitudes of the second to sixth low-frequency components of NSI-HKS(x) are taken as local features are sampled.

Preferably, the K-means clustering process includes the steps of:

S410) Randomly select K objects as initial cluster centers;

S420) Calculate the distance between each object and each seed cluster center, assign each object to the cluster center closest to it, and the cluster centers and the objects assigned to them represent a cluster;

S430) After all the objects are allocated, the allocation center of each cluster will be recalculated according to the existing objects in the cluster;

S440) Repeat steps S420 and S430 continuously until the data members of each cluster no longer change;

S450) Obtain the cluster to which each data object belongs.

Preferably, the value of K in the K-means clustering process is 60.

Preferably, the method for measuring the similarity includes the Minkowski distance comparison method.

Preferably, the Minkowski distance formula is:

Preferably, the steps of the similarity measurement include:

S510) compare the Minkowski distances between the first point of the A model and all the points of the B model, and select a group with the smallest distance for matching;

S520 compares the Minkowski distance between the second point of the A model and all points of the B model (excluding the matched points), and selects a group with the smallest distance to match until all 60 points are matched;

S530) Calculate the average value of the distances between all matched points, the smaller the average value, the more similar the samples, and the smaller the difference; the larger the average value, the less similar the samples, and the larger the difference.

The beneficial effects of the present invention are: the present invention provides a thermonuclear-based three-dimensional model identification and retrieval method, which utilizes thermonuclear features to improve the invariance of scale transformation, and then improves the collection of data samples, followed by k-means processing , so that the features between different models can be compared. Finally, the distance comparison method based on Minkowski distance is used to improve the efficiency and accuracy of recognition and retrieval.

Description of drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only These are some embodiments of the present invention. For those skilled in the art, other drawings can also be obtained according to these drawings on the premise of not paying creative efforts.

Fig. 1 shows a flow chart of a thermonuclear-based three-dimensional model recognition and retrieval method;

Fig. 2 shows the flow chart of extracting the thermonuclear feature independent of the size of the three-dimensional model;

Fig. 3 is a flowchart of an improved scale-independent thermonuclear feature processing method;

Fig. 4 shows the flow chart of the K-means clustering process;

FIG. 5 is a flow chart showing the steps of the similarity measurement.

Detailed ways

The idea, specific structure and technical effects of the present invention will be clearly and completely described below in conjunction with the embodiments and accompanying drawings, so as to fully understand the purpose, features and effects of the present invention. Apparently, the described embodiments are only some of the embodiments of the present invention, rather than all of them. Based on the embodiments of the present invention, other embodiments obtained by those skilled in the art without creative efforts belong to The protection scope of the present invention. The various technical features in the invention can be combined interactively on the premise of not conflicting with each other.

Fig. 1 is a flow chart of a thermonuclear-based three-dimensional model identification and retrieval method disclosed in the present invention. According to a method embodiment of the present invention, the steps of a thermonuclear-based three-dimensional model identification and retrieval method include :

S100) extracting the size-independent thermonuclear features of the 3D model, and expressing the thermonuclear features of the 3D model as a function HKS(x) in the time domain:

Where λ _i and φ _i (x) are the i-th eigenvalue and eigenfunction of the Laplace-Beltrami operator of the shape;

S200) Improving the thermonuclear feature, so that the thermonuclear feature has scale transformation invariance, and obtains the improved thermonuclear feature NSI-HKS(x);

S300) Select the amplitudes of the second to sixth low-frequency components of NSI-HKS(x) as local features for sampling;

S400) Perform K-means clustering processing on the sampled thermonuclear features to obtain the cluster to which each data object belongs;

S500) Measure the similarity of the 3D model, and identify and retrieve the 3D model.

Fig. 2 shows the flowchart of extracting the size-independent thermonuclear feature of a three-dimensional model. According to an embodiment of the present invention, the steps include:

S110) Calculate Laplace-beltrami operator Δ _X =A ^-1 W according to the formula, wherein A and W are area normalization matrix and cosine weight matrix respectively;

S120) Eigendecomposing the Laplace-beltrami operator to obtain λ _i where φ _i is the i-th eigenvalue and eigenvector respectively.

Fig. 3 is a flowchart of an improved scale-independent thermonuclear feature processing method, according to a method embodiment of the present invention, the steps include:

S210) For each point x on the model, use time t=α ^τ to sample thermal characteristics, and the discrete function is as shown in formula (1):

h _τ ＝h(x,α ^τ ) (1)

S220) The scaling ratio β of the model will be converted into a time shift s=2log _α β and an amplitude scaling β ² , as shown in formula (2):

h _τ ′=β ² h _τ+s (2);

S230) h takes the logarithmic form, and then seeks the derivative of the discrete form to eliminate the constant β ² , as shown in formula (3):

in,

which is

S240) to Perform discrete-time Fourier transform, as shown in formula (4):

H'(ω)＝H(ω)e ^2πωs (4)

Among them, H and H' are respectively and The Fourier transform of , ω∈[0,2π]

S250) Then, e ^2πωs is eliminated by taking the modulus, that is, |H'(ω)|=|H(ω)|, and |H(ω)| is recorded as NSI-HKS(x).

