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CN109934120A - A kind of substep point cloud noise remove method based on space density and cluster - Google Patents

A kind of substep point cloud noise remove method based on space density and cluster Download PDF

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CN109934120A
CN109934120A CN201910125531.6A CN201910125531A CN109934120A CN 109934120 A CN109934120 A CN 109934120A CN 201910125531 A CN201910125531 A CN 201910125531A CN 109934120 A CN109934120 A CN 109934120A
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point cloud
cluster
noise
denoising
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CN109934120B (en
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惠振阳
胡海瑛
程朋根
王乐洋
聂运菊
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East China Institute of Technology
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Abstract

The substep point cloud noise remove method based on space density and cluster that the invention discloses a kind of, it include: S1, its point of the point cloud computing of extraction point cloud total amount of data preset ratio Yun Midu, averag density as entire point cloud data, count its r × r × r cubic space midpoint cloud par Q, using Q as the reference value of space density Denoising Algorithm density threshold, and define threshold value O;S2, each of traversal point cloud data point, seeks the point cloud quantity K in r × r × r cubic space of the point, if K is less than threshold value O, is determined as spotted noise point and removes;If K is more than or equal to threshold value O, retain, to obtain the first denoising point cloud data for eliminating spotted noise point;S3 clusters first denoising point cloud data, reads point cloud data set;S4 counts the point cloud quantity M in each set, if M is less than reference value Q, is determined as tufted noise spot and removes;If M is more than or equal to reference value Q, retain to obtain final denoising result.The present invention can filter out spotted noise and tufted noise simultaneously.

Description

A kind of substep point cloud noise remove method based on space density and cluster
Technical field
The present invention relates to geospatial information system technical fields, more particularly to a kind of based on space density and cluster Substep point cloud noise remove method.
Background technique
Airborne laser radar (LiDAR, Light Detection and Ranging) system is a kind of collection laser ranging skill Art, computer technology, Inertial Measurement Unit (IMU)/DGPS differential position are in the active earth observation systems of one.It should System can not only measure the three-dimensional coordinate of ground object, moreover it is possible to obtain the Reflection intensity information of the laser point.With automation Degree is high, by weather influenced small, data are with short production cycle, precision is high, do not influenced by external condition the advantages that, therefore answered extensively For obtaining spatial surface information.But when it obtains spatial surface information, due to LiDAR system itself or area's environment is surveyed Reason usually contains noise in the point cloud data of acquisition.
Noise spot can be divided into two classes according to its aggregation properties, and the first kind is spotted noise, and spotted noise is divided into a high position again and makes an uproar Sound and low level noise, feature is irregular and discrete be distributed in entirely surveys area.This noise like is since LiDAR system is in Laser emission It is generated when with return apart from exceptional value or having received repeatedly invalid laser diffusion causes;Second class is tufted noise spot, Feature is that a few noise spot is assembled at tufted, this noise like is largely that the institute on flying object is beaten by laser pulse signal It is caused.
Noise spot will cause very big influence to the subsequent processing of point cloud data, such as filter in most of LiDAR point cloud data It is that this hypothesis carries out using local elevation minimum point as ground point in wave algorithm, if low level noise does not remove, will makes Part topographic(al) point is obtained to be mistaken for culture point and be filtered out.In three-dimensional modeling, the presence of noise spot equally also will affect modeling Precision.
Influence in order to avoid noise spot to follow-up works such as point cloud data filtering, modelings, the prior art provides a variety of Denoising method, such as: 1. based on the denoising method of distance, this method is based primarily upon the noise spot characteristic distributions different with available point It is denoised.It is much bigger at a distance from neighbor point compared with available point at a distance from neighbor point since noise spot distribution is at random, thus Settable distance threshold is distinguished and is rejected.2. the denoising method based on mathematical morphology, this method mainly utilize opening operation It is filtered with closed operation, can be used for filtering out noise spot when window size is arranged very small.
But these above-mentioned denoising methods can only all remove partial noise point, and the performance on removal tufted noise is not enough managed Think there are problems that spotted noise and tufted noise can not be filtered out simultaneously.
Summary of the invention
It is an object of the invention to solve the problems, such as that spotted noise and tufted noise can not be filtered out simultaneously, propose that one kind is based on Space density and the substep of cluster point cloud noise remove method.
