CN115880189A - Submarine topography multi-beam point cloud filtering method - Google Patents

Submarine topography multi-beam point cloud filtering method Download PDF

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CN115880189A
CN115880189A CN202310147519.1A CN202310147519A CN115880189A CN 115880189 A CN115880189 A CN 115880189A CN 202310147519 A CN202310147519 A CN 202310147519A CN 115880189 A CN115880189 A CN 115880189A
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point cloud
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CN115880189B (en
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罗宇
石少营
崔行宇
姚英硕
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Shandong University of Science and Technology
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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 submarine topography multi-beam point cloud filtering method which comprises the following steps: s1, constructing an original multi-beam point cloud set based on original multi-beam sounding data; s2, performing trend surface filtering on the original multi-beam point cloud set to obtain a first multi-beam point cloud set; s3, performing 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; and S4, generating a submarine three-dimensional terrain model based on the submarine terrain point cloud set. According to the submarine topography multi-beam point cloud filtering method, the edge beam filtering effect is improved according to specific data characteristics of multi-beam sounding data, meanwhile, the retention of edge topography details and the processing speed of mass point cloud data are considered, and the advantage complementation and organic combination of multiple algorithms are achieved.

Description

一种海底地形多波束点云滤波方法A multi-beam point cloud filtering method for seafloor topography

技术领域Technical Field

本申请属于海洋测绘与勘探以及水声信号处理技术领域，具体地，提供一种海底地形多波束点云滤波方法。The present application belongs to the field of ocean surveying and exploration and underwater acoustic signal processing technology, and specifically provides a seabed topography multi-beam point cloud filtering method.

背景技术Background Art

多波束测深系统是目前最为先进的海洋勘查测量仪器之一。该系统将传统的测深技术从原来的点、线扩展到面，并进一步发展到立体测深和自动成图。它的出现深刻地改变了海洋学科领域的调查研究方式及最终的成果质量。因其具有覆盖范围大、速度快、精度和效率高、记录数字化等优点，广泛应用在海洋勘查测绘领域。The multi-beam bathymetric system is one of the most advanced marine survey and measurement instruments. The system expands the traditional bathymetric technology from the original point and line to the surface, and further develops it into stereo bathymetric and automatic mapping. Its emergence has profoundly changed the survey and research methods and the quality of the final results in the field of marine disciplines. Because of its advantages such as large coverage, fast speed, high accuracy and efficiency, and digital records, it is widely used in the field of marine survey and mapping.

多波束测量过程中，由于仪器自噪声、海况因素、设备参数设置不合理及海中生物的影响，导致多波束测深数据存在较多噪点，对海底地形的真实性表达造成严重影响。为获取真实的海底地形，必须对多波束数据进行滤波处理，消除虚假信号，恢复、保留真实信息。传统的人工滤波处理根据操作人员自身经验进行粗差数据的剔除，可靠性较高，但工作量较大，滤波效率较低，目前已逐渐被基于滤波算法的自动滤波代替。During the multi-beam measurement process, due to the self-noise of the instrument, sea conditions, unreasonable equipment parameter settings and the influence of marine organisms, there are many noise points in the multi-beam bathymetric data, which seriously affects the true expression of the seabed topography. In order to obtain the true seabed topography, the multi-beam data must be filtered to eliminate false signals and restore and retain the true information. Traditional manual filtering removes gross error data based on the operator's own experience. It has high reliability, but the workload is large and the filtering efficiency is low. It has gradually been replaced by automatic filtering based on filtering algorithms.

目前常见的对多波束测深数据进行滤波的算法包括趋势面滤波法、基于半径滤波点云去噪方法。其中，趋势面滤波法操作简单，对于平坦地形非常适用，但边缘波束点云稀疏，导致滤波不彻底；基于半径滤波的点云去噪方法具有处理速度快、通用性强、去噪效果稳定的优点，但是由于多波束测深系统的特性，其中央波束点云密度与边缘波束点云密度差异较大，使得该类方法存在真实地形点被误删，造成细节损失较严重的缺点，使得该方法在处理复杂海底地形时精度不高。At present, the common algorithms for filtering multi-beam bathymetric data include trend surface filtering and radius filtering based point cloud denoising. Among them, the trend surface filtering method is simple to operate and is very suitable for flat terrain, but the edge beam point cloud is sparse, resulting in incomplete filtering; the point cloud denoising method based on radius filtering has the advantages of fast processing speed, strong versatility, and stable denoising effect, but due to the characteristics of the multi-beam bathymetric system, the density of the central beam point cloud is quite different from that of the edge beam point cloud, which makes this type of method have the disadvantage of mistakenly deleting real terrain points and causing serious loss of details, making this method not very accurate when dealing with complex seabed terrain.

发明内容Summary of the invention

本申请的目的在于解决现有技术中存在的问题，提供一种兼顾滤波精度与处理速度的海底地形多波束点云滤波方法。The purpose of the present application is to solve the problems existing in the prior art and to provide a multi-beam point cloud filtering method for seabed topography that takes into account both filtering accuracy and processing speed.

本申请的实施例可以通过以下技术方案实现：The embodiments of the present application can be implemented through the following technical solutions:

一种海底地形多波束点云滤波方法，包括以下步骤：A method for filtering a multi-beam point cloud of a seafloor topography comprises the following steps:

S1，基于原始多波束测深数据构造原始多波束点云集合；S1, constructs the original multi-beam point cloud set based on the original multi-beam bathymetric data;

S2，对所述原始多波束点云集合进行趋势面滤波，得到第一多波束点云集合；S2, performing trend surface filtering on the original multi-beam point cloud set to obtain a first multi-beam point cloud set;

S3，对所述第一多波束点云集合进行基于动态半径滤波与密度聚类的组合滤波，得到海底地形点云集合；S3, performing combined filtering based on dynamic radius filtering and density clustering on the first multi-beam point cloud set to obtain a seabed terrain point cloud set;

S4，基于所述海底地形点云集合生成海底三维地形模型。S4, generating a three-dimensional seabed terrain model based on the seabed terrain point cloud set.