FIG. 4 shows a flow chart of the K-means clustering process. According to an embodiment of the present invention, the steps include:

S410) Randomly select K objects as initial cluster centers;

S420) Calculate the distance between each object and each seed cluster center, assign each object to the cluster center closest to it, and the cluster centers and the objects assigned to them represent a cluster;

S430) After all the objects are allocated, the allocation center of each cluster will be recalculated according to the existing objects in the cluster;

S440) Repeat steps S420 and S430 continuously until the data members of each cluster no longer change;

S450) Obtain the cluster to which each data object belongs.

Fig. 5 shows the flow chart of the steps of the similarity measure, according to an embodiment of the present invention, the steps include:

S510) compare the Minkowski distances between the first point of the A model and all the points of the B model, and select a group with the smallest distance for matching;

S520) compare the Minkowski distance between the second point of the A model and all the points of the B model (excluding the matched points), select a group with the smallest distance to match, until 60 points are all matched;

S530) Calculate the average value of the distances between all matched points, the smaller the average value, the more similar the samples, and the smaller the difference; the larger the average value, the less similar the samples, and the larger the difference.

According to an embodiment of the present invention, further illustrate thermonuclear characteristic below, for a compact Riemannian fluid (possibly with boundary) M, then the heat diffusion process on M depends on heat equation (5):

where _ΔM is the Laplace-beltrami operator on M. If M is a bounded Riemannian fluid, u is also required to satisfy the Dirichlet boundary condition, that is, for all time t, all points x on the fluid M must satisfy u(x,t)=0. Given an initial heat distribution f:M→R, let _Ht (f) denote the heat distribution of fluid M at time t, so _Ht (f) satisfies heat equation (6) for all time t, and:

where _Ht is the heat operator. Both _Ht and _ΔM are real function operators defined on fluid M, so it is easy to prove that these two operators satisfy the relation Since these two operators share the same eigenfunction, if λ is one of the eigenvalues of _ΔM , then e ^-λt is one of the eigenvalues of _Ht . For any Riemannian fluid M, there is a function k _t (x,y):R ⁺ ×M×M→R such that:

where dy is the convolutional form of y ∈ M. The minimum value k _t (x, t) that satisfies the formula (7) is the heat core, which can be regarded as the heat value of heat conduction from point x to point y in a given time t. That is to say k _t (x, )=H _t (δ _x ), where δ _x is a δ (Dirac) function, that is, to satisfy any z≠x, δ _x (z)=0 and For a compact fluid M, the thermonucleus has the following eigendecomposition:

The thermonucleus can also be understood as the transition density function of Brownian motion on the Riemannian fluid M, which means that for any Borel subset of the Riemannian fluid M The transition probability of Brownian motion starting from point x at time t is Brownian motion It is the most basic continuous-time Markov process of Riemannian fluid M, which well explains the rich characteristic information of the model contained in the thermonucleus. Since the transition probability of Brownian motion is not only related to the shortest path between two points, but also related to the weighted average of all possible paths at time t, the heat kernel contains more information than the shortest distance between two points. The thermonucleus contains a lot of redundant information, because the heat diffusion process depends on the heat equation (1), which means that the characteristic equation of the space domain will change with time. In order to overcome the above difficulties, Sun et al. proposed the thermonuclear feature (HKS), which discards all the information of the thermonuclear space domain. For a point x on the Riemannian fluid M, the thermonuclear feature is defined as a function HKS(x) in the time domain:

Among them, λ _i and φ _i (x) are the i-th eigenvalue and eigenfunction of the Laplace-Beltrami operator of the shape.

According to another embodiment of the present invention, most of the signal information is contained in the low-frequency part after Fourier transform, so a compact local descriptor is established by sampling |H(ω)| low-frequency, so take the former The magnitudes of the six low-frequency components are used as local features.

According to another embodiment of the present invention, different choices of time parameters will affect the characteristics of models of different scales. In order to make the time parameters better adapt to models of different scales, the time parameters are determined according to the median value of the radius of the semi-enclosing sphere, namely τ _min ＝floor(lbt _min ), τ _max ＝ceil(lbt _max ), when τ＞lbt _max , HKS will no longer change, and for models with different scales, t _max is different, the larger the scale of the model, t The bigger _{the max} .

