CN115880189B - Multi-beam point cloud filtering method for submarine topography - Google Patents
Multi-beam point cloud filtering method for submarine topography Download PDFInfo
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Abstract
The application belongs to the technical field of ocean mapping and exploration and underwater acoustic signal processing, and provides a multi-beam point cloud filtering method for submarine topography, which comprises the following steps: s1, constructing an original multi-beam point cloud set based on original multi-beam sounding data; s2, carrying out trend surface filtering on the original multi-beam point cloud set to obtain a first multi-beam point cloud set; s3, carrying out combined filtering based on dynamic radius filtering and density clustering on the first multi-beam point cloud set to obtain a submarine topography point cloud set; s4, generating a submarine three-dimensional terrain model based on the submarine topography point cloud set. According to the submarine topography multi-beam point cloud filtering method, aiming at specific data characteristics of multi-beam sounding data, the edge beam filtering effect is improved, meanwhile, reservation of edge topography details and processing speed of mass point cloud data are considered, and complementary advantages and organic combination of various algorithms are achieved.
Description
Technical Field
The application belongs to the technical field of marine mapping and exploration and underwater acoustic signal processing, and particularly provides a submarine topography multi-beam point cloud filtering method.
Background
The multi-beam sounding system is one of the most advanced marine survey measuring instruments at present. The system expands the traditional sounding technology from original points and lines to surfaces, and further develops stereo sounding and automatic imaging. Its appearance has profoundly changed the investigation and research mode in the field of marine disciplines and the quality of the final results. The method has the advantages of large coverage, high speed, high precision and efficiency, digital recording and the like, and is widely applied to the field of marine investigation and mapping.
In the multi-beam measurement process, due to the influence of instrument self-noise, sea condition factors, unreasonable equipment parameter setting and marine organisms, more noise points exist in multi-beam sounding data, and the authenticity expression of submarine topography is seriously influenced. In order to obtain the real submarine topography, the multi-beam data must be filtered to eliminate false signals, recover and retain real information. The traditional manual filtering process carries out the removal of coarse data according to the experience of operators, has higher reliability, but has larger workload and lower filtering efficiency, and is gradually replaced by automatic filtering based on a filtering algorithm at present.
The conventional algorithm for filtering the multi-beam sounding data comprises a trend surface filtering method and a point cloud denoising method based on radius filtering. The trend surface filtering method is simple to operate and is very suitable for flat terrain, but edge beam point clouds are sparse, so that the filtering is incomplete; the point cloud denoising method based on radius filtering has the advantages of high processing speed, strong universality and stable denoising effect, but due to the characteristics of the multi-beam sounding system, the difference between the point cloud density of the central beam and the point cloud density of the edge beam is large, so that the method has the defects of incorrect deletion of real terrain points and serious detail loss, and the method has low precision in processing complex submarine terrains.
Disclosure of Invention
The purpose of the application is to solve the problems existing in the prior art and provide a submarine topography multi-beam point cloud filtering method which takes the filtering precision and the processing speed into consideration.
The embodiment of the application can be realized through the following technical scheme:
a multi-beam point cloud filtering method for submarine topography comprises the following steps:
s1, constructing an original multi-beam point cloud set based on original multi-beam sounding data;
s2, carrying out trend surface filtering on the original multi-beam point cloud set to obtain a first multi-beam point cloud set;
s3, carrying out combined filtering based on dynamic radius filtering and density clustering on the first multi-beam point cloud set to obtain a submarine topography point cloud set;
s4, generating a submarine three-dimensional terrain model based on the submarine topography point cloud set.
