CN109671152B - Line point cloud geometric characteristic estimation method based on Gaussian weighted discrete derivative - Google Patents

Line point cloud geometric characteristic estimation method based on Gaussian weighted discrete derivative Download PDF

Info

Publication number
CN109671152B
CN109671152B CN201811460397.7A CN201811460397A CN109671152B CN 109671152 B CN109671152 B CN 109671152B CN 201811460397 A CN201811460397 A CN 201811460397A CN 109671152 B CN109671152 B CN 109671152B
Authority
CN
China
Prior art keywords
discrete
derivative
point
point cloud
line
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201811460397.7A
Other languages
Chinese (zh)
Other versions
CN109671152A (en
Inventor
王磊
安毅
马蕊
王晋豫
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Dalian University of Technology
Original Assignee
Dalian University of Technology
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Dalian University of Technology filed Critical Dalian University of Technology
Priority to CN201811460397.7A priority Critical patent/CN109671152B/en
Publication of CN109671152A publication Critical patent/CN109671152A/en
Application granted granted Critical
Publication of CN109671152B publication Critical patent/CN109671152B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
    • G06T17/10—Constructive solid geometry [CSG] using solid primitives, e.g. cylinders, cubes
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2200/00—Indexing scheme for image data processing or generation, in general
    • G06T2200/08—Indexing scheme for image data processing or generation, in general involving all processing steps from image acquisition to 3D model generation

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Mathematical Physics (AREA)
  • Theoretical Computer Science (AREA)
  • Mathematical Analysis (AREA)
  • Pure & Applied Mathematics (AREA)
  • Computational Mathematics (AREA)
  • Data Mining & Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Geometry (AREA)
  • Software Systems (AREA)
  • Operations Research (AREA)
  • Algebra (AREA)
  • Computer Graphics (AREA)
  • Databases & Information Systems (AREA)
  • General Engineering & Computer Science (AREA)
  • Complex Calculations (AREA)
  • Length Measuring Devices By Optical Means (AREA)

Abstract

The invention relates to the technical field of three-dimensional point cloud data processing and three-dimensional scene reconstruction, in particular to a line point cloud geometric characteristic estimation method based on Gaussian weighted discrete derivatives, which comprises the following steps: the method comprises the steps of (1) obtaining line point cloud data, (2) calculating line point cloud parameters, (3) defining Gaussian weighted discrete derivatives, (4) deducing a parameterized curve geometric characteristic calculation formula, and (5) estimating line point cloud geometric characteristics. The invention has the following advantages: firstly, calculating a discrete tangent line by using Gaussian weighted least square, defining a Gaussian weighted discrete derivative by the slope of the tangent line, and adjusting the contribution of the introduced Gaussian weight to the discrete derivative of a given point according to the distance from an adjacent point to the given point so as to reduce the influence of noise; secondly, a geometric characteristic formula of a common parametric curve is deduced by using a space analytic geometry theory, a classical differential geometry is discretized by combining a Gaussian weighted discrete derivative, a unit tangent vector and curvature of the line point cloud are estimated, and estimation accuracy is improved.