具体地，步骤S2进一步包括以下步骤：Specifically, step S2 further includes the following steps:

S21，基于(1)式建立海底地形的趋势面模型：S21, based on formula (1), establish the trend surface model of seafloor topography:

Figure SMS_1
（1），
Figure SMS_1
(1),

其中，

Figure SMS_2
为海底地形的趋势面模型函数，
Figure SMS_3
为测点平面坐标，
Figure SMS_4
为测点深度，
Figure SMS_5
为多项式曲面系数；in,
Figure SMS_2
is the trend surface model function of the seafloor topography,
Figure SMS_3
is the plane coordinate of the measuring point,
Figure SMS_4
is the depth of the measuring point,
Figure SMS_5
are the polynomial surface coefficients;

S22，将(1)式变为(2)式的矩阵形式：S22, transform equation (1) into the matrix form of equation (2):

Figure SMS_6
（2），
Figure SMS_6
(2),

其中，

Figure SMS_7
，
Figure SMS_8
为模型系数矩阵，
Figure SMS_9
为观测深度矩阵；in,
Figure SMS_7
,
Figure SMS_8
is the model coefficient matrix,
Figure SMS_9
is the observation depth matrix;

S23，基于原始多波束点云集合中各个离散测点的三维坐标，利用最小二乘法解得(3)式：S23, based on the three-dimensional coordinates of each discrete measurement point in the original multi-beam point cloud set, the least squares method is used to solve equation (3):

Figure SMS_10
(3)；
Figure SMS_10
(3);

S24，遍历所述原始多波束点云集合的各个离散测点，并基于(4)式确定属于第一多波束点云集合的离散测点以得到第一多波束点云集合：S24, traverse each discrete measurement point of the original multi-beam point cloud set, and determine the discrete measurement points belonging to the first multi-beam point cloud set based on formula (4) to obtain the first multi-beam point cloud set:

Figure SMS_11
（4），
Figure SMS_11
(4),

其中，

Figure SMS_12
分别为原始多波束点云集合中第
Figure SMS_13
个离散测点的三维坐标，
Figure SMS_14
为基于第
Figure SMS_15
个离散测点的邻域内的多个离散测点深度确定的均方差，
Figure SMS_16
为趋势面滤波系数。in,
Figure SMS_12
They are the first
Figure SMS_13
The three-dimensional coordinates of discrete measurement points,
Figure SMS_14
Based on
Figure SMS_15
The mean square error of the depth determination of multiple discrete measurement points in the neighborhood of a discrete measurement point,
Figure SMS_16
is the trend surface filter coefficient.

优选地，所述

Figure SMS_17
。Preferably, the
Figure SMS_17
.

具体地，步骤S3进一步包括以下步骤：Specifically, step S3 further includes the following steps:

S31，基于动态半径滤波将所述第一多波束点云集合中的各个离散测点分类为接受测点与标定测点，将所述接受测点归入海底地形点云集合；S31, classifying each discrete measurement point in the first multi-beam point cloud set into an acceptance measurement point and a calibration measurement point based on dynamic radius filtering, and classifying the acceptance measurement point into a seabed terrain point cloud set;

S32，对所述标定测点进行密度聚类，将密度聚类结果为非噪声的标定测点归入海底地形点云集合。S32, density clustering is performed on the calibration points, and calibration points with non-noise density clustering results are classified into a seabed terrain point cloud set.

优选地，所述动态半径滤波基于(5)式进行：Preferably, the dynamic radius filtering is performed based on formula (5):

Figure SMS_18
（5），
Figure SMS_18
(5),

其中，

Figure SMS_19
为第一多波束点云集合中离散测点的个数，
Figure SMS_20
为第一多波束点云集合中各个离散测点的序号，
Figure SMS_21
为起始半径滤波点数阈值，
Figure SMS_22
为第一多波束点云集合在第
Figure SMS_23
个离散测点的滤波半径内包含的离散测点的个数，
Figure SMS_24
为
Figure SMS_25
的阈值变换系数。in,
Figure SMS_19
is the number of discrete measurement points in the first multi-beam point cloud set,
Figure SMS_20
is the serial number of each discrete measurement point in the first multi-beam point cloud set,
Figure SMS_21
is the starting radius filter point threshold,
Figure SMS_22
The first multi-beam point cloud is collected in
Figure SMS_23
The number of discrete measurement points contained in the filter radius of discrete measurement points,
Figure SMS_24
for
Figure SMS_25
The threshold transformation coefficient.

优选地，所述

Figure SMS_26
基于(6)式确定：Preferably, the
Figure SMS_26
Based on formula (6), we determine:

Figure SMS_27
（6），
Figure SMS_27
(6),

其中，

Figure SMS_28
为第一多波束点云集合中第
Figure SMS_29
个离散测点的邻域距离，
Figure SMS_30
为第一多波束点云集合中全部离散测点的邻域距离的均值，
Figure SMS_31
为第一多波束点云集合中任意一个离散测点的邻域距离小于
Figure SMS_32
的概率。in,
Figure SMS_28
is the first multi-beam point cloud set
Figure SMS_29
The neighborhood distance of discrete measurement points,
Figure SMS_30
is the mean of the neighborhood distances of all discrete measurement points in the first multi-beam point cloud set,
Figure SMS_31
The neighborhood distance of any discrete measurement point in the first multi-beam point cloud set is less than
Figure SMS_32
probability.

具体地，每个离散测点的邻域距离基于该离散测点与其最接近的K个离散测点的距离的均值确定。Specifically, the neighborhood distance of each discrete measurement point is determined based on the average of the distances between the discrete measurement point and its K closest discrete measurement points.

优选地，所述

Figure SMS_33
基于(7)式确定：Preferably, the
Figure SMS_33
Based on formula (7), we determine:

Figure SMS_34
（7），
Figure SMS_34
(7),

其中，

Figure SMS_35
为误差函数，
Figure SMS_36
分别由(8)式、(9)式确定：in,
Figure SMS_35
is the error function,
Figure SMS_36
Determined by equations (8) and (9) respectively:

Figure SMS_37
（8），
Figure SMS_37
(8),

Figure SMS_38
（9）。
Figure SMS_38
(9).

优选地，所述滤波半径为

Figure SMS_39
，其中
Figure SMS_40
为大于等于1的整数。Preferably, the filtering radius is
Figure SMS_39
,in
Figure SMS_40
is an integer greater than or equal to 1.