A kind of substep point cloud noise remove method based on space density and cluster, comprising the following steps:
S1, the point cloud computing of extraction point cloud total amount of data preset ratio its point Yun Midu, using this cloud density as entire The averag density of point cloud data counts its r × r × r cubic space midpoint cloud par Q, denoises Q as space density The reference value of method density threshold, and threshold value O is defined according to the reference value;
S2, each of traversal point cloud data point, seeks the point cloud quantity K in r × r × r cubic space of the point, If K is less than threshold value O, it is determined as spotted noise point and removes;If K is more than or equal to threshold value O, retain, is eliminated a little with obtaining The first denoising point cloud data of shape noise spot;
S3 clusters above-mentioned first denoising point cloud data, reads point cloud data set;
S4 counts the point cloud quantity M in each set, if M is less than reference value Q, is determined as tufted noise spot and removes; If M is more than or equal to reference value Q, retain to obtain final denoising result.
Wherein, the step S1 specifically includes the following steps:
S11, the point cloud computing of extraction point cloud total amount of data 10% its point Yun Midu, to represent being averaged for entire point cloud data Density counts its r × r × r cubic space midpoint cloud par Q, the reference as space density Denoising Algorithm density threshold Value;
S12 defines a r × r × r cubic space, if currently judgement point X1Coordinate is X1、Y1、Z1, then in point X1R The X, Y, Z coordinate at any point meet (1) formula condition in × r × r cubic space range;
S13 will meet X after traversing the point cloud data1, X2…XNThe sum of the point of coordinate condition adds up, at this time the point Par Q of the cloud data packet contained in r × r × r cubic space point is obtained by (2) formula;
Wherein N is 10%, K of the point cloud data point cloud quantityNTo be present in point XNR × r × r cubic space in The sum of point.
Wherein, in the step S2, threshold value O is preferably the 1/4 of reference value Q.
Wherein, the step S3 specifically includes the following steps:
Point cloud quantity in S31, the set I of the first denoising point cloud data of reading, set I at this time is P, constructs first reading Access point x0R × r × r cubic space, and by the point and point x in the region0It is put into the same null set A1In, and will collection Close A1It is deleted from set I, at this time to cluster for the first time, if the points for clustering addition at this time are M1, then set A at this time1Interior new addition M1Coordinate (the x of a point1, y1, z1) meet (3) formula condition;
Wherein k is cluster number, at this time k=1;x0、y0、z0The coordinate of point, remaining point in set I are read in for first Quantity PsFor shown in (4) formula;
Wherein k is cluster number, at this time k=1;MkSet A is added for kth time cluster1Point number;
S32 carries out second and clusters, traverses remaining point in set I, and set A is added in the point that coordinate meets (3) formula1 In, and set A will be added1In M2A point is deleted from set I, at this time set A1In always count M as shown in (5) formula;
S33, judges whether last cluster is a little added set A1, Rule of judgment such as (6) formula, if m > 0, then it represents that Set A is a little added in last time cluster1, then continue to cluster next time, collection be added in the point for meeting (3) formula remaining in set I Close A1In, and the M that will be newly addedkA point is deleted from set I;
S34, circulation step S33 are until m=0, set A at this time1It is that first point for completing cluster converges conjunction in set I, And it is deleted from set I.
Wherein, the step S4 specifically includes the following steps:
S41 judges set A1Point cloud quantity whether be greater than threshold value, herein the value of threshold value be step S1 in reference value Q then will set A if more than threshold value1It is added in empty set B, if it is not, then without the operation;
S42 judges set I point cloud volume residual PsWhether 0 is greater than, if so, step S31-S34 is repeated, if it is not, then calculating Method terminates, and final point cloud data is classified as set A1, set A2... set AiThe set of several difference cloud quantity, midpoint Set B is added in the set that cloud quantity is greater than threshold value, and set B is then the point cloud data not comprising tufted noise.
The substep point cloud noise remove method based on space density and cluster provided according to the present invention, this method use former Beginning point cloud data is less than effective dot density and cluster using spotted noise density according to the noise spot characteristic different with available point Shape noise aggregates quantity is less than the characteristics of available point aggregation quantity, first removes spotted noise based on space density, then based on cluster Tufted noise is further removed, thus realize substep removal spotted noise and tufted noise, our experiments show that, this method can not only Above two noise like is enough effectively filtered out, but also the not misjudged rejecting of available point can be protected, obtains smaller denoising error, Shandong Stick is higher.