Description

Line point cloud geometric characteristic estimation method based on Gaussian weighted discrete derivative
Technical Field
The invention relates to a line point cloud geometric characteristic estimation method based on Gaussian weighted discrete derivatives, and belongs to the technical field of three-dimensional point cloud data processing and three-dimensional scene reconstruction.
Background
With the continuous development of three-dimensional scanning ranging technology, the three-dimensional point cloud data is more and more widely applied in the fields of reverse engineering, industrial detection, autonomous navigation, cultural relic protection, virtual reality and the like. The three-dimensional point cloud data processing technology plays a crucial role as a basis for realizing the application. In the three-dimensional point cloud data processing technology, the geometric characteristic estimation of the three-dimensional point cloud data is a very key technology, is the basis of subsequent processing such as multi-view registration, region segmentation, model reconstruction and the like, and has obvious influence on the application effect of the three-dimensional point cloud data. Therefore, the research on how to accurately estimate the geometric characteristics from the three-dimensional point cloud data has important significance for improving the application level of the three-dimensional point cloud data.
Geometrically, three-dimensional point cloud data can be divided into two types: line point cloud data and surface point cloud data. The two-dimensional laser scanning range finder is used for scanning a scene object, and line point cloud data of the scene object can be obtained, wherein the line point cloud data is a group of ordered discrete points distributed on an intersection line of the surface of the object and a scanning plane. The method comprises the steps of scanning a scene object by using a three-dimensional laser scanning range finder, obtaining surface point cloud data of the scene object, wherein the surface point cloud data is a group of discrete points distributed on the surface of the object, and extracting line point cloud data from the surface point cloud data. The estimation of the geometrical characteristics of the line point cloud refers to estimating the geometrical characteristics of tangent vectors, curvatures and the like at discrete points by using the coordinate information of the discrete points in the line point cloud data.
The principle of the estimation method is that according to the definition of discrete tangent, the discrete tangent of a given point is calculated by a solution method with a constraint optimization problem, the discrete derivative of the discrete curve is estimated by using the slope of the discrete tangent, and the geometric characteristic of the given point is estimated by the discrete derivative. The invention is different from the following: according to the method, the influence of data noise and adjacent point distance on the estimation of the geometrical characteristics of the line point cloud is fully considered, the Gaussian weighted discrete derivative is defined, the classical differential geometry is discretized through the Gaussian weighted discrete derivative, the geometrical characteristic estimation of the line point cloud data is realized, and the estimation accuracy and robustness are improved.
Disclosure of Invention
In order to solve the defects in the prior art, the invention aims to provide a line point cloud geometric characteristic estimation method based on Gaussian weighted discrete derivatives. Aiming at an actual scene, firstly, a two-dimensional laser scanning range finder is utilized to scan a scene object, line point cloud data of the scene object is obtained, parameterization is conducted on the line point cloud data, a Gaussian weighted discrete derivative is defined, the discrete derivative of the line point cloud is calculated according to the definition of the Gaussian weighted discrete derivative, and the unit tangent vector