CN108510591A - A kind of improvement Poisson curve reestablishing method based on non-local mean and bilateral filtering - Google Patents
A kind of improvement Poisson curve reestablishing method based on non-local mean and bilateral filtering Download PDFInfo
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Abstract
The present invention provides a kind of improvement Poisson curve reestablishing method based on non-local mean and bilateral filtering.The improvement Poisson curve reestablishing method based on non-local mean and bilateral filtering includes the following steps：Data prediction：It obtains original point cloud data and builds point cloud data collection, carrying out non-local mean to point cloud data collection is filtered；Curve reestablishing：Reconstruction curved surface is carried out after carrying out bilateral filtering processing three times to the point cloud data collection after being filtered in data prediction step.The beneficial effects of the invention are as follows：The shown improvement Poisson curve reestablishing method based on non-local mean and bilateral filtering, the shortcomings that for traditional Poisson algorithm, introduce non-local mean and bilateral filtering algorithm, realize the controllable constraint of the noise filtering to model surface, realize that better details is kept while removing noise, to improve curve reestablishing precision.
Description
Technical field
The invention belongs to point cloud surfaces to rebuild field, more particularly to a kind of changing based on non-local mean and bilateral filtering
Into Poisson curve reestablishing method.
Background technology
Point cloud data refers to utilizing laser measuring equipment or spatial digitizer, and it is vertical to obtain objective body surface from real world
Volume data can accurately express testee surface information with it.And due to human interference, scanner self-defect, object
Surface smooth degree is different, and the three-dimensional data of acquisition usually carries much noise, is unfavorable for data processing, after seriously affecting reconstruction
Model accuracy, or even cause model deformation.Poisson surface algorithm for reconstructing is compared with other algorithms, it is by combining global drawn game
The advantages of portion's approximating method, noise that can be in effectively smooth dispersion point cloud, but exist and be easy excess smoothness model detail characteristic
It is insufficient.
Invention content
It is a kind of based on non-local mean and bilateral filtering it is an object of the invention in view of the drawbacks of the prior art, provide
Poisson curve reestablishing method is improved, the shortcomings that for traditional Poisson algorithm, non-local mean and bilateral filtering algorithm is introduced, realizes
Controllable constraint to the noise filtering of model surface realizes that better details is kept, to improve curved surface while removing noise
Reconstruction precision.
Technical scheme is as follows：A kind of improvement Poisson curve reestablishing side based on non-local mean and bilateral filtering
Method includes the following steps：Data prediction：It obtains original point cloud data and builds point cloud data collection, non-office is carried out to point cloud data collection
Portion's mean filter processing；Curve reestablishing：Point cloud data collection after being filtered in data prediction step is carried out bilateral three times
Reconstruction curved surface is carried out after being filtered.
Preferably, in data prediction step, non-local mean is carried out using mean filter function pair point cloud data collection
It is filtered, the expression formula of wherein mean filter function is：
Wherein, B1(i) non-local mean filter function is indicated；I, j is i-th, j-th of the pixel a little concentrated, i, j ∈
I, I are point cloud data set；W (i, j) is weight function；Exp is indicated using natural constant e as the exponential function at bottom；F (j) is indicated
The pixel value of j-th of pixel；Indicate pixel between Gauss weighted euclidean distance, wherein N (i) be with
Image block centered on pixel i, α are the standard deviations of Gaussian kernel, and h is smoothing factor.Wherein 0≤w (i, j)≤1 and
Preferably, include the following steps in curve reestablishing step：
A, Octree topological relation is established, and the point cloud data after being filtered in data prediction step is all added eight
In fork tree；
B, the cubic convolution operation of the gaussian filtering based on spatial distribution is carried out to point cloud data collection, recycles indicator function
Gradient fields are calculated in conjunction with bilateral filtering function；
C, according to the normal direction information of point cloud data collection itself, the curve surface integral of approximate calculation sampled point, and estimate vector field；
D, according to the relationship between indicator function and vector field, Poisson's equation is built, and use Gauss-Seidel matrixes
Iterative manner solves Poisson's equation；
E, it chooses threshold value appropriate to splice the dough sheet of extraction by isosurface extraction, you can obtain resurfacing
Result.
