CN107274367A - A kind of 3-D geometric model denoising method described based on architectural feature - Google Patents
A kind of 3-D geometric model denoising method described based on architectural feature Download PDFInfo
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Abstract
The present invention is a kind of 3-D geometric model denoising method described based on architectural feature, is characterized in, comprises the following steps：Inner product is done by summit Laplce vector and its normal direction first and constructs summit signal；Architectural feature description for being then based on the normal direction tensor construction summit on threedimensional model summit portrays the feature of geometrical model, and is carried out smoothly as the calculation basis opposite vertexes signal of non-local mean filter weights；Smooth signal progress curve reestablishing is finally obtained into denoising model.This method can preferably keep the feature of model while geometrical model noise is removed, and achieve good denoising effect.
Description
Technical field
The present invention relates to a kind of 3-D geometric model denoising method described based on architectural feature.
Background technology
With the popularization of digital scanning technology, the 3-D geometric model that acquisition large scale measurement point is rebuild is got over
Come more field extensive uses, such as video display amusement, virtual reality, medical diagnosis, industry manufacture, historical relic's protection.Due to number
Word equipment precision error, three-dimensional rebuilding method defect and some human factors etc., the model of acquisition is inevitably present respectively
Noise and disturbance are planted, the presence of which is extremely unfavorable for display transmission and other follow-up geometric manipulations and analysis operation, such as geometry
Model parameterization, three-dimensional watermark, distortion of the mesh etc., it is therefore desirable to which denoising is carried out to the geometrical model of acquisition.
The work of geometrical model denoising early stage mainly has the fairing based on Laplce, the diffusion based on curvature flow and base
In methods such as the filtering of frequency domain.Although these methods can be good at removing the noise of model, but be due in denoising process
In feature and noise are not made a distinction, it is easy to produced fairing and removed some features of geometrical model.In order to pick
Intrinsic geometric properties are kept while except geometrical model noise, those skilled in the art, which propose some, can keep geometry mould
The anisotropic smoothing method of type feature, such as denoising based on bilateral filtering, the Smoothing Algorithm based on anisotropy parameter,
The denoising optimized based on full variation, denoising based on compressed sensing etc..However, the geometrical model denoising side of existing local iteration
Method is general it cannot be guaranteed that the convergence of result, is easier geometrical model volume contraction phenomenon, the denoising side of global optimization occur
Method is usually required archetype information as constraint, easily by noise regard feature as and can not denoising well, and for
The processing speed of extensive geometrical model is slower.
The content of the invention
The invention aims to the sharp features for reducing holding input geometrical model while noise, there is provided a kind of base
The 3-D geometric model denoising method described in architectural feature, it builds a kind of effective several from the angle of geometry signals
What architectural feature description, and the progress geometrical model denoising in non-local mean filter frame is incorporated, prevent geometry mould
The volume contraction of type, improves the validity and robustness of denoising.
The purpose of the present invention is achieved through the following technical solutions：A kind of three-dimensional geometry described based on architectural feature
Model denoising method, it is characterized in that, it comprises the following steps：
1) structure of geometry signals
For the 3-D geometric model represented with triangle gridding, Laplace operator and summit by geometrical model summit
Normal direction carries out inner product and builds geometry signals, and the signal can portray the local detail feature of geometrical model；
2) calculating of architectural feature description based on normal direction tensor
By all characteristic values of vertex normal tensor and and least unit characteristic vector be used as architectural feature and estimate
Description, description can portray the characteristic information of angle point on geometrical model, edge point and millet cake；
3) the non-local mean filtering of geometry signals
By each summit, architectural feature estimates the weights meter that the difference of description is filtered as non-local mean each other
Foundation is calculated, the discrete Laplace operator of opposite vertexes carries out non-with signal on the geometrical model obtained by corresponding vertex normal vector inner product
Local mean value is filtered, and obtains a new geometry signals；
4) Geometric model reconstruction
Using original geometry model vertices as constraints, as by step 3) obtained by filtering after new geometry signals enter
Row Laplce's curve reestablishing, obtains the corresponding geometrical model of non-local mean filtered signal；
The step 1) in the constructions of geometry signals be implemented as：
If { vi| i=1,2 ..., n } for the n summit of 3-D geometric model that is represented with triangle gridding, Δ (vi) it is summit
viDiscrete Laplace operator, vertex scheme vector be ni, geometry signals are defined as both inner product forms for (1) formula：
si=(Δ (vi),ni) (1)
For the geometry signals on all summits on geometrical model, it can be write as the matrix form of (2) formula：
LV=SN (2)
Wherein V represents the position vector matrix on geometrical model summit, S=diag (s1,s2,…,sn) represent with summit signal
siAs the matrix of diagonal entry, N is the normal direction matrix on summit, and L is the Laplacian Matrix of geometrical model, with (3) formula
Form：
Wherein wij=cot αij+cotβij, αij,βijIt is vertex viWith vjSide formed by line to two angles, N (i) is
Vertex viA ring neighborhood point set.