Specifically, step S2 further includes the steps of:
s21, establishing a trend surface model of the submarine topography based on the following steps:
wherein, the liquid crystal display device comprises a liquid crystal display device,
for trend surface model functions of submarine topography +.>
For measuring point plane coordinates, < >>
For measuring point depth->
Is a polynomial surface coefficient;
s22, changing the formula (1) into a matrix form of the formula (2):
wherein, the liquid crystal display device comprises a liquid crystal display device,
，/>
for the model coefficient matrix>
Is an observation depth matrix;
s23, based on three-dimensional coordinates of each discrete measuring point in the original multi-beam point cloud set, solving the formula (3) by using a least square method:
s24, traversing each discrete measuring point of the original multi-beam point cloud set, and determining the discrete measuring points belonging to the first multi-beam point cloud set based on the step (4) to obtain the first multi-beam point cloud set:
wherein, the liquid crystal display device comprises a liquid crystal display device,
respectively the +.f in the original multi-beam point cloud set>
Three-dimensional coordinates of discrete measuring points +.>
Is based on->
Mean square error determined by depths of a plurality of discrete measuring points in the neighborhood of the discrete measuring points, +.>
Is a trend surface filter coefficient.
Preferably, the said
。
Specifically, step S3 further includes the steps of:
s31, classifying each discrete measuring point in the first multi-beam point cloud set into a receiving measuring point and a calibration measuring point based on dynamic radius filtering, and classifying the receiving measuring point into a submarine topography point cloud set;
s32, carrying out density clustering on the calibration measuring points, and classifying the calibration measuring points with the density clustering result of non-noise into a submarine topography point cloud set.
Preferably, the dynamic radius filtering is performed based on the formula (5):
wherein, the liquid crystal display device comprises a liquid crystal display device,
for the number of discrete measuring points in the first multi-beam point cloud set, +.>
For the serial numbers of each discrete measuring point in the first multi-beam point cloud set,/for the serial numbers of each discrete measuring point in the first multi-beam point cloud set>
For the starting radius filter point threshold, < >>
In +.>
The number of discrete measuring points contained in the filter radius of the discrete measuring points, +.>
Is->
Is included in the threshold transform coefficients of (a).
Preferably, the said
Determining based on formula (6):
wherein, the liquid crystal display device comprises a liquid crystal display device,
is the first multi-beam point cloud set +.>
Neighborhood distance of discrete measuring points, +.>
The mean value of neighborhood distances of all discrete measuring points in the first multi-beam point cloud set is>
The neighborhood distance of any one discrete measuring point in the first multi-beam point cloud set is smaller than +.>
Is a probability of (2). />
Specifically, the neighborhood distance of each discrete measurement point is based on the closest proximity of the discrete measurement point to itKAnd determining the average value of the distances of the discrete measuring points.
Preferably, the said
Determining based on the formula (7):
wherein, the liquid crystal display device comprises a liquid crystal display device,
as an error function +.>
Respectively determined by the formula (8) and the formula (9):
preferably, the filter radius is
Wherein->
Is an integer of 1 or more.
The multi-beam point cloud filtering method for the submarine topography has the following advantages:
the filtering method improves various existing filtering algorithms in terms of specific data characteristics of multi-beam sounding data in an organic combination mode, improves the filtering effect of edge beams, simultaneously reserves edge topography details and processes massive point cloud data, and realizes the advantage complementation and organic combination of various algorithms;
according to the filtering method, firstly, multi-beam point cloud preprocessing is carried out by adopting a trend surface method aiming at dense noise, then, an efficient and simple radius filtering mode is adopted aiming at the problem of poor filtering effect of trend surface edge beam point clouds, the filtering effect of the edge beam point clouds is improved, meanwhile, the problem of mistakenly deleting edge topography points in the multi-beam point cloud filtering process of traditional radius filtering is improved, and edge topography details are well reserved through density clustering and dynamic radius threshold setting;
the filtering method replaces the whole point cloud data with the mode of density clustering on the in-doubt data to carry out density clustering, shortens clustering convergence time, ensures the whole efficiency of the algorithm, and is suitable for processing massive multi-beam point cloud data.