Preferably, in stepb, the expression formula of bilateral filtering function is：
B1(i) non-local mean filter function, B are indicated2(B1(i)) it is bilateral filtering function, i, j are i-th a little concentrated
A, j-th of pixel；N (i) is the image block centered on pixel i；W (i, j) is weight function, and expression formula is：
Wherein, ws(i,j)、wτ(i, j) indicates the spatial simlanty and grey similarity of pixel i and pixel j respectively；
σs、στThe Gaussian kernel standard deviation of metric space similitude and grey similarity is indicated respectively.
Preferably, in the cubic convolution operation for carrying out the gaussian filtering based on spatial distribution to point cloud data collection of step b
In, the value of sampled point p is converted to by spatial neighbor degree and pixel value similarity in conjunction with image by bilateral filtering three times, three times
The expression formula of bilateral filtering process is：
F (p)=F (x, y, z)=(B2(B1(x))·B2(B1(y))·B2(B1(z)))*3,
Wherein x, y, z is the corresponding three-dimensional coordinates of sampled point p, and F (p) is filter function, and F (x, y, z) indicates meaning and F
(p) identical, B2(B1(x))、B2(B1(y))、B2(B1(z)) the bilateral filtering function of the three-dimensional coordinate of respectively corresponding sampled point p.
Preferably, in step b calculates gradient fields step using indicator function combination bilateral filtering function, defining point cloud
The boundary of data acquisition system isIt is χ that point cloud data set, which corresponds to indicator function,MIf point sets indicator function outside curved surface
Value is 0；If it is 1 that point, which in curved surface, sets indicator function value, the gradient of indicator function is the interior law vector that curved surface is put at certain,
Only just there is nonzero value on curved surface, other positions are all zero substantially in space；
It enablesFor the inside surface normal of sampled point p；q0For in point set one pending point, F (q0) indicate about q0's
Filtering, Fp(q0) indicate q0To the translation of p points, by indicator function χMWith obtained by the Surface Method field of line vector field relationship by：
Wherein, ▽ is vector differentiating operator；Gradient fields ▽ (χ can be solved by solving above-mentioned relation formulaM*F)。
Preferably, in step c, by the boundary of point cloud data setIt is divided into different dough sheets, carries out dough sheet integral
Linear summation：
Wherein, s indicates s block dough sheets, κsFor the integral of s block dough sheets, V (q0) indicate q0Vector field.
Preferably, in step d, the limiting value of Gauss-Seidel matrix iterations is the accurate solution of required Poisson's equation.
Technical solution provided by the invention has the advantages that：
1, " details holding and noise cannot effectively be met in point cloud data for the processing of traditional Poisson surface algorithm for reconstructing
Equilibrium problem smoothly ", by adjusting the smoothing factor h of non-local mean, while by adjusting non-local mean and bilateral filter
Gaussian kernel standard deviation α, σ of waves、στ, can reach the equalization point kept to noise smoothing and details -- Gaussian kernel is filtered with standard
Difference is incremented by, and the weight of the neighborhood point cloud at center tapers into, and the smooth effect of noise is more apparent, and the part details of model is also corresponding
It loses；Conversely, details keeps degree higher, false dough sheet is also incremented by therewith caused by noise, therefore, by adjusting Gaussian kernel mark
It is accurate poor, while reaching and smoothly being kept with details, can visually preferably approximate model details, raising Poisson arithmetic accuracy；
2, using non-local mean filtering algorithm and bilateral filtering algorithm, there is better denoising effect, for a cloud
The promotion of data de-noising quality has certain practical value, meanwhile, when defining gradient fields with loud field is estimated, reduce dry
The factor is disturbed, accuracy in computation is improved.
3, it compared with the algorithm for reconstructing of traditional Poisson surface, while more efficient approaching to reality object boundary model, improves
Point cloud boundary extractive technique performance afterwards is stablized, and efficiency is higher.
Description of the drawings
Fig. 1 is that the present invention is based on the signals of the flow of non-local mean and the improvement Poisson curve reestablishing method of bilateral filtering
Figure；
Fig. 2 is involved in the improvement Poisson curve reestablishing method based on non-local mean and bilateral filtering shown in Fig. 1
Octree structure figure based on point cloud model；
Fig. 3 is involved in the improvement Poisson curve reestablishing method based on non-local mean and bilateral filtering shown in Fig. 1
Indicator function simulates schematic diagram.
Specific implementation mode
In order to make the purpose , technical scheme and advantage of the present invention be clearer, with reference to the accompanying drawings and embodiments, right
The present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and
It is not used in the restriction present invention.