The step 2) in based on normal direction tensor architectural feature description son calculating be implemented as：
For given geometrical model vertex vi, the unit normal vector for the tri patch that its normal direction tensor can be around it determines
Justice is (4) formula：
Wherein F (vi) represent vertex viThe index set of the triangle of surrounding,For the weight coefficient of (5) formula：
A(fk) it is triangle fkArea, AmaxIt is vertex viThe maximum area of the triangle of surrounding,It is triangle fkWeight
The heart；
Because normal direction tensor is three rank symmetric positive semidefinite matrix, its eigenvalue λ can be obtained1≥λ2≥λ3>=0 and corresponding
Unit character vector e1,e2,e3, because the characteristic value corresponding to angle point, edge point and millet cake on geometrical model has obvious poor
Away from, and the direction e of minimal characteristic vector3The characteristic direction on summit is correspond to, it is special as summit structure using the measurement of (6) formula
Levy and estimate description：
Des(vi)={ di,ti} (6)
Wherein di=λ1+λ2+λ3, tiThe minimal characteristic vector of corresponding vertex normal direction tensor；
On this basis, by (7) formula, measurement describes sub difference to calculate architectural feature between each summit as follows：
D(vi,vj)=(di-dj)2+(1-|(tj,ti)|) (7)
Wherein (tj,ti) inner product in apex feature direction is represented, the difference value is smaller, illustrates the architectural feature on two summits
It is more similar.
The step 3) in geometry signals non-local mean filtering be implemented as：
Using step 2) defined in architectural feature estimate description son as non-local mean filter weights calculation basis, it is right
Step 1) the middle geometry signals s constructediCarry out non-local mean filtering and obtain a new geometry signals s 'i, calculating formula is (8)
Formula：
Wherein Nσ(i) it is vertex viNeighborhood point set by radius of σ, σ is the β ∈ [1.5,3] of geometrical model average side length
Times, weight coefficient wijEstimate description by architectural feature between each summit to be calculated, as formula (9)-(10) formula：
H represents the intensity of geometrical model denoising, can be taken as h ∈ [0.05,0.35].
The step 4) in Geometric model reconstruction be implemented as：
By by signal s ' new after filteringiCarry out least square solution and obtain new geometrical model summit V ', i.e., it is minimum
Turn to the energy that (11) formula is represented：
The energy can be rewritten as (12) formula：
It can be converted into 2n × n system of linear equations (13) formula：
Wherein S '=diag (s '1,s′2,…,s′n) represent with step 3) in gained summit signal s 'iIt is used as diagonal
The matrix of element, n is the number on geometrical model summit, and L is the Laplacian Matrix of original geometry model, In×nFor n rank unit squares
Battle array, N be original geometry model vertices normal direction matrix, V be original geometry model vertices position vector matrix, μ be summit about
The weight factor of beam, the constraint weight of border vertices is 1, and the constraint weight of internal vertex is 0.1.
Advantages of the present invention is embodied in：
1. architectural feature description proposed by the present invention based on normal direction tensor not only considers the geometric sense of single-point on model,
The uniformity in global feature direction is further contemplated, to there is the spy of the CAD model of sharp features and non-CAD model with minutia
Levying can preferably portray, with preferable robustness；
2. the present invention is used as constraint for filtered signal progress Laplce's mould by introducing original geometry model vertices
Type is rebuild, and border and volume contraction can be prevented in geometrical model smoothing process；
3. non-local mean filtering is incorporated into Laplce's geometric manipulations frame by the present invention from the angle of geometry signals
In frame, with higher execution efficiency and good universality.