Drawings
Fig. 1 is a flowchart of a method of multi-beam point cloud filtering of a seafloor terrain according to an embodiment of the present application;
FIG. 2 shows that the neighborhood distance of any one of the discrete measurement points obtained from the statistics of multi-beam sounding data and from the lognormal distribution is smaller thanLProbability of (2)pRelative toLIs a change in conditions of (2);
FIG. 3 is a flow chart showing the implementation of embodiment 1 of the present application;
FIG. 4 is a schematic illustration of a three-dimensional terrain model of the seafloor obtained according to example 1 of the present application;
FIG. 5 is a schematic illustration of a three-dimensional topography model of the ocean floor obtained using trend surface filtering alone;
FIG. 6 is a schematic representation of a model of three-dimensional topography of the ocean floor obtained using radius filtering alone.
Detailed Description
The present application will be further described below based on preferred embodiments with reference to the accompanying drawings.
In addition, various components on the drawings are enlarged or reduced for ease of understanding, but this is not intended to limit the scope of the present application.
The singular forms also include the plural and vice versa.
In the description of the embodiments of the present application, it should be noted that, if the terms "upper," "lower," "inner," "outer," and the like indicate an azimuth or a positional relationship based on the azimuth or the positional relationship shown in the drawings, or an azimuth or a positional relationship that a product of the embodiments of the present application conventionally puts in use, it is merely for convenience of describing the present application and simplifying the description, and does not indicate or imply that the device or element to be referred to must have a specific azimuth, be configured and operated in a specific azimuth, and therefore should not be construed as limiting the present application. Furthermore, in the description of the present application, the terms first, second, etc. are used herein for distinguishing between different elements, but not necessarily for describing a sequential or chronological order of manufacture, and may not be construed to indicate or imply a relative importance, and their names may be different in the detailed description of the present application and the claims.
The terminology used in this description is for the purpose of describing the embodiments of the present application and is not intended to be limiting of the present application. It should also be noted that unless explicitly stated or limited otherwise, the terms "disposed," "connected," and "connected" should be construed broadly, and may be, for example, fixedly connected, detachably connected, or integrally connected; the two components can be connected mechanically, directly or indirectly through an intermediate medium, and can be communicated internally. The specific meaning of the terms in this application will be specifically understood by those skilled in the art.
The embodiment of the application provides a multi-beam point cloud filtering method for submarine topography, which filters multi-beam sounding data to obtain a point cloud set capable of accurately describing the submarine topography. Fig. 1 is a flowchart of a method for filtering multi-beam point clouds on a submarine topography according to an embodiment of the present application, as shown in fig. 1, the method includes the following steps:
s1, constructing an original multi-beam point cloud set based on original multi-beam sounding data;
s2, carrying out trend surface filtering on the original multi-beam point cloud set to obtain a first multi-beam point cloud set;
s3, carrying out combined filtering based on dynamic radius filtering and density clustering on the first multi-beam point cloud set to obtain a submarine topography point cloud set;
s4, generating a submarine three-dimensional terrain model based on the submarine topography point cloud set.
Step S1 is used for reading and integrating original multi-beam sounding data to construct an original multi-beam point cloud set, wherein the original multi-beam sounding data stores sounding data of a plurality of channels according to beam angles and transmitting and receiving sequences, and extracts sounding data at each measuring point
Plane coordinates and water depth->
The three-dimensional coordinates of each discrete measurement point can be determined. And summarizing the three-dimensional coordinates of all the discrete measuring points to construct and obtain an original multi-beam point cloud set. The above embodiments for extracting and constructing the original multi-beam point cloud set from the original multi-beam sounding data are known to those skilled in the art, and will not be described herein.