Detailed description of the invention
The above-mentioned and/or additional aspect and advantage of the embodiment of the present invention are from the description of the embodiment in conjunction with the following figures It will be apparent and be readily appreciated that, in which:
Fig. 1 is according to the substep point cloud noise remove method provided in an embodiment of the present invention based on space density and cluster Flow chart;
Fig. 2 is experimental data view, wherein (a) samp21 view;(b) samp24 view;(c) samp41 view;
Fig. 3 is three groups of experimental datas denoising result comparison diagram twice, wherein (a) samp21 denoising result comparison diagram twice; (b) samp24 denoising result comparison diagram twice;(c) samp41 denoising result comparison diagram twice;
Fig. 4 is samp21 denoising result comparison diagram, wherein (a) initial data;(b) SOR denoising method result;(c) this hair The result of bright providing method;
Fig. 5 is samp24 denoising result comparison diagram, wherein (a) initial data;(b) SOR denoising method result;(c) this hair The result of bright providing method;
Fig. 6 is samp41 denoising result comparison diagram, wherein (a) initial data;(b) SOR denoising method result;(c) this hair The result of bright providing method.
Specific embodiment
In order to make the object, technical scheme and advantages of the embodiment of the invention clearer, below in conjunction with the embodiment of the present invention In attached drawing, technical scheme in the embodiment of the invention is clearly and completely described, it is clear that described embodiment is A part of the embodiment of the present invention, instead of all the embodiments.Based on the embodiments of the present invention, those of ordinary skill in the art Every other embodiment obtained without making creative work, shall fall within the protection scope of the present invention.
Referring to Fig. 1, the substep point cloud noise remove method provided in an embodiment of the present invention based on space density and cluster, Including step S1~S4:
S1, the point cloud computing of extraction point cloud total amount of data preset ratio its point Yun Midu, using this cloud density as entire The averag density of point cloud data counts its r × r × r cubic space midpoint cloud par Q, denoises Q as space density The reference value of method density threshold, and threshold value O is defined according to the reference value;
Wherein, for spotted noise compared with available point cloud, distribution is discrete and irregular, close using the settable space of the feature The small spotted noise of density is removed by degree threshold value.Due to different point cloud datas, its cloud density is different, in order to be applicable in In the point cloud data of various difference cloud density, before carrying out space density Denoising Algorithm, the default ratio of first extraction point cloud total amount of data Point cloud computing its point Yun Midu of example, to represent the averag density of entire point cloud data, it is preferred that first extraction point cloud total amount of data 10% point cloud computing its point Yun Midu, to represent the averag density of entire point cloud data.
Specifically, step S1 includes step S11~S13:
S11, the point cloud computing of extraction point cloud total amount of data 10% its point Yun Midu, to represent being averaged for entire point cloud data Density counts its r × r × r cubic space midpoint cloud par Q, the reference as space density Denoising Algorithm density threshold Value;
S12 defines a r × r × r cubic space, if currently judgement point X1Coordinate is X1、Y1、Z1, then in point X1R The X, Y, Z coordinate at any point meet (1) formula condition in × r × r cubic space range;
S13 will meet X after traversing the point cloud data1, X2…XNThe sum of the point of coordinate condition adds up, at this time the point Par Q of the cloud data packet contained in r × r × r cubic space point is obtained by (2) formula;
Wherein N is 10%, K of the point cloud data point cloud quantityNTo be present in point XNR × r × r cubic space in The sum of point.
S2, each of traversal point cloud data point, seeks the point cloud quantity K in r × r × r cubic space of the point, If K is less than threshold value O, it is determined as spotted noise point and removes;If K is more than or equal to threshold value O, retain, is eliminated a little with obtaining The first denoising point cloud data of shape noise spot;
Wherein, when the value of threshold value O is excessive, to will cause II class error excessive, too small, and ideal denoising effect may be not achieved Fruit.Preferably, threshold value O is the 1/4 of reference value Q.
S3 clusters above-mentioned first denoising point cloud data, reads point cloud data set;
Wherein, after the denoising of S1~S2, part point cloud data still has tufted noise, because of tufted noise density It with available point similar density, only can not effectively be distinguished using this characteristic of density, therefore the purpose of second stage denoising exists In the remaining tufted noise of removal.