Brief description of the drawings
Fig. 1 is a kind of flow chart of 3-D geometric model denoising method described based on architectural feature of the present invention；
Fig. 2 is the discrepancy mappings schematic diagram that the architectural feature based on normal direction tensor estimates description during the present invention is embodied；
Fig. 3 is that during the present invention is embodied geometry signals are carried out with contrast schematic diagram before and after non-local mean filtering；
Fig. 4 is the denoising result schematic diagram to Octahedron models during the present invention is embodied；
Fig. 5 is the denoising result schematic diagram to Fandisk models during the present invention is embodied；
Fig. 6 is the denoising result schematic diagram to Mannequin models during the present invention is embodied；
Fig. 7 is the denoising result schematic diagram to Julius models during the present invention is embodied；
Fig. 8 is the denoising result schematic diagram to Angle models during the present invention is embodied；
Fig. 9 is the denoising result schematic diagram to Moai models during the present invention is embodied.
Embodiment
Below with accompanying drawing and example, the invention will be further described.
Reference picture 1, a kind of 3-D geometric model denoising method described based on architectural feature of the invention, including following step
Suddenly：
1) structure of geometry signals
Read in noisy geometrical model, the non-CAD moulds to the CAD model with sharp features and with minutia
Type is applicable；For the 3-D geometric model represented with triangle gridding, Laplace operator and top by geometrical model summit
Point normal direction carries out inner product constructive geometry signal, and the signal can portray the local detail feature of geometrical model；
The step 1) in the constructions of geometry signals be implemented as：
If { vi| i=1,2 ..., n } for the n summit of 3-D geometric model that is represented with triangle gridding, Δ (vi) it is summit
viDiscrete Laplace operator, vertex scheme vector be ni, geometry signals are defined as both inner product forms for (1) formula：
si=(Δ (vi),ni) (1)
For the geometry signals on all summits on geometrical model, it can be write as the matrix form of (2) formula：
LV=SN (2)
Wherein V represents the position vector matrix on geometrical model summit, S=diag (s1,s2,…,sn) represent with summit signal
siAs the matrix of diagonal entry, N is the normal direction matrix on summit, and L is the Laplacian Matrix of geometrical model, with (3) formula
Form：
Wherein wij=cot αij+cotβij, αij,βijIt is vertex viWith vjSide formed by line to two angles, N (i) is
Vertex viA ring neighborhood point set.
2) calculating of architectural feature description based on normal direction tensor
By all characteristic values of vertex normal tensor and and least unit characteristic vector be used as architectural feature and estimate
Description, description can portray the characteristic information of angle point on geometrical model, edge point and millet cake；
The calculating of architectural feature description based on normal direction tensor is implemented as：
For given geometrical model vertex vi, the unit normal vector for the tri patch that its normal direction tensor can be around it determines
Justice is (4) formula：
Wherein F (vi) represent vertex viThe index set of the triangle of surrounding,For the weight coefficient of (5) formula：
A(fk) it is triangle fkArea, AmaxIt is vertex viThe maximum area of the triangle of surrounding, cfkIt is triangle fkWeight
The heart,
Because normal direction tensor is three rank symmetric positive semidefinite matrix, its eigenvalue λ can be obtained1≥λ2≥λ3>=0 and corresponding
Unit character vector e1,e2,e3, because the characteristic value corresponding to angle point, edge point and millet cake on geometrical model has obvious poor
Away from, and the direction e of minimal characteristic vector3The characteristic direction on summit is correspond to, it is special as summit structure using the measurement of (6) formula
Levy and estimate description：
Des(vi)={ di,ti} (6)
Wherein di=λ1+λ2+λ3, tiThe minimal characteristic vector of corresponding vertex normal direction tensor；
On this basis, by (7) formula, measurement describes sub difference to calculate architectural feature between each summit as follows：
D(vi,vj)=(di-dj)2+(1-|(tj,ti)|) (7)
Wherein (tj,ti) inner product in apex feature direction is represented, the difference value is smaller, illustrates the architectural feature on two summits
It is more similar.