本申请的实施例提供的一种海底地形多波束点云滤波方法至少具有以下有益效果：The embodiment of the present application provides a method for filtering seabed topography multi-beam point cloud, which has at least the following beneficial effects:

本申请的滤波方法通过有机结合的方式，针对多波束测深数据的具体数据特征，对现有的各种滤波算法进行了改进，在提高边缘波束滤除效果的同时，兼顾边缘地形细节的保留与海量点云数据的处理速度，实现了多种算法的优势互补和有机结合；The filtering method of the present application improves various existing filtering algorithms by organically combining the specific data characteristics of multi-beam bathymetric data, while improving the edge beam filtering effect, taking into account the retention of edge terrain details and the processing speed of massive point cloud data, thus achieving complementary advantages and organic combination of multiple algorithms;

本申请的滤波方法首先针对密集噪声采用趋势面方法进行多波束点云预处理，进而针对趋势面边缘波束点云滤波效果不佳的问题采用高效简便的半径滤波方式，提升边缘波束点云滤波效果，同时针对传统半径滤波在多波束点云滤波过程中误删边缘地形点的问题进行了改进，通过密度聚类和动态半径阈值设定良好地保留了边缘地形细节；The filtering method of the present application firstly adopts the trend surface method to pre-process the multi-beam point cloud for dense noise, and then adopts an efficient and simple radius filtering method to improve the filtering effect of the edge beam point cloud. At the same time, the problem of the traditional radius filtering mistakenly deleting the edge terrain points in the multi-beam point cloud filtering process is improved, and the edge terrain details are well preserved through density clustering and dynamic radius threshold setting;

本申请的滤波方法采用对存疑数据进行密度聚类的方式代替整体点云数据进行密度聚类，缩短聚类收敛时间，保证本发明算法整体的效率，使其适用于海量多波束点云数据的处理。The filtering method of the present application adopts the method of density clustering of questionable data instead of density clustering of the entire point cloud data, shortening the clustering convergence time, ensuring the overall efficiency of the algorithm of the present invention, and making it suitable for processing massive multi-beam point cloud data.

附图说明BRIEF DESCRIPTION OF THE DRAWINGS

图1为根据本申请实施例的海底地形多波束点云滤波方法的流程图；FIG1 is a flow chart of a method for filtering a multi-beam point cloud of a seafloor topography according to an embodiment of the present application;

图2为根据多波束测深数据统计结果以及根据对数正态分布得到的任意一个离散测点的邻域距离小于L的概率p相对于L的变化情况；FIG2 shows the variation of the probability p of the neighborhood distance of any discrete measuring point being less than L relative to L , obtained based on the statistical results of multi-beam bathymetric data and the log-normal distribution;

图3为本申请实施例1的具体实施流程；FIG3 is a specific implementation process of Example 1 of the present application;

图4为根据本申请实施例1得到的海底三维地形模型的示意图；FIG4 is a schematic diagram of a three-dimensional seabed terrain model obtained according to Example 1 of the present application;

图5为单独使用趋势面滤波法得到的海底三维地形模型的示意图；FIG5 is a schematic diagram of a three-dimensional seabed terrain model obtained by using the trend surface filtering method alone;

图6为单独使用半径滤波法得到的海底三维地形模型的示意图。FIG6 is a schematic diagram of a three-dimensional seabed terrain model obtained by using the radius filtering method alone.

具体实施方式DETAILED DESCRIPTION

以下，基于优选的实施方式并参照附图对本申请进行进一步说明。Hereinafter, the present application will be further described based on preferred embodiments with reference to the accompanying drawings.

此外，为了方便理解，放大或者缩小了图纸上的各种构件，但这种做法不是为了限制本申请的保护范围。In addition, various components on the drawings are enlarged or reduced in size for ease of understanding, but this practice is not intended to limit the scope of protection of the present application.

单数形式的词汇也包括复数含义，反之亦然。Words importing the singular also include the plural and vice versa.

在本申请实施例中的描述中，需要说明的是，若出现术语“上”、“下”、“内”、“外”等指示的方位或位置关系为基于附图所示的方位或位置关系，或者是本申请实施例的产品使用时惯常摆放的方位或位置关系，仅是为了便于描述本申请和简化描述，而不是指示或暗示所指的装置或元件必须具有特定的方位、以特定的方位构造和操作，因此不能理解为对本申请的限制。此外，本申请的描述中，为了区分不同的单元，本说明书上用了第一、第二等词汇，但这些不会受到制造的顺序限制，也不能理解为指示或暗示相对重要性，其在本申请的详细说明与权利要求书上，其名称可能会不同。In the description of the embodiments of the present application, it should be noted that if the terms "upper", "lower", "inside", "outside", etc. indicate an orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship in which the products of the embodiments of the present application are usually placed when in use, it is only for the convenience of describing the present application and simplifying the description, and does not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present application. In addition, in the description of the present application, in order to distinguish different units, the words first, second, etc. are used in this specification, but these are not limited by the order of manufacture, nor can they be understood as indicating or implying relative importance, and their names may be different in the detailed description and claims of the present application.

本说明书中词汇是为了说明本申请的实施例而使用的，但不是试图要限制本申请。还需要说明的是，除非另有明确的规定和限定，若出现术语“设置”、“相连”、“连接”应做广义理解，例如，可以是固定连接，也可以是可拆卸连接，或一体地连接；可以是机械连接，可以是直接相连，也可以通过中间媒介间接连接，可以是两个元件内部的连通。对于本领域的技术人员而言，可以具体理解上述术语在本申请中的具体含义。The vocabulary in this specification is used to illustrate the embodiments of the present application, but is not intended to limit the present application. It should also be noted that, unless otherwise clearly specified and limited, the terms "disposed", "connected", and "connected" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection, a direct connection, an indirect connection through an intermediate medium, or a connection between the two elements. For those skilled in the art, the specific meanings of the above terms in this application can be specifically understood.

本申请通过实施例提供一种海底地形多波束点云滤波方法，该滤波方法对多波束测深数据进行滤波，以获取能够精确地描述海底地形的点云集合。图1为本申请实施例提供的一种海底地形多波束点云滤波方法的流程图，如图1所示，该方法包括以下步骤：The present application provides a method for filtering a multi-beam point cloud of seabed topography through an embodiment. The filtering method filters multi-beam bathymetric data to obtain a point cloud set that can accurately describe the seabed topography. FIG1 is a flow chart of a method for filtering a multi-beam point cloud of seabed topography provided by an embodiment of the present application. As shown in FIG1, the method includes the following steps:

S1，基于原始多波束测深数据构造原始多波束点云集合；S1, constructs the original multi-beam point cloud set based on the original multi-beam bathymetric data;

S2，对所述原始多波束点云集合进行趋势面滤波，得到第一多波束点云集合；S2, performing trend surface filtering on the original multi-beam point cloud set to obtain a first multi-beam point cloud set;

S3，对所述第一多波束点云集合进行基于动态半径滤波与密度聚类的组合滤波，得到海底地形点云集合；S3, performing combined filtering based on dynamic radius filtering and density clustering on the first multi-beam point cloud set to obtain a seabed terrain point cloud set;

S4，基于所述海底地形点云集合生成海底三维地形模型。S4, generating a three-dimensional seabed terrain model based on the seabed terrain point cloud set.