and the curvature of the line point cloud are estimated by combining the Gaussian weighted discrete derivative and the geometric characteristics of a common parameterized curve. According to the method, the influence of data noise and the distance between adjacent points on the estimation of the geometrical characteristics of the point cloud is fully considered, the Gaussian weighted discrete derivative is defined, the unit tangent vector and the curvature of the point cloud are calculated, the contribution of the introduced Gaussian weighted discrete derivative to the given point is adjusted according to the distance between the adjacent points and the given point, the influence caused by the noise is reduced, and the accuracy of the unit tangent vector and the curvature estimation is improved.
In order to achieve the purpose of the invention and solve the problems in the prior art, the invention adopts the technical scheme that: a line point cloud geometric characteristic estimation method based on Gaussian weighted discrete derivatives comprises the following steps:
step 1, line point cloud data is obtained, a scene object is scanned by using a two-dimensional laser scanning range finder, and line point cloud data P = { P } of the scene object is obtained i ＝(x i ,y i ,z i ) I is more than or equal to 1 and less than or equal to n, which is a group of ordered discrete points distributed on the intersection line of the scanning plane and the object surface, wherein p i ＝(x i ,y i ,z i ) Discrete points on the line point cloud P are shown, i is the serial number of the discrete points, and n is the number of the discrete points;
step 2, calculating line point cloud parameters, and calculating each discrete point P in the line point cloud P by utilizing an accumulative chord length parameterization method i Chord length parameter t i Described according to the formula (1),
Figure BDA0001888545530000021
parameter t i Is epsilon of S and discrete point p i ＝(x i ,y i ,z i ) Form a one-to-one mapping relation alpha by epsilon P d S → P, for each parameter t i All e S have a discrete point p i ＝(x i ,y i ,z i ) E P corresponds to it and is expressed as: p is a radical of i ＝α d (t i )＝(x d (t i ),y d (t i ),z d (t i ))，t i E.g. S, wherein S = { t = i I is more than or equal to 1 and less than or equal to n is taken as a parameter set, x i ＝x d (t i )、y i ＝y d (t i ) And z i ＝z d (t i ) Is a discrete function of the parameter;
step 3, defining Gaussian weighted discrete derivative, defining derivative of discrete function by using geometric meaning of derivative of continuous function, and calculating discrete function x i ＝x d (t i )、y i ＝y d (t i ) And z i ＝z d (t i ) Specifically, the following substeps are included:
step (a), geometrically, the derivative of the continuous function at a given point is equivalent to the slope of the tangent of the continuous function at that point, thus, first defining the tangent of the discrete function at the given point, called discrete tangent; discrete function x i ＝x d (t i ) At a given point (t) i ,x i ) The discrete tangent line of (A) is defined as a straight line satisfying the following three conditions
Figure BDA0001888545530000037
1) Straight line
Figure BDA0001888545530000035
Passing a given point (t) i ,x i )；
2) Straight line
Figure BDA0001888545530000036
With a given point (t) i ,x i ) Neighboring point of { (t) j ,x j ) J is more than or equal to | i-m and less than or equal to i + m } and the sum of squares of distances in the x-axis direction is the minimum;
3) The farther the adjacent point is from the given point, the smaller the influence on the straight line is;
wherein m is the radius of the neighborhood, j is the serial number of the neighboring point, a is the slope of the discrete tangent, and b is the intercept of the discrete tangent on the x axis;
step (b) of calculating the solution of the constrained optimization problem at a given point (t) according to the definition of the discrete tangent i ,x i ) Discrete tangent of (2), constrained optimization problemThe problem is described in terms of equation (2),