Fig. 2 gives selectes one on the sharp features side of the vertical direction with noisy Fandisk geometrical models
Behind summit, difference when description method opposite vertexes are described is estimated by the architectural feature proposed by the present invention based on normal direction tensor
Different mapping schematic diagram.Therefrom it can be seen that, the similitude on summit in vertical direction characteristic edge and selected summit closely,
Illustrate that description can preferably describe the similitude on the summit with identical architectural feature, can be effectively applied to non local
In the denoising framework of mean filter.
3) the non-local mean filtering of geometry signals
By each summit, architectural feature estimates the weights meter that the difference of description is filtered as non-local mean each other
Foundation is calculated, the discrete Laplace operator of opposite vertexes carries out non-with signal on the geometrical model obtained by corresponding vertex normal vector inner product
Local mean value is filtered, and obtains a new geometry signals；Fig. 3 gives signal contrast schematic diagram before and after non-local mean filtering.
What the non-local mean of geometry signals was filtered is implemented as：
Using step 2) defined in architectural feature estimate description son as non-local mean filter weights calculation basis, it is right
Step 1) the middle geometry signals s builtiCarry out non-local mean filtering and obtain a new geometry signals s 'i, calculating formula is (8)
Formula：
Wherein Nσ(i) it is vertex viNeighborhood point set by radius of σ, σ is the β ∈ [1.5,3] of geometrical model average side length
Times, weight coefficient wijEstimate description by architectural feature between each summit to be calculated, as formula (9)-(10) formula：
H represents the intensity of geometrical model denoising, can be taken as h ∈ [0.05,0.35].
4) Geometric model reconstruction
Using original geometry model vertices as constraints, as by step 3) obtained by filtering after new geometry signals enter
Row Laplce's curve reestablishing, obtains the corresponding geometrical model of non-local mean filtered signal.
Geometric model reconstruction is implemented as：
By by signal s ' new after filteringiCarry out least square solution and obtain new geometrical model summit V ', i.e., it is minimum
Turn to the energy that (11) formula is represented：
The energy can be rewritten as (12) formula：
It can be converted into 2n × n system of linear equations (13) formula：
Wherein S '=diag (s '1,s′2,…,s′n) represent with step 3) in gained summit signal s 'iIt is used as diagonal
The matrix of element, n is the number on geometrical model summit, and L is the Laplacian Matrix of original geometry model, In×nFor n rank unit squares
Battle array, N be original geometry model vertices normal direction matrix, V be original geometry model vertices position vector matrix, μ be summit about
The weight factor of beam, the constraint weight of border vertices is 1, and the constraint weight of internal vertex is 0.1.
Fig. 4 and Fig. 5 give the denoising result added for the CAD model with sharp features after Gaussian noise；Fig. 6 and
Fig. 7 gives the denoising result added to the non-CAD model with minutia after Gaussian noise；Fig. 8 and Fig. 9 give containing
The denoising result of the model data of real noise.
The present invention embodiment it is not exhaustive, those skilled in the art without creative work simple copy
And improvement, the protection domain of patent requirements of the present invention should be belonged to.
Claims (5)
1. a kind of 3-D geometric model denoising method described based on architectural feature, it is characterized in that, it comprises the following steps：
1) structure of geometry signals
For the 3-D geometric model represented with triangle gridding, pass through the Laplace operator and vertex normal on geometrical model summit
Carry out inner product and build geometry signals, the signal can portray the local detail feature of geometrical model；
2) calculating of architectural feature description based on normal direction tensor
By all characteristic values of vertex normal tensor and and least unit characteristic vector be used as architectural feature and estimate description
Son, description can portray the characteristic information of angle point on geometrical model, edge point and millet cake；
3) the non-local mean filtering of geometry signals
By each summit each other architectural feature estimate description son difference as non-local mean filter weights calculating according to
According to the discrete Laplace operator of opposite vertexes carries out non local with signal on the geometrical model obtained by corresponding vertex normal vector inner product
Mean filter, obtains a new geometry signals；
4) Geometric model reconstruction
Using original geometry model vertices as constraints, as by step 3) obtained by filtering after new geometry signals drawn
This curve reestablishing of pula, obtains the corresponding geometrical model of non-local mean filtered signal.