The description of specific distinct unless the context otherwise, the present invention in element and component, the shape that quantity both can be single
Formula exists, and form that can also be multiple exists, and the present invention is defined not to this.Although step in the present invention with label into
It has gone arrangement, but is not used to limit the precedence of step, unless expressly stated the order of step or holding for certain step
Based on row needs other steps, otherwise the relative rank of step is adjustable.It is appreciated that used herein
Term "and/or" one of is related to and covers associated Listed Items or one or more of any and all possible groups
It closes.
As shown in Figure 1, the improvement Poisson curved surface weight provided in an embodiment of the present invention based on non-local mean and bilateral filtering
Construction method specifically comprises the following steps：
1, data prediction：It obtains original point cloud data and builds point cloud data collection, point cloud data collection is carried out non local equal
Value filtering processing.
Specifically, in data prediction step, original at random is obtained by equipment such as spatial digitizer or laser measurements
Beginning point cloud data, each original point cloud data contain mass data noise while including abundant image information.
Non-local mean is carried out using mean filter function pair point cloud data collection to be filtered, wherein mean filter function
Expression formula is：
Wherein, B1(i) non-local mean filter function is indicated；I, j is i-th, j-th of the pixel a little concentrated, i, j ∈
I, I are point cloud data set；W (i, j) is weight function；expIt indicates using natural constant e as the exponential function at bottom；F (j) is indicated
The pixel value of j-th of pixel；||N(i)-N(j)||2 2,aIndicate that the Gauss weighted euclidean distance between pixel, wherein N (i) are
Image block centered on pixel i, α are the standard deviations of Gaussian kernel, and h is smoothing factor, wherein 0≤w (i, j)≤1 and
2, curve reestablishing：Point cloud data collection after being filtered in data prediction step is carried out at bilateral filtering three times
Reconstruction curved surface is carried out after reason.
Specifically, curve reestablishing step includes the following steps：
A, Octree topological relation is established, and the point cloud data after being filtered in data prediction step is all added eight
In fork tree.
Specifically, as shown in Fig. 2, in step a, classification processing is carried out in order to facilitate point cloud data, according to sampled point it
Between distance build Octree topological relation, first by and by point cloud number after being filtered in data prediction step
According in all addition Octrees.
B, the cubic convolution operation of the gaussian filtering based on spatial distribution is carried out to point cloud data collection, recycles indicator function
Gradient fields are calculated in conjunction with bilateral filtering function.
Specifically, in stepb, carrying out secondary filtering to point cloud data, and further remove data noise.In order to obtain
Better filter effect is obtained, bilateral filtering function is built, expression formula is：
Wherein, B1(i) non-local mean filter function, B are indicated2(B1(i)) it is bilateral filtering function, i, j are a little to concentrate
I-th, j-th of pixel；N (i) is the image block centered on pixel i；W (i, j) is weight function, and expression formula is：
Wherein, ws(i,j)、wτ(i, j) indicates the spatial simlanty and grey similarity of pixel i and pixel j respectively；
σs、στThe Gaussian kernel standard deviation of metric space similitude and grey similarity is indicated respectively.
It should be noted that when distance is larger between pixel, ws(i, j) is reduced, when gray scale difference is larger, wτ(i, j) subtracts
Small, corresponding weight value function w also changes therewith.
Moreover, carrying out the cubic convolution operation of the gaussian filtering based on spatial distribution to point cloud data collection, it is as based on institute
Bilateral filtering function is stated, the value of sampled point p is converted to spatial neighbor degree and pixel in conjunction with image by bilateral filtering three times
It is worth similarity, the expression formula of bilateral filtering process is three times：
F (p)=F (x, y, z)=(B2(B1(x))·B2(B1(y))·B2(B1(z)))*3,
Wherein x, y, z is the corresponding three-dimensional coordinates of sampled point p, and F (p) is filter function, and F (x, y, z) indicates meaning and F
(p) identical, B2(B1(x))、B2(B1(y))、B2(B1(z)) the bilateral filtering function of the three-dimensional coordinate of respectively corresponding sampled point p.
Further, in the step of calculating gradient fields using indicator function combination bilateral filtering function, point cloud data is defined
The boundary of set isIt is χ that point cloud data set, which corresponds to indicator function,MIf point outside curved surface, set indicator function value as
0；If point in curved surface, sets indicator function value as 1, moreover, as shown in figure 3, the gradient of indicator function is curved surface in certain point
Interior law vector, only just have nonzero value on curved surface, other positions are all zero substantially in space.