The thought of Denoising Algorithm based on cluster is: multiple points being closer being placed in a set, may finally be incited somebody to action Entire point cloud data is divided into multiple set according to distance, while can learn the point cloud quantity for including in each set.Due to cluster Shape noise spot is largely caused by being beaten on flying object as laser pulse signal, so the quantity of the point of its aggregation is much small In the aggregation quantity of available point.It sets one and gathers the point cloud amount threshold for including, it can be by tufted noise and other available points It distinguishes.
Specifically, step S3 includes step S31~S34:
Point cloud quantity in S31, the set I of the first denoising point cloud data of reading, set I at this time is P, constructs first reading Access point x0R × r × r cubic space, and by the point and point x in the region0It is put into the same null set A1In, and will collection Close A1It is deleted from set I, at this time to cluster for the first time, if the points for clustering addition at this time are M1, then set A at this time1Interior new addition M1Coordinate (the x of a point1, y1, z1) meet (3) formula condition;
Wherein k is cluster number, at this time k=1;x0、y0、z0The coordinate of point, remaining point in set I are read in for first Quantity PsFor shown in (4) formula;
Wherein k is cluster number, at this time k=1;MkSet A is added for kth time cluster1Point number;
S32 carries out second and clusters, traverses remaining point in set I, and set A is added in the point that coordinate meets (3) formula1 In, and set A will be added1In M2A point is deleted from set I, at this time set A1In always count M as shown in (5) formula;
S33, judges whether last cluster is a little added set A1, Rule of judgment such as (6) formula, if m > 0, then it represents that Set A is a little added in last time cluster1, then continue to cluster next time, collection be added in the point for meeting (3) formula remaining in set I Close A1In, and the M that will be newly addedkA point is deleted from set I;
S34, circulation step S33 are until m=0, set A at this time1It is that first point for completing cluster converges conjunction in set I, And it is deleted from set I.
S4 counts the point cloud quantity M in each set, if M is less than reference value Q, is determined as tufted noise spot and removes; If M is more than or equal to reference value Q, retain to obtain final denoising result.
Wherein, step S4 specifically includes step S41~42:
S41 judges set A1Point cloud quantity whether be greater than threshold value, herein the value of threshold value be step S1 in reference value Q then will set A if more than threshold value1It is added in empty set B, if it is not, then without the operation;
S42 judges set I point cloud volume residual PsWhether 0 is greater than, if so, step S31-S34 is repeated, if it is not, then calculating Method terminates, and final point cloud data is classified as set A1, set A2... set AiThe set of several difference cloud quantity, midpoint Set B is added in the set that cloud quantity is greater than threshold value, and set B is then the point cloud data not comprising tufted noise.
In order to verify the validity the present embodiment provides method, the three groups of data provided in the website ISPRS is selected to be tried Test (https: //www.itc.nl/isprs/wgIII-3/filtertest/downloadsites/).The test point cloud data It is obtained by the airborne LiDAR system of OptechALTM, puts spacing between 1-1.5m.Three groups of test samples include different landform Feature, such as sample samp21 includes bridge, asymmetric buildings object, short vegetation etc., totally 12960 points;Sample samp24 It include building and terrace relief, totally 7492 points;Sample samp41 includes data blank, asymmetric buildings object, Totally 11231 points.This three groups of sample datas all include high-order noise and low level noise, spotted noise and tufted noise, such as Shown in Fig. 2.Therefore, be conducive to examine the validity and robustness of the method for the present invention.
The above-mentioned substep point cloud noise remove method based on space density and cluster is broadly divided into two stages, first rank Thought of the section based on space density removes spotted noise;Thought of the second stage based on cluster, not with increase II class error be Cost, the tufted noise remove that first stage is not removed.Judgment criteria is by I class error (T1), II class error (T2) and it is total Error (T3) determine.Specific formula is as shown in (7) formula.
Wherein, a is that noise spot mistake is determined as the points of available point, and b is that noise spot is appropriately determined points for noise spot, C is that available point mistake is determined as the points of noise spot, and d is that available point is appropriately determined points for available point.