Figure BDA0001888545530000031
wherein the content of the first and second substances,
Figure BDA0001888545530000032
is a neighboring point (t) j ,x j ) The Gaussian weight of (2) is described according to the formula (3),
Figure BDA0001888545530000033
wherein sigma is the bandwidth, the slope a of the discrete tangent can be solved by using a Lagrange multiplier method,
Figure BDA0001888545530000034
defining a discrete function x according to the slope a of the discrete tangent i ＝x d (t i ) At a given point (t) i ,x i ) Is described in equation (5),
Figure BDA0001888545530000041
wherein, x' i ＝x′ d (t i ) As a discrete function x i ＝x d (t i ) At a given point (t) i ,x i ) A derivative of (a);
step (c), using the same method as step 3 substeps (a) and (b), a discrete function y can be defined i ＝y d (t i ) And z i ＝z d (t i ) At a given point (t) i ,y i ) And (t) i ,z i ) Are described in equations (6) and (7), respectively,
Figure BDA0001888545530000042
Figure BDA0001888545530000043
wherein (t) j ,y j ) Is a given point (t) i ,y i ) (ii) neighbors of (t) j ,z j ) Is a given point (t) i ,z i ) Is the bandwidth y' i ＝y′ d (t i ) As a discrete function y i ＝y d (t i ) At a given point (t) i ,y i ) Derivative of, z' i ＝z′ d (t i ) As a discrete function z i ＝z d (t i ) At a given point (t) i ,z i ) The derivative of (a) of (b),
Figure BDA0001888545530000046
and
Figure BDA0001888545530000047
are Gaussian weights and are respectively described according to formulas (8) and (9),
Figure BDA0001888545530000044
Figure BDA0001888545530000045
then the vector discrete function p of the point cloud i ＝α d (t i )＝(x d (t i ),y d (t i ),z d (t i ) At t) i The derivative of (a) is defined as,
p′ i ＝α′ d (t i )＝(x′ d (t i ),y′ d (t i ),z′ d (t i )), (10)
wherein, p' i ＝α′ d (t i ) As a vector discrete function p i ＝α d (t i )＝(x d (t i ),y d (t i ),z d (t i ) At t) i The derivative of (a), referred to as discrete derivative;
step 4, deducing a calculation formula of the geometric characteristics of the parameterized curve, obtaining a unit tangent vector v (t) and a curvature kappa (t) of the ordinary parameterized curve alpha (t) = (x (t), y (t), z (t)) according to a space analytic geometry theory,
Figure BDA0001888545530000051
Figure BDA0001888545530000052
wherein α '(t) is the derivative of α (t) and v' (t) is the derivative of v (t);
step 5, estimating the geometrical characteristics of the point cloud of the line, and estimating the geometrical characteristics of the point cloud of the line at t by using the discrete derivative and the geometrical characteristics of a common parameterized curve i Unit tangent vector v of d (t i ) And curvature k d (t i ) Respectively, are as follows,
Figure BDA0001888545530000053
Figure BDA0001888545530000054
v 'of the total' d (t i ) As a vector discrete function v d (t i ) At t i The discrete derivatives of (c) are calculated using the same method as step 3.
The invention has the beneficial effects that: a line point cloud geometric characteristic estimation method based on Gaussian weighted discrete derivatives comprises the following steps: the method comprises the steps of (1) obtaining line point cloud data, (2) calculating line point cloud parameters, (3) defining Gaussian weighted discrete derivatives, (4) deducing a parameterized curve geometric characteristic calculation formula, and (5) estimating line point cloud geometric characteristics. Compared with the prior art, the invention has the following advantages: firstly, the discrete tangent is calculated by using a Gaussian weighted least square method, the Gaussian weighted discrete derivative is defined by the slope of the tangent, the introduced Gaussian weight adjusts the contribution of the introduced Gaussian weight to the discrete derivative of a given point according to the distance from an adjacent point to the given point, and the advantage of reducing the noise influence is fully exerted; secondly, the method deduces a geometric characteristic formula of a common parameterized curve by using a space analytic geometry theory, discretizes the classical differential geometry by combining a Gaussian weighted discrete derivative, estimates the unit tangent vector and curvature of the line point cloud, and improves the estimation accuracy.