After the original multi-beam point cloud set is constructed, trend surface filtering is carried out on the original multi-beam point cloud data through the step S2, and large-scale dense noise is filtered, so that the problem that the conventional radius filtering is incomplete for dense noise filtering is solved; in the step S4, dynamic radius filtering is firstly utilized, edge beam noise points are filtered, meanwhile, edge topography points of the multi-beam point cloud can be well reserved, the problem that edge topography points are deleted by mistake in the traditional radius filtering is solved, and edge topography details are well reserved; further, in the step S3, density clustering is further carried out on the dynamic radius filtered suspicious measurement points so as to further separate real submarine topography points from noise points, the problem that the convergence time of a clustering algorithm is long when the clustering algorithm is singly used is solved, and the algorithm has higher efficiency.
Specifically, in the embodiment of the present application, step S2 further includes the steps of:
s21, establishing a trend surface model of the submarine topography based on the following steps:
wherein, the liquid crystal display device comprises a liquid crystal display device,
for trend surface model functions of submarine topography +.>
For measuring point plane coordinates, < >>
For measuring point depth->
Is a polynomial surface coefficient;
s22, changing the formula (1) into a matrix form of the formula (2):
wherein, the liquid crystal display device comprises a liquid crystal display device,
，/>
for the model coefficient matrix>
Is an observation depth matrix;
s23, based on three-dimensional coordinates of each discrete measuring point in the original multi-beam point cloud set, solving the formula (3) by using a least square method:
s24, traversing each discrete measuring point of the original multi-beam point cloud set, and determining the discrete measuring points belonging to the first multi-beam point cloud set based on the step (4) to obtain the first multi-beam point cloud set:
wherein, the liquid crystal display device comprises a liquid crystal display device,
respectively the +.f in the original multi-beam point cloud set>
Three-dimensional coordinates of discrete measuring points +.>
Is based on->
Mean square error determined by depths of a plurality of discrete measuring points in the neighborhood of the discrete measuring points, +.>
Is a trend surface filter coefficient.
In the above steps, firstly, a seabed topography curved surface in the form of a polynomial curved surface is established through step S21, then, in steps S22 and S23, three-dimensional coordinates of each discrete measuring point in an original multi-beam point cloud set are utilized, and each polynomial curved surface coefficient in a trend surface model is determined through a least square method, so that a trend surface model for describing seabed topography is determined, and finally, measuring points far away from the trend surface are removed as noise through step S24, so that a first multi-beam point cloud set with trend surface filtering is obtained.
In some preferred embodiments of the present application,
。
in the implementation process, the filtering precision range of the large-scale noise points and the large-scale dense noise points can be controlled by adjusting the trend surface filtering coefficient.
The trend surface filtering is simple to operate and good in effect on flatter terrains, but for the measuring points corresponding to the edge beams with larger inclination angles, the phenomenon of incomplete filtering is easy to occur due to sparse point clouds, and therefore, in the embodiment of the application, the first multi-beam point cloud set obtained through the trend surface filtering is further subjected to filtering processing through the step S3.
In an embodiment of the present application, step S3 further comprises the steps of:
s31, classifying each discrete measuring point in the first multi-beam point cloud set into a receiving measuring point and a calibration measuring point based on dynamic radius filtering, and classifying the receiving measuring point into a submarine topography point cloud set.
S32, carrying out density clustering on the calibration measuring points, and classifying the calibration measuring points with the density clustering result of non-noise into a submarine topography point cloud set.
Step S31 further classifies each discrete measuring point in the first multi-beam point cloud set through dynamic radius filtering, and directly classifies the received measuring point into a submarine topography point cloud set; and then in step S32, performing density clustering operation on the marked measuring points with suspicious classification results, and extracting measuring points with clustering results not being noise from the marked measuring points to be classified into submarine topography point cloud sets. By combining the dynamic radius filtering with the density clustering algorithm, the problem of false deletion of edge topography points caused by sparsity of edge beam measuring points can be avoided, and the problem of low calculation efficiency caused by processing massive point cloud data by directly using the density clustering algorithm is also avoided.
Specific embodiments of step S31 and step S32 are described in detail below.