According to another embodiment of the present invention, the K-means clustering algorithm is further described. The K-means clustering algorithm first randomly selects K objects as initial cluster centers, and then calculates the distance between each object and each seed cluster center. Distance, assigning each object to the cluster center closest to it. The cluster centers and the objects assigned to them represent a cluster. Once all objects have been assigned, the cluster centers for each cluster are recalculated based on the existing objects in the cluster. This process will be repeated until a certain termination condition is met. The termination condition can be that no (or minimum number) objects are reassigned to different clusters, no (or minimum number) cluster centers change again, and the sum of squared errors is locally minimum.

According to an embodiment of the present invention, the similarity measure is further described, assuming that a given data set is X={x _m |m=1,2,...,total}, samples in X are described by d attributes A ₁ , A ₂ ,...,A _d to represent, and the d description attributes are continuous attributes. Data samples x _i =(x _i1 , x _i2 ,...,x _id ), x _j =(x _j1 , x _j2 ,...,x _jd ). Where x _i1 , x _i2 ,..., x _id and x _j1 , x _j2 ,..., x _jd are the specific values of d description attributes A ₁ , A ₂ ,...,A _d corresponding to samples _xi and x _j respectively . The similarity between samples x _i and x _j is usually expressed by the distance d( _xi , x _j ) between them. The smaller the distance, the more similar the samples are, and the smaller the difference is; otherwise, the less similar, the difference bigger.

While the description of the invention has been described in considerable detail and with particular reference to a few described embodiments, it is not intended to be limited to any such details or embodiments or to any particular embodiment, but rather it should be read by reference The appended claims provide the widest possible interpretation of these claims in view of the prior art, effectively encompassing the intended scope of the present invention. Furthermore, the invention has been described above in terms of embodiments foreseeable by the inventors for the purpose of providing a useful description, while insubstantial modifications of the invention which are not presently foreseeable may still represent equivalent modifications of the invention.

Claims (9)