It enablesFor the inside surface normal of sampled point p；q0For in point set one pending point, F (q0) indicate about q0's
Filtering, Fp(q0) indicate q0To the translation of p points, by indicator function χMWith obtained by the Surface Method field of line vector field relationship by：
Wherein, ▽ is vector differentiating operator；Gradient fields ▽ (χ can be solved by solving above-mentioned relation formulaM*F)。
C, according to the normal direction information of point cloud data collection itself, the curve surface integral of approximate calculation sampled point, and estimate vector field.
Specifically, in step c, the estimation of vector field is carried out, i.e., according to the normal direction information of point set itself, approximate calculation is adopted
The curve surface integral of sampling point.By the boundary of point cloud data setIt is divided into different dough sheets, the linear of dough sheet integral is carried out and asks
With：
Wherein, s indicates s block dough sheets, κsFor the integral of s block dough sheets, V (q0) indicate q0Vector field.
D, according to the relationship between indicator function and vector field, Poisson's equation is built, and use Gauss-Seidel matrixes
Iterative manner solves Poisson's equation.
Specifically, step b formula it is found thatWith V (q0) approximately equal, it is assumed that
Both sides take Graded factor to obtain simultaneously：
Then,Poisson's equation can be obtained：Cause
Curve reestablishing is converted into solving Poisson's equation by this.Moreover, in Poisson's equation solution procedure, using sparse symmetric system so that
The process of the minimum value of solution indicator function, which is converted to, seeks general formula：
Moreover, Poisson's equation equation is solved using Gauss-Seidel matrix iteration modes, its limiting value of the matrix iteration
It is the accurate solution of required Poisson's equation.
E, it chooses threshold value appropriate to splice the dough sheet of extraction by isosurface extraction, you can obtain resurfacing
Result.
It is obvious to a person skilled in the art that invention is not limited to the details of the above exemplary embodiments, Er Qie
In the case of without departing substantially from spirit or essential attributes of the invention, the present invention can be realized in other specific forms.Therefore, no matter
From the point of view of which point, the present embodiments are to be considered as illustrative and not restrictive, and the scope of the present invention is by appended power
Profit requires rather than above description limits, it is intended that all by what is fallen within the meaning and scope of the equivalent requirements of the claims
Variation is included within the present invention.Any reference signs in the claims should not be construed as limiting the involved claims.
In addition, it should be understood that although this specification is described in terms of embodiments, but not each embodiment is only wrapped
Containing an independent technical solution, this description of the specification is merely for the sake of clarity, and those skilled in the art should
It considers the specification as a whole, the technical solutions in the various embodiments may also be suitably combined, forms those skilled in the art
The other embodiment being appreciated that.
Claims (8)
1. a kind of improvement Poisson curve reestablishing method based on non-local mean and bilateral filtering, it is characterised in that：Including as follows
Step：
Data prediction：It obtains original point cloud data and builds point cloud data collection, non-local mean filtering is carried out to point cloud data collection
Processing；
Curve reestablishing：It is laggard that bilateral filtering processing three times is carried out to the point cloud data collection after being filtered in data prediction step
Row rebuilds curved surface.
2. a kind of improvement Poisson curve reestablishing method based on non-local mean and bilateral filtering according to claim 1,
It is characterized in that：In data prediction step, non-local mean filtering is carried out using mean filter function pair point cloud data collection
Processing, the expression formula of wherein mean filter function are：
Wherein, B1(i) non-local mean filter function is indicated；I, j is i-th, j-th of the pixel a little concentrated, and i, j ∈ I, I are
Point cloud data set；W (i, j) is weight function；Exp is indicated using natural constant e as the exponential function at bottom；F (j) is indicated j-th
The pixel value of pixel；Indicate that the Gauss weighted euclidean distance between pixel, wherein N (i) are with pixel
Image block centered on point i, α are the standard deviations of Gaussian kernel, and h is smoothing factor, wherein 0≤w (i, j)≤1 and
3. a kind of improvement Poisson curve reestablishing method based on non-local mean and bilateral filtering according to claim 1,
It is characterized in that：Include the following steps in curve reestablishing step：
A, Octree topological relation is established, and Octree is all added in the point cloud data after being filtered in data prediction step
In；
B, the cubic convolution operation of the gaussian filtering based on spatial distribution is carried out to point cloud data collection, and indicator function is recycled to combine
Bilateral filtering function calculates gradient fields；
C, according to the normal direction information of point cloud data collection itself, the curve surface integral of approximate calculation sampled point, and estimate vector field；
D, according to the relationship between indicator function and vector field, Poisson's equation is built, and use Gauss-Seidel matrix iterations
Mode solves Poisson's equation；
E, it chooses threshold value appropriate to splice the dough sheet of extraction by isosurface extraction, you can obtain the knot of resurfacing
Fruit.