The basic principle of radius filtering is to examine the number of adjacent points in a specified radius space range with a certain point as a center in the point cloud as a basis for judging whether the point is an isolated point or not. If the number of adjacent points is greater than or equal to the specified threshold, the points are non-isolated points and are reserved, otherwise, the isolated points are removed. When a point cloud set of multi-beam sounding data structure is processed by using a traditional radius filtering algorithm, as the density of discrete measuring points corresponding to edge beams is obviously lower than that of discrete measuring points corresponding to central beams, if a fixed threshold is used, the problem that corresponding measuring points at the edge of a terrain are deleted by mistake is caused, so that edge terrain details are lost in post-terrain modeling, and the submarine topography is difficult to describe accurately.
In some preferred embodiments of the present application, the dynamic radius filtering is performed based on equation (5):
wherein, the liquid crystal display device comprises a liquid crystal display device,
for the number of discrete measuring points in the first multi-beam point cloud set, +.>
For the serial numbers of each discrete measuring point in the first multi-beam point cloud set,/for the serial numbers of each discrete measuring point in the first multi-beam point cloud set>
For the starting radius filter point threshold, < >>
In +.>
The number of discrete measuring points contained in the filter radius of the discrete measuring points, +.>
Is->
In some preferred embodiments,/-in>
Determining based on formula (6):
wherein, the liquid crystal display device comprises a liquid crystal display device,
is the first multi-beam point cloud set +.>
The neighborhood distance of a discrete measurement point, in particular, based on the discrete measurement point and its nearest neighborKDetermining the average value of the distances of the discrete measuring points; />
The mean value of neighborhood distances of all discrete measuring points in the first multi-beam point cloud set is>
The neighborhood distance of any one discrete measuring point in the first multi-beam point cloud set is smaller than +.>
Is a probability of (2).
In the specific implementation process of the dynamic radius filtering, the filtering radius and the threshold value of the number of the initial radius filtering points are kept to be fixed values by
And adjusting the actual point threshold value corresponding to each discrete measuring point. Wherein, for any one discrete measuring point +.>
When it is located in the central beam region, its neighborhood distance +.>
The density of discrete measuring points near the position where the dynamic point threshold value is smaller is kept as +.>
The method comprises the steps of carrying out a first treatment on the surface of the When it is positioned in the edge beam area, the discrete measuring points are comparedIs a coefficient, and the more deviated from the central beam, +.>
The smaller the probability value is, so +.>
Correspondingly smaller, so that the dynamic point threshold +.>
The smaller the edge topography point is, thereby avoiding erroneous deletion.
In the calculation
In general, the individual discrete measurement points +.>
Corresponding->
However, when the number of discrete points in the first multi-beam point cloud set is too large, ordering all the discrete points will greatly reduce the efficiency of generating the submarine topography, for which reason it is necessary to guarantee +.>
Further improvement of the calculation on the basis of the accuracy>
Is a function of the speed of the machine.
FIG. 2 shows that the neighborhood distance of any one discrete measurement point obtained by statistics of a large number of multi-beam sounding data is smaller thanLProbability of (2)pRelative toLFIG. 2 also shows the variation of the discrete measurement points when they are distributed in a lognormal mannerp～LIs a relative change in condition(s). As shown in FIG. 2, the neighborhood distances of the discrete measurement points are statistically substantially in accordance with the log-normal distribution, and thus, in some preferred embodiments, may also be based on the log of equation (7)Normal distribution function determination
To accelerate the filtering speed:
wherein, the liquid crystal display device comprises a liquid crystal display device,
as an error function +.>
Respectively determined by the formula (8) and the formula (9):
further, in some preferred embodiments, the filter radius is, when dynamic radius filtering is performed
Wherein->
Is an integer of 1 or more.