1. A thermonuclear-based three-dimensional model identification and retrieval method, characterized in that, comprising steps: S100) extracting the size-independent thermonuclear features of the 3D model, and expressing the thermonuclear features of the 3D model as a function HKS(x) in the time domain: <mrow><mi>H</mi><mi>K</mi><mi>S</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>:</mo><msup><mi>R</mi><mo>+</mo></msup><mo>&amp;RightArrow;</mo><mi>R</mi><mo>,</mo><mi>H</mi><mi>K</mi><mi>S</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><msub><mi>k</mi><mi>t</mi></msub><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><munderover><mi>&amp;Sigma;</mi><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mi>&amp;infin;</mi></munderover><msup><mi>e</mi><mrow><mo>-</mo><msub><mi>&amp;lambda;</mi><mi>i</mi></msub><mi>t</mi></mrow></msup><msup><msub><mi>&amp;phi;</mi><mi>i</mi></msub><mn>2</mn></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow> Where λ _i and φ _i (x) are the i-th eigenvalue and eigenfunction of the Laplace-Beltrami operator of the shape; S200) Improving the thermonuclear feature, so that the thermonuclear feature has scale transformation invariance, and obtains the improved thermonuclear feature NSI-HKS(x); S300) Select the amplitudes of the second to sixth low-frequency components of NSI-HKS(x) as local features for sampling; S400) Perform K-means clustering processing on the sampled thermonuclear features to obtain the cluster to which each data object belongs; S500) Measure the similarity of the 3D model, and identify and retrieve the 3D model. 2. A kind of three-dimensional model identification and retrieval method based on thermonucleus according to claim 1, is characterized in that, the step of belonging to extracting the thermonucleus feature that has nothing to do with the size of three-dimensional model comprises: S110) Calculate Laplace-beltrami operator Δ _X =A ^-1 W according to the formula, wherein A and W are area normalization matrix and cosine weight matrix respectively; S120) Eigendecomposing the Laplace-beltrami operator to obtain λ _i where φ _i is the i-th eigenvalue and eigenvector respectively. 3. A kind of thermonuclear-based three-dimensional model recognition and retrieval method according to claim 1, is characterized in that, described step of improving thermonuclear feature comprises: S210) For each point x on the model, use time t=α ^τ to sample thermal characteristics, and the discrete function is as shown in formula (1): h _τ ＝h(x,α ^τ ) (1) The scaling ratio β of the S220 model will be converted into a time shift s=2log _α β and an amplitude scaling β ² , as shown in formula (2): h′ _τ = β ² h _τ+s (2); S230) h takes the logarithmic form, and then seeks the derivative of the discrete form to eliminate the constant β ² , as shown in formula (3): <mrow><msubsup><mover><mi>h</mi><mo>&amp;CenterDot;</mo></mover><mi>&amp;tau;</mi><mo>&amp;prime;</mo></msubsup><mo>=</mo><msub><mover><mi>h</mi><mo>&amp;CenterDot;</mo></mover><mrow><mi>&amp;tau;</mi><mo>+</mo><mi>s</mi></mrow></msub><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow></mrow> in, which is <mrow><mover><mi>h</mi><mo>~</mo></mover><mrow><mo>(</mo><mi>x</mi><mo>,</mo><msup><mi>&amp;alpha;</mi><mi>&amp;tau;</mi></msup><mo>)</mo></mrow><mo>=</mo><mfrac><mrow><mo>-</mo><munderover><mo>&amp;Sigma;</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mi>&amp;infin;</mi></munderover><msub><mi>&amp;lambda;</mi><mi>i</mi></msub><msup><mi>&amp;alpha;</mi><mi>&amp;tau;</mi></msup><msup><mi>log&amp;alpha;e</mi><mrow><mo>-</mo><msub><mi>&amp;lambda;</mi><mi>i</mi></msub><msup><mi>&amp;alpha;</mi><mi>&amp;tau;</mi></msup></mrow></msup><msubsup><mi>&amp;phi;</mi><mi>i</mi><mn>2</mn></msubsup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><munderover><mo>&amp;Sigma;</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mi>&amp;infin;</mi></munderover><msup><mi>e</mi><mrow><mo>-</mo><msub><mi>&amp;lambda;</mi><mi>i</mi></msub><msup><mi>&amp;alpha;</mi><mi>&amp;tau;</mi></msup></mrow></msup><msubsup><mi>&amp;phi;</mi><mi>i</mi><mn>2</mn></msubsup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></mfrac><mo>;</mo></mrow> S240) to Perform discrete-time Fourier transform, as shown in formula (4): H'(ω)＝H(ω)e ^2πωs (4) Among them, H and H' are respectively and The Fourier transform of , ω∈[0,2π] S250) Then, e ^2πωs is eliminated by taking the modulus, that is, |H'(ω)|=|H(ω)|, and |H(ω)| is recorded as NSI-HKS(x). 4. A heat-kernel-based three-dimensional model recognition and retrieval method according to claim 3, characterized in that, the selection of τ in the characteristic function NSI-HKS(x) is τ∈[τ _min ,τ _max ], take the amplitudes of the second to sixth low-frequency components of NSI-HKS(x) as local features for sampling. 5. a kind of three-dimensional model identification and retrieval method based on thermonucleus according to claim 1, is characterized in that, described K-means clustering process comprises steps: S410) Randomly select K objects as initial cluster centers; S420) Calculate the distance between each object and each seed cluster center, assign each object to the cluster center closest to it, and the cluster centers and the objects assigned to them represent a cluster; S430) After all the objects are allocated, the allocation center of each cluster will be recalculated according to the existing objects in the cluster; S440) Repeat steps S420 and S430 continuously until the data members of each cluster no longer change; S450) Obtain the cluster to which each data object belongs. 6 . A thermonuclear-based three-dimensional model recognition and retrieval method according to claim 5 , wherein K is 60 in the K-means clustering process. 7 . 7. A thermonuclear-based three-dimensional model recognition and retrieval method according to claim 1, wherein the method for measuring similarity comprises Minkowski distance comparison. 8. a kind of thermonuclear-based three-dimensional model identification and retrieval method according to claim 7, is characterized in that, described Minkowski distance formula is: <mrow><mi>d</mi><mrow><mo>(</mo><msub><mi>x</mi><mi>i</mi></msub><mo>,</mo><msub><mi>x</mi><mi>j</mi></msub><mo>)</mo></mrow><mo>=</mo><msup><mrow><mo>(</mo><munderover><mo>&amp;Sigma;</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>d</mi></munderover><mo>|</mo><msub><mi>x</mi><mrow><mi>i</mi><mi>k</mi></mrow></msub><mo>-</mo><msub><mi>x</mi><mrow><mi>j</mi><mi>k</mi></mrow></msub><msup><mo>|</mo><mi>q</mi></msup><mo>)</mo></mrow><mrow><mn>1</mn><mo>/</mo><mi>q</mi></mrow></msup></mrow> 9. A kind of three-dimensional model recognition and retrieval method based on thermal core according to claim 7, is characterized in that, the step of described similarity measure comprises: S510) compare the Minkowski distances between the first point of the A model and all the points of the B model, and select a group with the smallest distance for matching; S520) compare the Minkowski distance between the second point of the A model and all the points of the B model (excluding the matched points), select a group with the smallest distance to match, until 60 points are all matched; S530) Calculate the average value of the distances between all matched points, the smaller the average value, the more similar the samples, and the smaller the difference; the larger the average value, the less similar the samples, and the larger the difference.