2. a kind of 3-D geometric model denoising method described based on architectural feature according to claim 1, it is characterized in that,
The step 1) in the structures of geometry signals be implemented as：
If { vi| i=1,2 ..., n } for the n summit of 3-D geometric model that is represented with triangle gridding, Δ (vi) it is vertex vi's
Discrete Laplace operator, vertex scheme vector is ni, geometry signals are defined as both inner product forms for (1) formula：
si=(Δ (vi),ni) (1)
For the geometry signals on all summits on geometrical model, it can be write as the matrix form of (2) formula：
LV=SN (2)
Wherein V represents the position vector matrix on geometrical model summit, S=diag (s1,s2,…,sn) represent with summit signal siMake
For the matrix of diagonal entry, N is the normal direction matrix on summit, and L is the Laplacian Matrix of geometrical model, with (3) formula form：
Wherein wij=cot αij+cotβij, αij,βijIt is vertex viWith vjSide formed by line to two angles, N (i) is summit
viA ring neighborhood point set.
3. a kind of 3-D geometric model denoising method described based on architectural feature according to claim 1, it is characterized in that,
The step 2) in based on normal direction tensor architectural feature description son calculating be implemented as：
For the vertex v of given geometrical modeli, the unit normal vector for the tri patch that its normal direction tensor can be around it defines
For (4) formula：
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A(fk) it is triangle fkArea, AmaxIt is vertex viThe maximum area of the triangle of surrounding,It is triangle fkCenter of gravity；
Because normal direction tensor is three rank symmetric positive semidefinite matrix, its eigenvalue λ can be obtained1≥λ2≥λ3>=0 and corresponding list
Position characteristic vector e1,e2,e3, because the characteristic value corresponding to angle point, edge point and millet cake on geometrical model has obvious gap, and
And the direction e of minimal characteristic vector3The characteristic direction on summit is correspond to, is surveyed using the measurement of (6) formula as summit architectural feature
Degree description：
Des(vi)={ di,ti} (6)
Wherein di=λ1+λ2+λ3, tiThe minimal characteristic vector of corresponding vertex normal direction tensor；
On this basis, architectural feature describes sub difference between each summit is calculated by (7) formula：
D(vi,vj)=(di-dj)2+(1-|(tj,ti)|) (7)
Wherein (tj,ti) inner product in apex feature direction is represented, the difference value is smaller, illustrates that the architectural feature on two summits gets over phase
Seemingly.
4. a kind of 3-D geometric model denoising method described based on architectural feature according to claim 1, it is characterized in that,
The step 3) in geometry signals non-local mean filtering be implemented as：
Using step 2) defined in architectural feature estimate description son as non-local mean filter weights calculation basis, to step
1) the geometry signals s of construction iniCarry out non-local mean filtering and obtain a new geometry signals s 'i, calculating formula is (8) formula：
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Wherein Nσ(i) it is vertex viNeighborhood point set by radius of σ, σ is β ∈ [1.5,3] times of geometrical model average side length, power
Weight coefficient wijEstimate description by architectural feature between each summit to be calculated, as formula (9)-(10) formula：
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<mo>&Element;</mo>
<msub>
<mi>N</mi>
<mi>&sigma;</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
</mrow>
</mrow>
</munder>
<mi>exp</mi>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mfrac>
<mrow>
<mi>D</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>v</mi>
<mi>i</mi>
</msub>
<mo>,</mo>
<msub>
<mi>v</mi>
<mi>j</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mn>2</mn>
<msup>
<mi>h</mi>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>10</mn>
<mo>)</mo>
</mrow>
</mrow>
H represents the intensity of geometrical model denoising, can be taken as h ∈ [0.05,0.35].