其中，步骤S1用于读取原始多波束测深数据并进行整合以构造原始多波束点云集合，其中，原始多波束测深数据按照波束角度及发射接收顺序存储了多个通道的测深数据，从中提取每个测点处的

Figure SMS_41
平面坐标及水深
Figure SMS_42
，即可确定每个离散测点的三维坐标。将全部离散测点的三维坐标进行汇总，即可构造得到原始多波束点云集合。上述从原始多波束测深数据中提取并构造原始多波束点云集合的实施方式已为本领域技术人员所知晓，在此不再赘述。Step S1 is used to read the original multi-beam bathymetric data and integrate them to construct an original multi-beam point cloud set, where the original multi-beam bathymetric data stores the bathymetric data of multiple channels according to the beam angle and the transmission and reception order, and extracts the bathymetric data at each measuring point.
Figure SMS_41
Plane coordinates and water depth
Figure SMS_42
, the three-dimensional coordinates of each discrete measurement point can be determined. The three-dimensional coordinates of all discrete measurement points are summarized to construct the original multi-beam point cloud set. The above-mentioned implementation method of extracting and constructing the original multi-beam point cloud set from the original multi-beam bathymetric data is already known to those skilled in the art and will not be repeated here.

在构造完成原始多波束点云集合后，通过步骤S2对原始多波束点云数据进行趋势面滤波，滤除大尺度的密集噪声，以解决传统半径滤波对于密集噪声滤波不完全的问题；接着在步骤S4中首先利用动态半径滤波，在滤除边缘波束噪点的同时，能够较好的保留多波束点云边缘地形点，解决了传统半径滤波边缘地形点误删的问题，较好的保留了边缘地形细节；进一步地，在步骤S3中还对动态半径滤波的存疑测点进行密度聚类以进一步分离真实海底地形点与噪声点，解决了单独使用聚类算法收敛时间长的问题，使本发明算法具有较高的效率。After the original multi-beam point cloud set is constructed, trend surface filtering is performed on the original multi-beam point cloud data through step S2 to filter out large-scale dense noise, so as to solve the problem of incomplete dense noise filtering by traditional radius filtering; then in step S4, dynamic radius filtering is first used to filter out edge beam noise points while better retaining edge terrain points of the multi-beam point cloud, solving the problem of mistaken deletion of edge terrain points in traditional radius filtering, and better retaining edge terrain details; further, in step S3, density clustering is also performed on the questionable measurement points of the dynamic radius filtering to further separate the real seabed terrain points from the noise points, solving the problem of long convergence time when using the clustering algorithm alone, so that the algorithm of the present invention has higher efficiency.

具体地，在本申请的实施例中，步骤S2进一步包括以下步骤：Specifically, in an embodiment of the present application, step S2 further includes the following steps:

S21，基于(1)式建立海底地形的趋势面模型：S21, based on formula (1), establish the trend surface model of seafloor topography:

Figure SMS_43
（1），
Figure SMS_43
(1),

其中，

Figure SMS_44
为海底地形的趋势面模型函数，
Figure SMS_45
为测点平面坐标，
Figure SMS_46
为测点深度，
Figure SMS_47
为多项式曲面系数；in,
Figure SMS_44
is the trend surface model function of the seafloor topography,
Figure SMS_45
is the plane coordinate of the measuring point,
Figure SMS_46
is the depth of the measuring point,
Figure SMS_47
are the polynomial surface coefficients;

S22，将(1)式变为(2)式的矩阵形式：S22, transform equation (1) into the matrix form of equation (2):

Figure SMS_48
（2），
Figure SMS_48
(2),

其中，

Figure SMS_49
，
Figure SMS_50
为模型系数矩阵，
Figure SMS_51
为观测深度矩阵；in,
Figure SMS_49
,
Figure SMS_50
is the model coefficient matrix,
Figure SMS_51
is the observation depth matrix;

S23，基于原始多波束点云集合中各个离散测点的三维坐标，利用最小二乘法解得(3)式：S23, based on the three-dimensional coordinates of each discrete measurement point in the original multi-beam point cloud set, the least squares method is used to solve equation (3):

Figure SMS_52
(3)；
Figure SMS_52
(3);

S24，遍历所述原始多波束点云集合的各个离散测点，并基于(4)式确定属于第一多波束点云集合的离散测点以得到第一多波束点云集合：S24, traverse each discrete measurement point of the original multi-beam point cloud set, and determine the discrete measurement points belonging to the first multi-beam point cloud set based on formula (4) to obtain the first multi-beam point cloud set:

Figure SMS_53
（4），
Figure SMS_53
(4),

其中，

Figure SMS_54
分别为原始多波束点云集合中第
Figure SMS_55
个离散测点的三维坐标，
Figure SMS_56
为基于第
Figure SMS_57
个离散测点的邻域内的多个离散测点深度确定的均方差，
Figure SMS_58
为趋势面滤波系数。in,
Figure SMS_54
They are the first
Figure SMS_55
The three-dimensional coordinates of discrete measurement points,
Figure SMS_56
Based on
Figure SMS_57
The mean square error of the depth determination of multiple discrete measurement points in the neighborhood of a discrete measurement point,
Figure SMS_58
is the trend surface filter coefficient.

上述各步骤中，首先通过步骤S21建立多项式曲面形式的海底地形曲面，然后在步骤S22、S23中利用原始多波束点云集合中各个离散测点的三维坐标，通过最小二乘法确定趋势面模型中的各个多项式曲面系数，从而确定用于描述海底地形的趋势面模型，最后利用步骤S24将远离上述趋势面的测点作为噪声剔除，从而得到经过趋势面滤波的第一多波束点云集合。In the above steps, first, a seabed topography surface in the form of a polynomial surface is established through step S21, and then in steps S22 and S23, the three-dimensional coordinates of each discrete measurement point in the original multi-beam point cloud set are used to determine each polynomial surface coefficient in the trend surface model through the least squares method, thereby determining the trend surface model used to describe the seabed topography, and finally, in step S24, the measurement points far away from the above trend surface are removed as noise, thereby obtaining the first multi-beam point cloud set after trend surface filtering.

在本申请的一些优选的实施例中，

Figure SMS_59
。In some preferred embodiments of the present application,
Figure SMS_59
.

在具体实施过程中，通过调节上述趋势面滤波系数，能够控制对大尺度噪声点以及大尺度密集噪声点的滤除精度范围。In a specific implementation process, by adjusting the trend surface filter coefficient, the filtering accuracy range for large-scale noise points and large-scale dense noise points can be controlled.

上述趋势面滤波虽然操作简单，且对较为平坦的地形效果较好，但是对于倾斜角度较大的边缘波束所对应的测点，由于其点云稀疏，容易出现滤波不彻底的现象，为此，在本申请的实施例中，通过步骤S3对经过趋势面滤波得到的第一多波束点云集合进一步进行滤波处理。Although the above-mentioned trend surface filtering is simple to operate and has a better effect on relatively flat terrain, for the measurement points corresponding to the edge beams with larger inclination angles, due to their sparse point clouds, incomplete filtering is prone to occur. For this reason, in an embodiment of the present application, the first multi-beam point cloud set obtained by trend surface filtering is further filtered through step S3.