Drawings
FIG. 1 is a flow chart of the method steps of the present invention.
Fig. 2 is a schematic diagram of discrete tangent lines.
Fig. 3 is a diagram of the result of tangent vector estimation.
Fig. 4 is a graph of curvature estimation results.
In the figure: (a) The curvature estimation result of the longitudinal line point cloud is shown in the figure, and the curvature estimation result of the transverse line point cloud is shown in the figure.
Detailed Description
The invention will be further described with reference to the accompanying drawings.
As shown in fig. 1, a method for estimating geometrical characteristics of a point cloud based on gaussian weighted discrete derivatives includes the following steps:
step 1, line point cloud data is obtained, a scene object is scanned by using a two-dimensional laser scanning range finder, and line point cloud data P = { P } of the scene object is obtained i ＝(x i ,y i ,z i ) I 1 ≦ i ≦ n }, which is a set of ordered discrete points distributed across the intersection of the scan plane and the object surface, where p i ＝(x i ,y i ,z i ) Discrete points on the line point cloud P are shown, i is the serial number of the discrete points, and n is the number of the discrete points;
step 2, calculating line point cloud parameters, and calculating each discrete point P in the line point cloud P by utilizing an accumulative chord length parameterization method i Chord length parameter t i Described according to the formula (1),
Figure BDA0001888545530000061
parameter t i E S and discrete point p i ＝(x i ,y i ,z i ) Form a one-to-one mapping relation alpha by epsilon P d S → P, for each parameter t i Has a discrete point p for both epsilon and S i ＝(x i ,y i ,z i ) E P corresponds to it and is expressed as: p is a radical of i ＝α d (t i )＝(x d (t i ),y d (t i ),z d (t i ))，t i E S, where S = { t i I is more than or equal to 1 and less than or equal to n is taken as a parameter set, x i ＝x d (t i )、y i ＝y d (t i ) And z i ＝z d (t i ) As a discrete function of the parameter;
step 3, defining Gaussian weighted discrete derivative, defining the derivative of the discrete function by using the geometric meaning of the derivative of the continuous function, and calculating the discrete function x i ＝x d (t i )、y i ＝y d (t i ) And z i ＝z d (t i ) Specifically, the following substeps are included:
step (a), geometrically, the derivative of the continuous function at a given point is equivalent to the slope of the tangent of the continuous function at that point, thus, first defining the tangent of the discrete function at the given point, called discrete tangent; discrete function x i ＝x d (t i ) At a given point (t) i ,x i ) Is defined as a straight line which simultaneously satisfies the following three conditions
Figure BDA0001888545530000071
1) Straight line
Figure BDA0001888545530000072
Passing a given point (t) i ,x i )；
2)Straight line
Figure BDA0001888545530000073
With a given point (t) i ,x i ) Neighboring point of { (t) j ,x j ) J is more than or equal to | i-m and less than or equal to i + m } and the sum of squares of distances in the x-axis direction is the minimum;
3) The farther the adjacent point is from the given point, the smaller the influence on the straight line is;
wherein m is the radius of the neighborhood, j is the serial number of the neighboring point, a is the slope of the discrete tangent, b is the intercept of the discrete tangent on the x-axis, as shown in fig. 2;
step (b) of calculating at a given point (t) by means of a solution to a constrained optimization problem according to the definition of the discrete tangent i ,x i ) The constrained optimization problem is described in equation (2),
Figure BDA0001888545530000074
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0001888545530000075
is a neighboring point (t) j ,x j ) The Gaussian weight of (2) is described according to the formula (3),