4. a kind of improvement Poisson curve reestablishing method based on non-local mean and bilateral filtering according to claim 3,
It is characterized in that：In stepb, the expression formula of bilateral filtering function is：
Wherein, B1(i) non-local mean filter function, B are indicated2(B1(i)) it is bilateral filtering function, i, j are i-th a little concentrated
A, j-th of pixel；N (i) is the image block centered on pixel i；W (i, j) is weight function, and expression formula is：
W (i, j)=ws(i,j)wτ(i,j)
Wherein, ws(i,j)、wτ(i, j) indicates the spatial simlanty and grey similarity of pixel i and pixel j respectively；σs、στ
The Gaussian kernel standard deviation of metric space similitude and grey similarity is indicated respectively.
5. a kind of improvement Poisson curve reestablishing method based on non-local mean and bilateral filtering according to claim 4,
It is characterized in that：In the cubic convolution operation for carrying out the gaussian filtering based on spatial distribution to point cloud data collection of step b, lead to
It crosses bilateral filtering three times and the value of sampled point p is converted into spatial neighbor degree and pixel value similarity in conjunction with image, it is bilateral three times
The expression formula of filtering is：
F (p)=F (x, y, z)=(B2(B1(x))·B2(B1(y))·B2(B1(z)))*3,
Wherein x, y, z is the corresponding three-dimensional coordinates of sampled point p, and F (p) is filter function, and F (x, y, z) indicates meaning and F (p) phases
Together, B2(B1(x))、B2(B1(y))、B2(B1(z)) the bilateral filtering function of the three-dimensional coordinate of respectively corresponding sampled point p.
6. a kind of improvement Poisson curve reestablishing method based on non-local mean and bilateral filtering according to claim 5,
It is characterized in that：In step b calculates gradient fields step using indicator function combination bilateral filtering function, point cloud data is defined
The boundary of set isIt is χ that point cloud data set, which corresponds to indicator function,MIf point outside curved surface, set indicator function value as
0；If it is 1 that point, which in curved surface, sets indicator function value, the gradient of indicator function is the interior law vector that curved surface is put at certain, only
Just there is nonzero value on curved surface, other positions are all zero substantially in space；
It enablesFor the inside surface normal of sampled point p；q0For in point set one pending point, F (q0) indicate about q0Filtering,
Fp(q0) indicate q0To the translation of p points, by indicator function χMWith obtained by the Surface Method field of line vector field relationship by：
Wherein, ▽ is vector differentiating operator；Gradient fields ▽ (χ can be solved by solving above-mentioned relation formulaM*F)。
7. a kind of improvement Poisson curve reestablishing method based on non-local mean and bilateral filtering according to claim 6,
It is characterized in that：In step c, by the boundary of point cloud data setIt is divided into different dough sheets, carries out the line of dough sheet integral
Property summation：
Wherein, s indicates s block dough sheets, κsFor the integral of s block dough sheets, V (q0) indicate q0Vector field.
8. a kind of improvement Poisson curve reestablishing method based on non-local mean and bilateral filtering according to claim 3,
It is characterized in that：In step d, the limiting value of Gauss-Seidel matrix iterations is the accurate solution of required Poisson's equation.
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| CN109118582B (en) * | 2018-09-19 | 2020-06-16 | 东北大学 | Commodity three-dimensional reconstruction system and reconstruction method |
| CN109754459A (en) * | 2018-12-18 | 2019-05-14 | 湖南视觉伟业智能科技有限公司 | It is a kind of for constructing the method and system of human 3d model |
| CN116843563A (en) * | 2023-06-25 | 2023-10-03 | 成都飞机工业（集团）有限责任公司 | Point cloud noise reduction processing method |
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