在本申请的实施例中，步骤S3进一步包括以下步骤：In an embodiment of the present application, step S3 further includes the following steps:

S31，基于动态半径滤波将所述第一多波束点云集合中的各个离散测点分类为接受测点与标定测点，将所述接受测点归入海底地形点云集合。S31, classifying each discrete measurement point in the first multi-beam point cloud set into an acceptance measurement point and a calibration measurement point based on dynamic radius filtering, and classifying the acceptance measurement point into a seabed terrain point cloud set.

S32，对所述标定测点进行密度聚类，将密度聚类结果为非噪声的标定测点归入海底地形点云集合。S32, density clustering is performed on the calibration points, and calibration points with non-noise density clustering results are classified into a seabed terrain point cloud set.

其中，步骤S31通过动态半径滤波将第一多波束点云集合中的各个离散测点进行进一步分类，将接受测点直接归入海底地形点云集合；然后在步骤S32中将分类结果存疑的标定测点进行密度聚类操作，并从其中提取聚类结果不为噪声的测点归入海底地形点云集合。通过上述动态半径滤波结合密度聚类算法的处理，既能够避免由于边缘波束测点较稀疏导致的边缘地形点误删的问题，又避免了直接使用密度聚类算法处理海量点云数据造成计算效率过低的问题。Among them, step S31 further classifies each discrete measurement point in the first multi-beam point cloud set through dynamic radius filtering, and directly classifies the accepted measurement points into the seabed terrain point cloud set; then in step S32, the calibrated measurement points with questionable classification results are subjected to density clustering operation, and the measurement points whose clustering results are not noise are extracted from them and classified into the seabed terrain point cloud set. Through the above-mentioned dynamic radius filtering combined with the density clustering algorithm, it is possible to avoid the problem of mistaken deletion of edge terrain points due to the sparse edge beam measurement points, and avoid the problem of low computational efficiency caused by directly using the density clustering algorithm to process massive point cloud data.

以下对步骤S31及步骤S32的具体实施方式进行详细说明。The specific implementation of step S31 and step S32 is described in detail below.

半径滤波的基本原理是考察点云中以某个点为中心的指定半径空间范围内相邻点的数量作为判断该点是否为孤立点的依据。若相邻点数量大于等于指定阈值，则该点为非孤立点并予以保留，反之为孤立点予以去除。在使用传统的半径滤波算法对多波束测深数据构造的点云集合进行处理时，由于边缘波束对应的离散测点密度显著低于中心波束对应的离散测点密度，如使用固定的阈值，将导致地形边缘处对应的测点被误删除的问题，从而导致后期地形建模中边缘地形细节缺失，难以精确地对海底地形进行描述，为此，需要对传统的半径滤波算法进行改进，以适应对多波束测深得到的点云集合进行处理的需要。The basic principle of radius filtering is to examine the number of adjacent points within a specified radius space range centered on a certain point in the point cloud as the basis for judging whether the point is an isolated point. If the number of adjacent points is greater than or equal to the specified threshold, the point is a non-isolated point and is retained, otherwise it is an isolated point and is removed. When using the traditional radius filtering algorithm to process the point cloud set constructed from multi-beam bathymetry data, since the density of discrete measurement points corresponding to the edge beam is significantly lower than that of the discrete measurement points corresponding to the center beam, if a fixed threshold is used, the measurement points corresponding to the edge of the terrain will be mistakenly deleted, resulting in the loss of edge terrain details in the later terrain modeling, making it difficult to accurately describe the seabed terrain. For this reason, it is necessary to improve the traditional radius filtering algorithm to adapt to the needs of processing the point cloud set obtained by multi-beam bathymetry.

在本申请的一些优选的实施例中，所述动态半径滤波基于(5)式进行：In some preferred embodiments of the present application, the dynamic radius filtering is performed based on formula (5):

Figure SMS_60
（5），
Figure SMS_60
(5),

其中，

Figure SMS_63
为第一多波束点云集合中离散测点的个数，
Figure SMS_64
为第一多波束点云集合中各个离散测点的序号，
Figure SMS_66
为起始半径滤波点数阈值，
Figure SMS_62
为第一多波束点云集合在第
Figure SMS_65
个离散测点的滤波半径内包含的离散测点的个数，
Figure SMS_67
为
Figure SMS_68
的阈值变换系数，在一些优选的实施例中，
Figure SMS_61
基于(6)式确定：in,
Figure SMS_63
is the number of discrete measurement points in the first multi-beam point cloud set,
Figure SMS_64
is the serial number of each discrete measurement point in the first multi-beam point cloud set,
Figure SMS_66
is the starting radius filter point threshold,
Figure SMS_62
The first multi-beam point cloud is collected in
Figure SMS_65
The number of discrete measurement points contained in the filter radius of discrete measurement points,
Figure SMS_67
for
Figure SMS_68
In some preferred embodiments,
Figure SMS_61
Based on formula (6), we determine:

Figure SMS_69
（6），
Figure SMS_69
(6),

其中，

Figure SMS_70
为第一多波束点云集合中第
Figure SMS_71
个离散测点的邻域距离，具体地，基于该离散测点与距离其最近的K个离散测点的距离的均值确定；
Figure SMS_72
为第一多波束点云集合中全部离散测点的邻域距离的均值，
Figure SMS_73
为第一多波束点云集合中任意一个离散测点的邻域距离小于
Figure SMS_74
的概率。in,
Figure SMS_70
is the first multi-beam point cloud set
Figure SMS_71
The neighborhood distance of a discrete measuring point is specifically determined based on the average of the distances between the discrete measuring point and the K discrete measuring points closest to it;
Figure SMS_72
is the mean of the neighborhood distances of all discrete measurement points in the first multi-beam point cloud set,
Figure SMS_73
The neighborhood distance of any discrete measurement point in the first multi-beam point cloud set is less than
Figure SMS_74
probability.