Figure BDA0001888545530000076
wherein, sigma is the bandwidth, the slope a of the discrete tangent can be solved by utilizing the Lagrange multiplier method,
Figure BDA0001888545530000077
defining a discrete function x according to the slope a of the discrete tangent i ＝x d (t i ) At a given point (t) i ,x i ) Is described in equation (5),
Figure BDA0001888545530000078
wherein x is i ′＝x′ d (t i ) As a discrete function x i ＝x d (t i ) At a given point (t) i ,x i ) A derivative of (a);
step (c), using the same method as step 3 substeps (a) and (b), a discrete function y can be defined i ＝y d (t i ) And z i ＝z d (t i ) At a given point (t) i ,y i ) And (t) i ,z i ) Are described in equations (6) and (7), respectively,
Figure BDA0001888545530000081
Figure BDA0001888545530000082
wherein (t) j ,y j ) Is a given point (t) i ,y i ) (ii) neighbors of (t) j ,z j ) Is a given point (t) i ,z i ) Is the bandwidth, y i ′＝y′ d (t i ) As a discrete function y i ＝y d (t i ) At a given point (t) i ,y i ) Z '= z' d (t i ) As a discrete function z i ＝z d (t i ) At a given point (t) i ,z i ) The derivative of (a) of (b),
Figure BDA0001888545530000087
and
Figure BDA0001888545530000088
are Gaussian weights and are respectively described according to formulas (8) and (9),
Figure BDA0001888545530000083
Figure BDA0001888545530000084
then the vector discrete function p of the point cloud i ＝α d (t i )＝(x d (t i ),y d (t i ),z d (t i ) At t) i The derivative of (a) is defined as,
p′ i ＝α′ d (t i )＝(x′ d (t i ),y′ d (t i ),z′ d (t i )), (10)
wherein, p' i ＝α′ d (t i ) As a vector discrete function p i ＝α d (t i )＝(x d (t i ),y d (t i ),z d (t i ) At t) i The derivative of (b), referred to as discrete derivative;
step 4, deducing a calculation formula of the geometric characteristics of the parameterized curve, obtaining a unit tangent vector v (t) and a curvature kappa (t) of the ordinary parameterized curve alpha (t) = (x (t), y (t), z (t)) according to a space analytic geometry theory,
Figure BDA0001888545530000085
Figure BDA0001888545530000086
wherein α '(t) is the derivative of α (t) and v' (t) is the derivative of v (t);
step 5, estimating the geometrical characteristics of the point cloud of the line, and estimating the geometrical characteristics of the point cloud of the line at t by using the discrete derivative and the geometrical characteristics of a common parameterized curve i Unit tangent vector v of d (t i ) And curvature k d (t i ) Respectively, are as follows,
Figure BDA0001888545530000091
Figure BDA0001888545530000092
v 'of the total' d (t i ) As a vector discrete function v d (t i ) At t i Discrete derivatives of the points are calculated by the same method as that in the step 3, a tangent vector estimation result graph of a circular line point cloud is shown in fig. 3, surface point cloud data of a real office scene is shown in fig. 4, longitudinal line point clouds are extracted from the surface point cloud data according to scanning column numbers, transverse line point clouds are extracted according to scanning line numbers, then curvature estimation is carried out on the line point clouds respectively, and curvature estimation results are shown in fig. 4 (a) and fig. 4 (b).
The invention has the advantages that: firstly, the discrete tangent is calculated by using a Gaussian weighted least square method, the Gaussian weighted discrete derivative is defined by the slope of the tangent, the introduced Gaussian weight adjusts the contribution of the introduced Gaussian weight to the discrete derivative of a given point according to the distance from an adjacent point to the given point, and the advantage of reducing the noise influence is fully exerted; secondly, the method deduces a geometric characteristic formula of a common parameterized curve by using a space analytic geometry theory, discretizes the classical differential geometry by combining a Gaussian weighted discrete derivative, estimates the unit tangent vector and curvature of the line point cloud, and improves the estimation accuracy.