Table 1 is that three groups of experimental datas denoise and the precision evaluation result of second denoising for the first time:
The denoising for the first time of table 1 and second denoising precision evaluation
As can be seen from the above data, the I class error after second denoising in three groups of experimental datas is effectively reduced, Overall error slightly reduces.Wherein two groups of data of samp21 and samp24 reduce I class in the case where its II class error does not increase Error, although the II class error of samp41 is risen, its I class error is largely reduced, and overall error also obtains It reduces.The I class error of two groups of experimental datas of samp21 and samp41 is because in first denoising with the presence of biggish reduction The reduction degree of the tufted noise spot not removed, I class error of samp24 experimental group is smaller, is because most of noise is dotted Noise has obtained comparatively ideal effect in first denoising.Comprehensive three groups of quality evaluation of the experimental data are as a result, it can be found that secondary go I class error can be effectively reduced as far as possible in the case where guaranteeing that II class error does not increase by making an uproar.
Effect picture comparison after three groups of experimental datas denoise twice is as shown in Figure 3.
It is denoised by three groups of experimental datas samp21, samp24 and samp41 and is gone for the first time it can be seen from comparison diagram twice The tufted noise not removed after making an uproar can be effectively removed by second of denoising, and available point is not by significantly sacrificing.
Using the included Statistical of Cloud Compare software (https: //www.danielgm.net/cc/) OutlierRemoval (SOR) denoising method is compared, and the principle of SOR denoising method is: asking judgement point to its arest neighbors Certain distance averages are more than that the overall a certain range of point of point cloud distance average is used as noise spot by the average value of the distance of point Removal.Fig. 4, Fig. 5 and Fig. 6 are that three groups of experimental datas use SOR denoising method and comparative result figure of the invention.
Initial data is organized by Fig. 4, Fig. 5 and Fig. 6 (a) and (b) group uses the data comparison of SOR denoising method, can be seen SOR denoising method can be effectively removed spotted noise out, but not can be removed tufted noise.Pass through Fig. 4, Fig. 5 and Fig. 6 (a) Group initial data, (b) group are compared using result of the data of SOR denoising method and (c) group method provided by the invention, can be with It was found that method provided by the invention can not only remove spotted noise, moreover it is possible to be effectively removed tufted noise.
Table 2 is the error comparison of SOR denoising method and method provided by the invention.It can be seen from Table 2 that the denoising side SOR II class error of method is big compared with II class error of method provided by the invention, and II class error shows that more greatly denoising dynamics is bigger, is removing Many available points are also determined as that noise spot is removed while more noises;I class error of method provided by the invention is compared with SOR I class error of denoising method is small, and the smaller noise spot ratio for showing removal of I class error is bigger.It is seen in conjunction with the two, SOR denoising method It cannot be removed effectively tufted noise, and can be easy excessively to remove available point, and method provided by the invention can not only remove tufted Noise, moreover it is possible to available point be protected not removed excessively.
The error of 2 SOR denoising method of table and method provided by the invention compares
Above-mentioned experiment show method provided by the invention can effectively remove the spotted noise in Various Complex landform and Tufted noise, and available point will not be filtered out, pre-existing topography is destroyed.It can also be in the comparison with SOR denoising method Find out, method provided by the invention can obtain smaller denoising error, and robustness is higher.
To sum up, the substep point cloud noise remove method based on space density and cluster provided according to the present invention, this method Using original point cloud data, according to the noise spot characteristic different with available point, it is less than effective dot density using spotted noise density, And tufted noise aggregates quantity is less than the characteristics of available point aggregation quantity, first removes spotted noise, then base based on space density Tufted noise is further removed in cluster, thus realize substep removal spotted noise and tufted noise, our experiments show that, this method Above two noise like can not only be effectively filtered out, but also the not misjudged rejecting of available point can be protected, obtains smaller denoising Error, robustness are higher.
In the description of this specification, reference term " one embodiment ", " some embodiments ", " example ", " specifically show The description of example " or " some examples " etc. means specific features, structure, material or spy described in conjunction with this embodiment or example Point is included at least one embodiment or example of the invention.In the present specification, schematic expression of the above terms are not Centainly refer to identical embodiment or example.Moreover, particular features, structures, materials, or characteristics described can be any One or more embodiment or examples in can be combined in any suitable manner.
Although an embodiment of the present invention has been shown and described, it will be understood by those skilled in the art that: not A variety of change, modification, replacement and modification can be carried out to these embodiments in the case where being detached from the principle of the present invention and objective, this The range of invention is defined by the claims and their equivalents.