上述动态半径滤波的具体实施过程中，在保持滤波半径及起始半径滤波点数阈值为固定值的前提下，通过

Figure SMS_75
调节每个离散测点对应的实际点数阈值。其中，对于任意一个离散测点
Figure SMS_76
，当其位于中心波束区域时，其邻域距离
Figure SMS_77
较小，且其所处位置附近离散测点的密度较大，此时其对应的动态点数阈值保持为
Figure SMS_78
；其位于边缘波束区域时，由于离散测点较为系数，且越偏离中心波束，
Figure SMS_79
概率值越小，使得
Figure SMS_80
相应地也越小，从而使得动态点数阈值
Figure SMS_81
也越小，从而避免了边缘地形点被误删除。In the specific implementation process of the above dynamic radius filtering, under the premise of keeping the filter radius and the starting radius filter point threshold as fixed values,
Figure SMS_75
Adjust the actual point count threshold corresponding to each discrete measurement point.
Figure SMS_76
, when it is located in the center beam area, its neighborhood distance
Figure SMS_77
is small, and the density of discrete measurement points near its location is large. At this time, the corresponding dynamic point threshold remains
Figure SMS_78
; When it is located in the edge beam area, the discrete measurement points are relatively coefficient and the further away from the center beam,
Figure SMS_79
The smaller the probability value, the
Figure SMS_80
The smaller the dynamic point threshold
Figure SMS_81
The smaller it is, the more likely it is that edge terrain points will be accidentally deleted.

在计算

Figure SMS_82
的过程中，一般地，可以通过对第一多波束点云集合中全部离散测点的邻域距离进行排序以确定各个离散测点
Figure SMS_83
对应的
Figure SMS_84
，然而，在第一多波束点云集合中离散测点的数量过大时，对全部离散测点进行排序将使得海底地形生成效率大大降低，为此，需要在保证
Figure SMS_85
精度的基础上进一步提高计算
Figure SMS_86
的速度。In calculation
Figure SMS_82
In the process, generally, the neighborhood distances of all discrete measurement points in the first multi-beam point cloud set can be sorted to determine the distances of each discrete measurement point.
Figure SMS_83
Corresponding
Figure SMS_84
However, when the number of discrete measurement points in the first multi-beam point cloud set is too large, sorting all the discrete measurement points will greatly reduce the efficiency of seabed terrain generation.
Figure SMS_85
Further improve the calculation accuracy
Figure SMS_86
speed.

图2示出了通过对大量多波束测深数据的统计得到的任意一个离散测点的邻域距离小于L的概率p相对于L的变化情况，同时，图2还示出了当各个离散测点按照对数正态分布时p～L的相对变化情况。如图2所示，统计得到各个离散测点的邻域距离基本符合对数正态分布，因此，在一些优选的实施例中，还可以基于(7)式的对数正态分布函数确定

Figure SMS_87
，以加快滤波速度：FIG2 shows the change of the probability p of the neighborhood distance of any discrete measuring point being less than L relative to L obtained by statistics of a large amount of multi-beam bathymetric data. At the same time, FIG2 also shows the relative change of p ～ L when each discrete measuring point is distributed according to the log-normal distribution. As shown in FIG2, the neighborhood distance of each discrete measuring point obtained by statistics basically conforms to the log-normal distribution. Therefore, in some preferred embodiments, it can also be determined based on the log-normal distribution function of formula (7)
Figure SMS_87
, to speed up filtering:

Figure SMS_88
（7），
Figure SMS_88
(7),

其中，

Figure SMS_89
为误差函数，
Figure SMS_90
分别由(8)式、(9)式确定：in,
Figure SMS_89
is the error function,
Figure SMS_90
Determined by equations (8) and (9) respectively:

Figure SMS_91
（8），
Figure SMS_91
(8),

Figure SMS_92
（9）。
Figure SMS_92
(9).

进一步地，在一些优选的实施例中，在进行动态半径滤波时，所述滤波半径为

Figure SMS_93
，其中
Figure SMS_94
为大于等于1的整数。Further, in some preferred embodiments, when dynamic radius filtering is performed, the filtering radius is
Figure SMS_93
,in
Figure SMS_94
is an integer greater than or equal to 1.

由于海洋动力会侵蚀海底不规则部分，因此海底自然地形是连续变化的，尽管有坡度，但是不会突兀出现，误删的边缘地形细节同样适用。根据这一特性和密度聚类对噪声敏感的特点，在步骤S32中，对动态半径滤波后的存疑数据(即标定测点)进行密度聚类，将聚类结果为噪声的标定测点剔除，将其他聚类结果为非噪声的标定测点归入海底地形点云集合。Since ocean dynamics will erode irregular parts of the seabed, the natural topography of the seabed changes continuously. Although there is a slope, it will not appear abruptly, and the same applies to the mistakenly deleted edge terrain details. According to this characteristic and the characteristic that density clustering is sensitive to noise, in step S32, the doubtful data (i.e., calibration points) after dynamic radius filtering are density clustered, and the calibration points with clustering results as noise are eliminated, and other calibration points with clustering results as non-noise are classified into the seabed terrain point cloud set.

具体地，密度聚类算法是将若干个d维数据样本聚集成多个类,使同一类中样本的相似性最大，而不同类中样本的相似性最小。聚类过程包含核心点搜索、初始核心点选取、聚类簇扩散三个主要步骤。先在待聚类数据集中搜索所有满足条件的核心点；随后从任意一个核心点集群(核心点及其邻域半径内的点)开始，利用密度相连关系不断向未分类的点扩展直至无法继续，由此得到一个所有点都彼此密度相连的点集群，此点集群即可称为一个聚类簇，聚类簇内所有数据点标记为同一类；然后继续查询是否还有未访问的核心点，并开始新一轮聚类簇扩展，并继续形成新的聚类簇，直至所有核心点都被访问为止，剩余未被任何聚类簇吸纳的点将被标记为噪声。该算法能够有效识别彼此孤立的多个密集点集群，并将不能组成集群的离散点标记为噪声。Specifically, the density clustering algorithm clusters several d-dimensional data samples into multiple classes, so that the similarity of samples in the same class is maximized, while the similarity of samples in different classes is minimized. The clustering process includes three main steps: core point search, initial core point selection, and cluster diffusion. First, search for all core points that meet the conditions in the data set to be clustered; then, starting from any core point cluster (core point and points within its neighborhood radius), use the density connection relationship to continuously expand to unclassified points until it cannot continue, thereby obtaining a point cluster in which all points are density-connected to each other. This point cluster can be called a cluster, and all data points in the cluster are marked as the same class; then continue to query whether there are any unvisited core points, and start a new round of cluster expansion, and continue to form new clusters until all core points are visited, and the remaining points that are not absorbed by any cluster will be marked as noise. The algorithm can effectively identify multiple dense point clusters that are isolated from each other, and mark discrete points that cannot form a cluster as noise.