5. a kind of 3-D geometric model denoising method described based on architectural feature according to claim 1, it is characterized in that,
The step 4) in Geometric model reconstruction be implemented as：
By by signal s ' new after filteringiCarry out least square solution and obtain new geometrical model summit V ', that is, be minimised as
(11) energy that formula is represented：
<mrow>
<mo>|</mo>
<mo>|</mo>
<msup>
<mi>LV</mi>
<mo>&prime;</mo>
</msup>
<mo>-</mo>
<msup>
<mi>S</mi>
<mo>&prime;</mo>
</msup>
<mi>N</mi>
<mo>|</mo>
<mo>|</mo>
<mo>+</mo>
<msup>
<mi>&mu;</mi>
<mn>2</mn>
</msup>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<mo>|</mo>
<mo>|</mo>
<msubsup>
<mi>v</mi>
<mi>i</mi>
<mo>&prime;</mo>
</msubsup>
<mo>-</mo>
<msub>
<mi>v</mi>
<mi>i</mi>
</msub>
<mo>|</mo>
<msup>
<mo>|</mo>
<mn>2</mn>
</msup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>11</mn>
<mo>)</mo>
</mrow>
</mrow>
The energy can be rewritten as (12) formula：
<mrow>
<mo>|</mo>
<mo>|</mo>
<mo>&lsqb;</mo>
<mfrac>
<mi>L</mi>
<mrow>
<msub>
<mi>&mu;I</mi>
<mrow>
<mi>n</mi>
<mo>&times;</mo>
<mi>n</mi>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>&rsqb;</mo>
<msup>
<mi>V</mi>
<mo>&prime;</mo>
</msup>
<mo>-</mo>
<mo>&lsqb;</mo>
<mfrac>
<mrow>
<msup>
<mi>S</mi>
<mo>&prime;</mo>
</msup>
<mi>N</mi>
</mrow>
<mrow>
<mi>&mu;</mi>
<mi>V</mi>
</mrow>
</mfrac>
<mo>&rsqb;</mo>
<mo>|</mo>
<msup>
<mo>|</mo>
<mn>2</mn>
</msup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>12</mn>
<mo>)</mo>
</mrow>
</mrow>
It can be converted into 2n × n system of linear equations (13) formula：
<mrow>
<mo>&lsqb;</mo>
<mfrac>
<mi>L</mi>
<mrow>
<msub>
<mi>&mu;I</mi>
<mrow>
<mi>n</mi>
<mo>&times;</mo>
<mi>n</mi>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>&rsqb;</mo>
<msup>
<mi>V</mi>
<mo>&prime;</mo>
</msup>
<mo>=</mo>
<mo>&lsqb;</mo>
<mfrac>
<mrow>
<msup>
<mi>S</mi>
<mo>&prime;</mo>
</msup>
<mi>N</mi>
</mrow>
<mrow>
<mi>&mu;</mi>
<mi>V</mi>
</mrow>
</mfrac>
<mo>&rsqb;</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>13</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein S '=diag (s '1,s′2,…,s′n) represent with step 3) in gained summit signal s 'iIt is used as diagonal entry
Matrix, n is the number on geometrical model summit, and L is the Laplacian Matrix of original geometry model, In×nFor n rank unit matrixs, N is
The normal direction matrix of original geometry model vertices, V is the position vector matrix of original geometry model vertices, and μ is the power of point constraint
Repeated factor, the constraint weight of border vertices is 1, and the constraint weight of internal vertex is 0.1.
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| CN110120069A (en) * | 2019-03-26 | 2019-08-13 | 深圳大学 | Triangle gridding filtering method and terminal device based on Laplace operator |
| CN112053296A (en) * | 2020-08-25 | 2020-12-08 | 五邑大学 | Robust geometric mean filtering grid denoising method |
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Cited By (5)
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| CN108447038A (en) * | 2018-03-27 | 2018-08-24 | 北京工业大学 | A kind of mesh denoising method based on non local full variation operator |
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| CN110120069A (en) * | 2019-03-26 | 2019-08-13 | 深圳大学 | Triangle gridding filtering method and terminal device based on Laplace operator |
| CN110120069B (en) * | 2019-03-26 | 2023-05-23 | 深圳大学 | Triangular mesh filtering method based on Laplacian operator and terminal equipment |
| CN112053296A (en) * | 2020-08-25 | 2020-12-08 | 五邑大学 | Robust geometric mean filtering grid denoising method |
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