Claims (5)

1. a kind of substep point cloud noise remove method based on space density and cluster, which comprises the following steps:
S1, the point cloud computing of extraction point cloud total amount of data preset ratio its point Yun Midu, using this cloud density as entire point cloud The averag density of data counts its r × r × r cubic space midpoint cloud par Q, and Q is close as space density Denoising Algorithm The reference value of threshold value is spent, and threshold value O is defined according to the reference value;
S2, each of traversal point cloud data point, seeks the point cloud quantity K in r × r × r cubic space of the point, if K Less than threshold value O, then it is determined as spotted noise point and removes;If K is more than or equal to threshold value O, retain, eliminates dotted make an uproar to obtain The first denoising point cloud data of sound point;
S3 clusters above-mentioned first denoising point cloud data, reads point cloud data set;
S4 counts the point cloud quantity M in each set, if M is less than reference value Q, is determined as tufted noise spot and removes;If M More than or equal to reference value Q, then retain to obtain final denoising result.
2. the substep point cloud noise remove method according to claim 1 based on space density and cluster, which is characterized in that The step S1 specifically includes the following steps:
S11, the point cloud computing of extraction point cloud total amount of data 10% its point Yun Midu, to represent the average close of entire point cloud data Degree, counts its r × r × r cubic space midpoint cloud par Q, the reference value as space density Denoising Algorithm density threshold;
S12 defines a r × r × r cubic space, if currently judgement point X1Coordinate is X1、Y1、Z1, then in point X1R × r × The X, Y, Z coordinate at any point meet (1) formula condition in r cubic space range;
S13 will meet X after traversing the point cloud data1, X2…XNThe sum of the point of coordinate condition adds up, at this time this cloud number It is obtained according to the par Q for being contained in r × r × r cubic space point by (2) formula;
Wherein N is 10%, K of the point cloud data point cloud quantityNTo be present in point XNR × r × r cubic space in point Sum.
3. the substep point cloud noise remove method according to claim 2 based on space density and cluster, which is characterized in that In the step S2, threshold value O is the 1/4 of reference value Q.
4. the substep point cloud noise remove method according to claim 3 based on space density and cluster, which is characterized in that The step S3 specifically includes the following steps:
Point cloud quantity in S31, the set I of the first denoising point cloud data of reading, set I at this time is P, constructs first reading point x0R × r × r cubic space, and by the point and point x in the region0It is put into the same null set A1In, and will set A1 It is deleted from set I, at this time to cluster for the first time, if the points for clustering addition at this time are M1, then set A at this time1The M being inside newly added1 Coordinate (the x of a point1, y1, z1) meet (3) formula condition;
Wherein k is cluster number, at this time k=1;x0、y0、z0The coordinate of point is read in for first, the number of remaining point in set I Measure PsFor shown in (4) formula;
Wherein k is cluster number, at this time k=1;MkSet A is added for kth time cluster1Point number;
S32 carries out second and clusters, traverses remaining point in set I, and set A is added in the point that coordinate meets (3) formula1In, and Set A will be added1In M2A point is deleted from set I, at this time set A1In always count M as shown in (5) formula;
S33, judges whether last cluster is a little added set A1, Rule of judgment such as (6) formula, if m > 0, then it represents that upper primary Set A is a little added in cluster1, then continue to cluster next time, set A be added in the point for meeting (3) formula remaining in set I1In, And the M that will be newly addedkA point is deleted from set I;
S34, circulation step S33 are until m=0, set A at this time1It is that first point for completing cluster converges conjunction in set I, and Through being deleted from set I.
5. the substep point cloud noise remove method according to claim 4 based on space density and cluster, which is characterized in that The step S4 specifically includes the following steps:
S41 judges set A1Point cloud quantity whether be greater than threshold value, herein the value of threshold value be step S1 in reference value Q, if It, then will set A greater than threshold value1It is added in empty set B, if it is not, then without the operation;
S42 judges set I point cloud volume residual PsWhether 0 is greater than, if so, step S31-S34 is repeated, if it is not, then algorithm knot Beam, final point cloud data are classified as set A1, set A2... set AiThe set of several difference cloud quantity, midpoint cloud number Set B is added in the set that amount is greater than threshold value, and set B is then the point cloud data not comprising tufted noise.
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