上述密度聚类算法已为本领域技术人员所知晓，但如直接将其应用于对原始多波束点云集合的去噪与滤波，则面临数据量过大，聚类过程过长等问题。因此，在本申请的实施例中，利用密度聚类对噪声敏感的特点，仅对经过动态半径滤波后得到的存疑数据进行密度聚类，以识别噪声点，将密度聚类标定的噪声点滤除，其余存疑数据保存为地形点。上述处理方式由于存疑数据相较于原始点云数据，数据量较小，聚类收敛时间短，使得算法具有较高的效率。The above density clustering algorithm is already known to those skilled in the art, but if it is directly applied to the denoising and filtering of the original multi-beam point cloud set, it will face problems such as too much data and too long clustering process. Therefore, in the embodiment of the present application, the characteristic of density clustering being sensitive to noise is utilized, and only the questionable data obtained after dynamic radius filtering is density clustered to identify noise points, and the noise points calibrated by density clustering are filtered out, and the remaining questionable data are saved as terrain points. The above processing method has a higher efficiency because the questionable data has a smaller data volume than the original point cloud data and the clustering convergence time is short.

进一步地，通过上述步骤S3获取海底地形点云集合后，即可通过步骤S4进行海底地形的建模。目前已经有多种基于点云数据的三维建模的方法，例如，可以根据海底地形点云集合中各个离散测点的空间位置信息建立互相之间的连接关系，进而形成三角/四角面片等形式的海底地形三维网格模型等。上述基于点云集合重建三维模型的方式已为本领域技术人员所知晓，在此不再赘述。Furthermore, after obtaining the seabed topography point cloud set through the above step S3, the seabed topography can be modeled through step S4. At present, there are many methods for three-dimensional modeling based on point cloud data. For example, a connection relationship between each other can be established according to the spatial position information of each discrete measurement point in the seabed topography point cloud set, thereby forming a three-dimensional grid model of the seabed topography in the form of a triangle/quadrant facet, etc. The above method of reconstructing a three-dimensional model based on a point cloud set is already known to those skilled in the art and will not be repeated here.

实施例1。Example 1.

本实施例采用上述海底地形多波束点云滤波方法对实测得到的多波束测深数据进行处理，图3为本实施例的具体实施流程。This embodiment uses the above-mentioned seabed topography multi-beam point cloud filtering method to process the measured multi-beam bathymetric data. FIG3 is a specific implementation flow of this embodiment.

在本实施例中，原始多波束测深数据共包含163227个离散测点，涵盖海底面积约为8542平方米，起始半径滤波点数阈值设置为100，通过对离散测点进行邻域距离的对数正态分布拟合并求取

Figure SMS_95
后，最终确定动态半径滤波的滤波半径为3.0717米。In this embodiment, the original multi-beam bathymetric data contains a total of 163,227 discrete measurement points, covering a seabed area of approximately 8,542 square meters. The threshold of the starting radius filter point number is set to 100. The logarithmic normal distribution of the neighborhood distance of the discrete measurement points is fitted and obtained.
Figure SMS_95
Finally, the filter radius of the dynamic radius filter is determined to be 3.0717 meters.

图4示意性地示出了使用上述海底地形多波束点云滤波方法得到的海底三维地形模型，作为对比，图5、图6分别示意性地示出了单独使用趋势面滤波方法、半径滤波方法得到的海底三维地形模型。通过将图4与图5至图6进行比较可以看出，使用本申请提出的海底地形多波束点云滤波方法，能够明显提升边缘波束部分滤波的精度与准确性，使得边缘地形细节得到较好的保留，同时避免了直接采用密度聚类算法造成的运算速度的降低，实现了多种算法的优势互补和有机结合。FIG4 schematically shows a three-dimensional seabed terrain model obtained by using the above-mentioned seabed terrain multi-beam point cloud filtering method. For comparison, FIG5 and FIG6 schematically show three-dimensional seabed terrain models obtained by using the trend surface filtering method and the radius filtering method alone. By comparing FIG4 with FIG5 to FIG6, it can be seen that the use of the seabed terrain multi-beam point cloud filtering method proposed in the present application can significantly improve the precision and accuracy of edge beam partial filtering, so that the edge terrain details are better preserved, while avoiding the reduction in computing speed caused by directly using the density clustering algorithm, and realizing the complementary advantages and organic combination of multiple algorithms.

以上对本申请的具体实施方式作了详细介绍，对于本技术领域的技术人员来说，在不脱离本申请原理的前提下，还可以对本申请进行若干改进和修饰，这些改进和修饰也属于本申请权利要求的保护范围。The above is a detailed introduction to the specific implementation methods of the present application. For those skilled in the art, several improvements and modifications may be made to the present application without departing from the principles of the present application. These improvements and modifications also fall within the scope of protection of the claims of the present application.

Claims (9)