Since ocean dynamics erode the seafloor irregularities, the natural topography of the seafloor is continuously changing, although sloped, but does not appear obtrusively, and erroneously deleted edge topography details are equally applicable. According to the characteristic and the characteristic that the density clustering is sensitive to noise, in step S32, density clustering is carried out on the in-doubt data (namely the calibration measuring points) after dynamic radius filtering, the calibration measuring points with the clustering result being noise are removed, and the calibration measuring points with other clustering results being non-noise are classified into submarine topography point cloud sets.
Specifically, the density clustering algorithm is to aggregate a plurality of d-dimensional data samples into a plurality of classes, so that the similarity of the samples in the same class is maximized, and the similarity of the samples in different classes is minimized. The clustering process comprises three main steps of core point searching, initial core point selecting and cluster diffusion. Searching all core points meeting the conditions in a data set to be clustered; then starting from any core point cluster (the core points and the points in the neighborhood radius thereof), continuously expanding to unclassified points by using a density connection relationship until the unclassified points cannot continue, thereby obtaining a point cluster with all the points connected with each other in density, wherein the point cluster can be called a cluster, and all the data points in the cluster are marked as the same type; and then continuously inquiring whether core points which are not accessed exist or not, starting a new round of cluster expansion, continuously forming new clusters until all the core points are accessed, and marking the points which are not absorbed by any clusters as noise. The algorithm can effectively identify a plurality of dense dot clusters isolated from each other and mark discrete dots which cannot form the clusters as noise.
The density clustering algorithm is known to those skilled in the art, but if the density clustering algorithm is directly applied to denoising and filtering of an original multi-beam point cloud set, the problems of overlarge data volume, overlong clustering process and the like are faced. Therefore, in the embodiment of the application, by utilizing the characteristic that the density clustering is sensitive to noise, only the suspicious data obtained after dynamic radius filtering is subjected to density clustering so as to identify noise points, the noise points marked by the density clustering are filtered, and the rest of the suspicious data are saved as terrain points. Compared with the original point cloud data, the processing mode has the advantages that the data quantity is small, the clustering convergence time is short, and the algorithm has high efficiency.
Further, after the submarine topography point cloud set is obtained through the step S3, the modeling of the submarine topography can be performed through the step S4. At present, there are various three-dimensional modeling methods based on point cloud data, for example, a connection relationship between the three-dimensional modeling methods can be established according to spatial position information of each discrete measurement point in a submarine topography point cloud set, so as to form a submarine topography three-dimensional grid model in the form of triangle/four-corner patches and the like. The above-mentioned manner of reconstructing a three-dimensional model based on a point cloud set is known to those skilled in the art, and will not be described in detail herein.
Example 1.
In this embodiment, the above-mentioned submarine topography multi-beam point cloud filtering method is used to process the multi-beam sounding data obtained by actual measurement, and fig. 3 is a specific implementation flow of this embodiment.
In this embodiment, the original multi-beam sounding data includes 163227 discrete measuring points, the covered seabed area is about 8542 square meters, the threshold value of the initial radius filter point is set to 100, and the discrete measuring points are obtained by performing log-normal distribution fitting of the neighborhood distance
The final dynamic radius filter was determined to have a filter radius of 3.0717 meters.
Fig. 4 schematically shows a three-dimensional model of the seabed obtained by using the multi-beam point cloud filtering method of the seabed, and fig. 5 and 6, by contrast, schematically show three-dimensional models of the seabed obtained by using the trend surface filtering method and the radius filtering method, respectively. As can be seen by comparing fig. 4 with fig. 5 to fig. 6, by using the submarine topography multi-beam point cloud filtering method provided by the application, the accuracy and the accuracy of the edge beam partial filtering can be obviously improved, so that the edge topography details are better reserved, the reduction of the operation speed caused by directly adopting a density clustering algorithm is avoided, and the complementary advantage and the organic combination of various algorithms are realized.
While the foregoing is directed to embodiments of the present application, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow.