Claims (1)

1. A method for estimating geometrical characteristics of a line point cloud based on Gaussian weighted discrete derivatives is characterized by comprising the following steps:
step 1, line point cloud data is obtained, a scene object is scanned by using a two-dimensional laser scanning range finder, and the line point cloud data P = { P } of the scene object is obtained i ＝(x i ,y i ,z i ) I is more than or equal to 1 and less than or equal to n, which is a group of ordered discrete points distributed on the intersection line of the scanning plane and the object surface, wherein p i ＝(x i ,y i ,z i ) Discrete points on the line point cloud P, i is the serial number of the discrete points, and n is the number of the discrete points;
step 2, calculating line point cloud parameters, and calculating each discrete point P in the line point cloud P by utilizing an accumulative chord length parameterization method i Chord length parameter t i Described according to the formula (1),
Figure FDA0001888545520000011
parameter t i E S and discrete point p i ＝(x i ,y i ,z i ) Form a one-to-one mapping relation alpha by epsilon P d S → P, for each parameter t i All e S have a discrete point p i ＝(x i ,y i ,z i ) E P corresponds to it and is expressed as: p is a radical of i ＝α d (t i )＝(x d (t i ),y d (t i ),z d (t i ))，t i E S, where S = { t i I is more than or equal to 1 and less than or equal to n is taken as a parameter set, x i ＝x d (t i )、y i ＝y d (t i ) And z i ＝z d (t i ) Is a discrete function of the parameter;
step 3, defining Gaussian weighted discrete derivative, defining derivative of discrete function by using geometric meaning of derivative of continuous function, and calculating discrete function x i ＝x d (t i )、y i ＝y d (t i ) And z i ＝z d (t i ) Specifically, the following substeps are included:
(a) Geometrically, the derivative of a continuous function at a given point is equivalent to the slope of the tangent of the continuous function at that point, thus first defining the tangent of the discrete function at the given point, called discrete tangent; discrete function x i ＝x d (t i ) At a given point (t) i ,x i ) Is defined as a straight line x = at + b satisfying the following three conditions at the same time,
1) Straight line x = at + b passes through a given point (t) i ,x i )；
2) Straight line x = at + b and given point (t) i ,x i ) Adjacent point of (t) j ,x j ) J is more than or equal to | i-m and less than or equal to i + m } and the sum of squares of distances in the x-axis direction is the minimum;
3) The farther the adjacent point is from the given point, the smaller the influence on the straight line is;
wherein m is the radius of the neighborhood, j is the serial number of the neighboring point, a is the slope of the discrete tangent, and b is the intercept of the discrete tangent on the x axis;
(b) Calculating at a given point (t) by a solution method of a constrained optimization problem based on the definition of the discrete tangent i ,x i ) The constrained optimization problem is described in equation (2),
Figure FDA0001888545520000021
wherein the content of the first and second substances,
Figure FDA0001888545520000022
is a neighboring point (t) j ,x j ) The Gaussian weight of (2) is described according to the formula (3),
Figure FDA0001888545520000023
wherein, sigma is the bandwidth, the slope a of the discrete tangent can be solved by utilizing the Lagrange multiplier method,
Figure FDA0001888545520000024
defining a discrete function x according to the slope a of the discrete tangent i ＝x d (t i ) At a given point (t) i ,x i ) Is described in equation (5),
Figure FDA0001888545520000025
wherein, x' i ＝x′ d (t i ) As a discrete function x i ＝x d (t i ) At a given point (t) i ,x i ) A derivative of (a);
(c) Defining a discrete function y using the same method as substeps (a) and (b) of step 3 i ＝y d (t i ) And z i ＝z d (t i ) At a given point (t) i ,y i ) And (t) i ,z i ) Are described in equations (6) and (7), respectively,
Figure FDA0001888545520000026
Figure FDA0001888545520000027
wherein (t) j ,y j ) Is a given point (t) i ,y i ) (t) neighbors j ,z j ) Is a given point (t) i ,z i ) σ is bandwidth, y' i ＝y′ d (t i ) As a discrete function y i ＝y d (t i ) At a given point (t) i ,y i ) Derivative of, z' i ＝z′ d (t i ) As a discrete function z i ＝z d (t i ) At a given point (t) i ,z i ) The derivative of (a) of (b),
Figure FDA0001888545520000031
and
Figure FDA0001888545520000032
are Gaussian weights and are respectively described according to formulas (8) and (9),
Figure FDA0001888545520000033
Figure FDA0001888545520000034
then the vector discrete function p of the point cloud i ＝α d (t i )＝(x d (t i ),y d (t i ),z d (t i ) At t) i The derivative of (a) is defined as,
p′ i ＝α′ d (t i )＝(x′ d (t i ),y′ d (t i ),z′ d (t i )), (10)
wherein, p' i ＝α′ d (t i ) As a vector discrete function p i ＝α d (t i )＝(x d (t i ),y d (t i ),z d (t i ) At t) i The derivative of (a), referred to as discrete derivative;
step 4, deducing a calculation formula of the geometric characteristics of the parameterized curve, obtaining a unit tangent vector v (t) and a curvature kappa (t) of the ordinary parameterized curve alpha (t) = (x (t), y (t), z (t)) according to a space analytic geometry theory,
Figure FDA0001888545520000035
Figure FDA0001888545520000036
wherein α '(t) is the derivative of α (t) and v' (t) is the derivative of v (t);
step 5, estimating the geometrical characteristics of the point cloud of the line, and estimating the geometrical characteristics of the point cloud of the line at t by using the discrete derivative and the geometrical characteristics of a common parameterized curve i Unit tangent vector v of d (t i ) And curvature k d (t i ) Respectively, are as follows,
Figure FDA0001888545520000037
Figure FDA0001888545520000041
wherein, v' d (t i ) As a vector discrete function v d (t i ) At t i The discrete derivatives of (c) are calculated using the same method as step 3.
CN201811460397.7A 2018-12-01 2018-12-01 Line point cloud geometric characteristic estimation method based on Gaussian weighted discrete derivative Active CN109671152B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201811460397.7A CN109671152B (en) 2018-12-01 2018-12-01 Line point cloud geometric characteristic estimation method based on Gaussian weighted discrete derivative