1.一种海底地形多波束点云滤波方法，其特征在于，包括以下步骤：1. A method for filtering a multi-beam point cloud of a seafloor topography, characterized in that it comprises the following steps: S1，基于原始多波束测深数据构造原始多波束点云集合；S1, constructs the original multi-beam point cloud set based on the original multi-beam bathymetric data; S2，对所述原始多波束点云集合进行趋势面滤波，得到第一多波束点云集合；S2, performing trend surface filtering on the original multi-beam point cloud set to obtain a first multi-beam point cloud set; S3，对所述第一多波束点云集合进行基于动态半径滤波与密度聚类的组合滤波，得到海底地形点云集合；S3, performing combined filtering based on dynamic radius filtering and density clustering on the first multi-beam point cloud set to obtain a seabed terrain point cloud set; S4，基于所述海底地形点云集合生成海底三维地形模型。S4, generating a three-dimensional seabed terrain model based on the seabed terrain point cloud set. 2.根据权利要求1所述的一种海底地形多波束点云滤波方法，其特征在于，步骤S2进一步包括以下步骤：2. The method for filtering a multi-beam point cloud of a submarine topography according to claim 1, wherein step S2 further comprises the following steps: S21，基于(1)式建立海底地形的趋势面模型：S21, based on formula (1), establish the trend surface model of seafloor topography:
Figure QLYQS_1
（1），
Figure QLYQS_1
(1), 其中，
Figure QLYQS_2
为海底地形的趋势面模型函数，
Figure QLYQS_3
为测点平面坐标，
Figure QLYQS_4
为测点深度，
Figure QLYQS_5
为多项式曲面系数；in,
Figure QLYQS_2
is the trend surface model function of the seafloor topography,
Figure QLYQS_3
is the plane coordinate of the measuring point,
Figure QLYQS_4
is the depth of the measuring point,
Figure QLYQS_5
are the polynomial surface coefficients; S22，将(1)式变为(2)式的矩阵形式：S22, transform equation (1) into the matrix form of equation (2):
Figure QLYQS_6
（2），
Figure QLYQS_6
(2), 其中，
Figure QLYQS_7
，
Figure QLYQS_8
为模型系数矩阵，
Figure QLYQS_9
为观测深度矩阵；in,
Figure QLYQS_7
,
Figure QLYQS_8
is the model coefficient matrix,
Figure QLYQS_9
is the observation depth matrix; S23，基于原始多波束点云集合中各个离散测点的三维坐标，利用最小二乘法解得(3)式：S23, based on the three-dimensional coordinates of each discrete measurement point in the original multi-beam point cloud set, the least squares method is used to solve equation (3):
Figure QLYQS_10
(3)；
Figure QLYQS_10
(3); S24，遍历所述原始多波束点云集合的各个离散测点，并基于(4)式确定属于第一多波束点云集合的离散测点以得到第一多波束点云集合：S24, traverse each discrete measurement point of the original multi-beam point cloud set, and determine the discrete measurement points belonging to the first multi-beam point cloud set based on formula (4) to obtain the first multi-beam point cloud set:
Figure QLYQS_11
（4），
Figure QLYQS_11
(4), 其中，
Figure QLYQS_12
分别为原始多波束点云集合中第
Figure QLYQS_13
个离散测点的三维坐标，
Figure QLYQS_14
为基于第
Figure QLYQS_15
个离散测点的邻域内的多个离散测点深度确定的均方差，
Figure QLYQS_16
为趋势面滤波系数。in,
Figure QLYQS_12
They are the first
Figure QLYQS_13
The three-dimensional coordinates of discrete measurement points,
Figure QLYQS_14
Based on
Figure QLYQS_15
The mean square error of the depth determination of multiple discrete measurement points in the neighborhood of a discrete measurement point,
Figure QLYQS_16
is the trend surface filter coefficient. 3.根据权利要求2所述的一种海底地形多波束点云滤波方法，其特征在于：3. The method for filtering seabed topography multi-beam point cloud according to claim 2, characterized in that: 所述
Figure QLYQS_17
。Said
Figure QLYQS_17
. 4.根据权利要求1所述的一种海底地形多波束点云滤波方法，其特征在于，步骤S3进一步包括以下步骤：4. The method for filtering a multi-beam point cloud of a submarine topography according to claim 1, wherein step S3 further comprises the following steps: S31，基于动态半径滤波将所述第一多波束点云集合中的各个离散测点分类为接受测点与标定测点，将所述接受测点归入海底地形点云集合；S31, classifying each discrete measurement point in the first multi-beam point cloud set into an acceptance measurement point and a calibration measurement point based on dynamic radius filtering, and classifying the acceptance measurement point into a seabed terrain point cloud set; S32，对所述标定测点进行密度聚类，将密度聚类结果为非噪声的标定测点归入海底地形点云集合。S32, density clustering is performed on the calibration points, and calibration points with non-noise density clustering results are classified into a seabed terrain point cloud set. 5.根据权利要求4所述的一种海底地形多波束点云滤波方法，其特征在于，所述动态半径滤波基于(5)式进行：5. A method for filtering a multi-beam point cloud of seafloor topography according to claim 4, characterized in that the dynamic radius filtering is performed based on formula (5):
Figure QLYQS_18
（5），
Figure QLYQS_18
(5), 其中，
Figure QLYQS_19
为第一多波束点云集合中离散测点的个数，
Figure QLYQS_20
为第一多波束点云集合中各个离散测点的序号，
Figure QLYQS_21
为起始半径滤波点数阈值，
Figure QLYQS_22
为第一多波束点云集合在第
Figure QLYQS_23
个离散测点的滤波半径内包含的离散测点的个数，
Figure QLYQS_24
为
Figure QLYQS_25
的阈值变换系数。in,
Figure QLYQS_19
is the number of discrete measurement points in the first multi-beam point cloud set,
Figure QLYQS_20
is the serial number of each discrete measurement point in the first multi-beam point cloud set,
Figure QLYQS_21
is the starting radius filter point threshold,
Figure QLYQS_22
The first multi-beam point cloud is collected in
Figure QLYQS_23
The number of discrete measurement points contained in the filter radius of discrete measurement points,
Figure QLYQS_24
for
Figure QLYQS_25
The threshold transformation coefficient. 6.根据权利要求5所述的一种海底地形多波束点云滤波方法，其特征在于，所述
Figure QLYQS_26
基于(6)式确定：6. The method for filtering seafloor topography multi-beam point cloud according to claim 5, characterized in that
Figure QLYQS_26
Based on formula (6), we determine:
Figure QLYQS_27
（6），
Figure QLYQS_27
(6), 其中，
Figure QLYQS_28
为第一多波束点云集合中第
Figure QLYQS_29
个离散测点的邻域距离，
Figure QLYQS_30
为第一多波束点云集合中全部离散测点的邻域距离的均值，
Figure QLYQS_31
为第一多波束点云集合中任意一个离散测点的邻域距离小于
Figure QLYQS_32
的概率。in,
Figure QLYQS_28
is the first multi-beam point cloud set
Figure QLYQS_29
The neighborhood distance of discrete measurement points,
Figure QLYQS_30
is the mean of the neighborhood distances of all discrete measurement points in the first multi-beam point cloud set,
Figure QLYQS_31
The neighborhood distance of any discrete measurement point in the first multi-beam point cloud set is less than
Figure QLYQS_32
probability. 7.根据权利要求6所述的一种海底地形多波束点云滤波方法，其特征在于：7. The method for filtering seafloor topography multi-beam point cloud according to claim 6, characterized in that: 每个离散测点的邻域距离基于该离散测点与其最接近的K个离散测点的距离的均值确定。The neighborhood distance of each discrete measurement point is determined based on the average of the distances between the discrete measurement point and its K closest discrete measurement points. 8.根据权利要求6所述的一种海底地形多波束点云滤波方法，其特征在于，所述
Figure QLYQS_33
基于(7)式确定：8. The method for filtering seafloor topography multi-beam point cloud according to claim 6, characterized in that
Figure QLYQS_33
Based on formula (7), we determine:
Figure QLYQS_34
（7），
Figure QLYQS_34
(7), 其中，
Figure QLYQS_35
为误差函数，
Figure QLYQS_36
分别由(8)式、(9)式确定：in,
Figure QLYQS_35
is the error function,
Figure QLYQS_36
Determined by equations (8) and (9) respectively:
Figure QLYQS_37
（8），
Figure QLYQS_37
(8),
Figure QLYQS_38
（9）。
Figure QLYQS_38
(9). 9.根据权利要求8所述的一种海底地形多波束点云滤波方法，其特征在于：9. The method for filtering seafloor topography multi-beam point cloud according to claim 8, characterized in that: 所述滤波半径为
Figure QLYQS_39
，其中
Figure QLYQS_40
为大于等于1的整数。The filtering radius is
Figure QLYQS_39
,in
Figure QLYQS_40
is an integer greater than or equal to 1.
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