Claims (6)
1. The multi-beam point cloud filtering method for the submarine topography is characterized by comprising the following steps of:
s1, constructing an original multi-beam point cloud set based on original multi-beam sounding data;
s2, carrying out trend surface filtering on the original multi-beam point cloud set to obtain a first multi-beam point cloud set;
s3, carrying out combined filtering based on dynamic radius filtering and density clustering on the first multi-beam point cloud set to obtain a submarine topography point cloud set;
s4, generating a submarine three-dimensional terrain model based on the submarine topography point cloud set;
step S2 further comprises the steps of:
s21, establishing a trend surface model of the submarine topography based on the following steps:
z＝f(x，y)＝a 0 +a 1 x+a 2 y+a 3 xy+a 4 x 2 +a 5 y 2 (1)，
wherein f (x, y) is a trend surface model function of the submarine topography, (x, y) is a measuring point plane coordinate, z is a measuring point depth, a 0 ，a 1 ，a 2 ，a 3 ，a 4 ，a 5 Is a polynomial surface coefficient;
s22, changing the formula (1) into a matrix form of the formula (2):
Z＝BX (2)，
wherein x= [ a ] 0 ，a 1 ，a 2 ，a 3 ，a 4 ，a 5 ]B is a model coefficient matrix, and z is an observation depth matrix;
s23, based on three-dimensional coordinates of each discrete measuring point in the original multi-beam point cloud set, solving the formula (3) by using a least square method:
X＝(B T B) T B T Z (3)；
s24, traversing each discrete measuring point of the original multi-beam point cloud set, and determining the discrete measuring points belonging to the first multi-beam point cloud set based on the step (4) to obtain the first multi-beam point cloud set:
wherein x is i ，y i ，z i Respectively, the ith in the original multi-beam point cloud setThe three-dimensional coordinates of the discrete measuring points, sigma is the mean square error determined based on the depths of a plurality of discrete measuring points in the neighborhood of the ith discrete measuring point, and k is a trend surface filter coefficient;
step S3 further comprises the steps of:
s31, classifying each discrete measuring point in the first multi-beam point cloud set into a receiving measuring point and a calibration measuring point based on dynamic radius filtering, and classifying the receiving measuring point into a submarine topography point cloud set;
s32, performing density clustering on the calibration measuring points, and classifying the calibration measuring points with the density clustering result of non-noise into a submarine topography point cloud set;
the dynamic radius filtering is performed based on equation (5):
wherein M is the number of discrete measuring points in the first multi-beam point cloud set, j is the serial number of each discrete measuring point in the first multi-beam point cloud set, N is the threshold value of the initial radius filtering point, N j The number k of the discrete measuring points contained in the filter radius of the jth discrete measuring point for the first multi-beam point cloud set j The thresholding coefficient for j.
2. The method for multi-beam point cloud filtering of seafloor terrain according to claim 1, wherein:
the k=2 or 3.
3. The method of multi-beam point cloud filtering of seafloor terrain of claim 1, wherein k is j Determining based on formula (6):
wherein L is j L is the neighborhood distance of the jth discrete measuring point in the first multi-beam point cloud set mean Is the average value of the neighborhood distances of all the discrete measuring points in the first multi-beam point cloud set, p j The neighborhood distance of any one discrete measuring point in the first multi-beam point cloud set is smaller than L j Is a probability of (2).
4. A method of multi-beam point cloud filtering of seafloor terrain according to claim 3, wherein:
the neighborhood distance of each discrete measurement point is determined based on the average of the distances of the discrete measurement point from its nearest K discrete measurement points.
5. A method of multi-beam point cloud filtering of seafloor terrain as claimed in claim 3, wherein said p j Determining based on the formula (7):
where erf () is the error function, μ p 、σ p Respectively determined by the formula (8) and the formula (9):
6. the method for multi-beam point cloud filtering of seafloor terrain of claim 5, wherein:
the filter radius is
Wherein n is an integer of 1 or more. />
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