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201811460397.7A CN109671152B (en) 2018-12-01 2018-12-01 Line point cloud geometric characteristic estimation method based on Gaussian weighted discrete derivative

Publications (2)

Publication Number Publication Date
CN109671152A CN109671152A (en) 2019-04-23
CN109671152B true CN109671152B (en) 2022-10-04

Family

ID=66143517

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201811460397.7A Active CN109671152B (en) 2018-12-01 2018-12-01 Line point cloud geometric characteristic estimation method based on Gaussian weighted discrete derivative

Country Status (1)

Country Link
CN (1) CN109671152B (en)

Families Citing this family (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110555826B (en) * 2019-08-04 2022-04-15 大连理工大学 Three-dimensional point cloud feature extraction method based on local outlier factors
CN114494271A (en) * 2022-02-18 2022-05-13 芙索特(上海)医疗科技有限公司 Method for calculating ATR angle of human back

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104318622A (en) * 2014-10-25 2015-01-28 大连理工大学 Triangular mesh modeling method of indoor scene inhomogeneous three dimension point cloud data
CN104463856A (en) * 2014-11-25 2015-03-25 大连理工大学 Outdoor scene three-dimensional point cloud data ground extraction method based on normal vector ball
CN104504709A (en) * 2014-12-28 2015-04-08 大连理工大学 Feature ball based classifying method of three-dimensional point-cloud data of outdoor scene

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104318622A (en) * 2014-10-25 2015-01-28 大连理工大学 Triangular mesh modeling method of indoor scene inhomogeneous three dimension point cloud data
CN104463856A (en) * 2014-11-25 2015-03-25 大连理工大学 Outdoor scene three-dimensional point cloud data ground extraction method based on normal vector ball
CN104504709A (en) * 2014-12-28 2015-04-08 大连理工大学 Feature ball based classifying method of three-dimensional point-cloud data of outdoor scene

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
散乱点云数据特征信息提取算法;史皓良等;《计算机工程》;20170815(第08期);全文 *
顾及几何特征的规则激光点云分割方法;方军等;《测绘通报》;20160825(第08期);全文 *

Also Published As

Publication number Publication date
CN109671152A (en) 2019-04-23

Similar Documents

Publication Publication Date Title
CN109887021B (en) Cross-scale-based random walk stereo matching method
CN106503837B (en) A kind of time optimal Route planner based on improvement level set algorithm
CN110246151B (en) Underwater robot target tracking method based on deep learning and monocular vision
CN109671152B (en) Line point cloud geometric characteristic estimation method based on Gaussian weighted discrete derivative
CN102708382B (en) Multi-target tracking method based on variable processing windows and variable coordinate systems
CN103942837B (en) The direct building method of blade point cloud model cross section curve based on Successive linear programming
CN107607107A (en) A kind of Slam method and apparatus based on prior information
CN114565616B (en) Unstructured road state parameter estimation method and system
WO2006082773A1 (en) Object measurement method and computer software program for measuring 3-dimensional shape of object by using computer system
CN105957097A (en) Image registration method based on mixed mutual information and improved particle swarm optimization
CN112862858A (en) Multi-target tracking method based on scene motion information
Djavareshkian et al. Neuro-fuzzy based approach for estimation of Hydrofoil performance
CN108871365B (en) State estimation method and system under course constraint
CN108460781A (en) A kind of active contour image partition method and device based on improvement SPF
CN104200434A (en) Non-local mean image denoising method based on noise variance estimation
CN103793924A (en) Flow field image self-adaption motion vector estimating method based on FHT-CC
CN110378199B (en) Rock-soil body displacement monitoring method based on multi-period images of unmanned aerial vehicle
CN110688440A (en) Map fusion method suitable for less sub-map overlapping parts
CN109816710B (en) Parallax calculation method for binocular vision system with high precision and no smear
CN103700095A (en) Log end surface image partitioning algorithm for improving active contour model based on circle constraint
CN107516007B (en) Method for calculating residence time of air mass
CN110555826B (en) Three-dimensional point cloud feature extraction method based on local outlier factors
Fan et al. A robust roll angle estimation algorithm based on gradient descent
Höllmann et al. Geometry-based regularisation for dense image matching via uncertainty-driven depth propagation
CN111460974A (en) Optimization-based global feature extraction method for scattered point cloud data

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant