CN104574333A

CN104574333A - LIDAR point cloud registration method under model straight line constraints

Info

Publication number: CN104574333A
Application number: CN201510005364.3A
Authority: CN
Inventors: 盛庆红; 肖晖; 张斌; 柳建锋; 王惠南
Original assignee: Nanjing University of Aeronautics and Astronautics
Current assignee: Suzhou Zhongketianqi Remote Sensing Technology Co ltd
Priority date: 2015-01-06
Filing date: 2015-01-06
Publication date: 2015-04-29
Anticipated expiration: 2035-01-06
Also published as: CN104574333B

Abstract

The invention discloses an LIDAR point cloud registration method under model straight line constraints and belongs to surveying and mapping fields. Homonymous straight lines are extracted from LIDAR point clouds on a reference survey station and a survey station to be registered respectively; homonymous model straight lines are established; a model straight line collinear condition equation is established, so that a model straight line to be registered is linearly zoomed, rotated and horizontally moved to coincide with a reference model straight line; registration parameters are calculated. LIDAR point cloud registration is conducted by means of the model straight lines, geometric constraint performance of the straight lines is brought into full play, geometric strength of a stereoscopic model can be enhanced, and therefore precision of LIDAR point cloud registration is improved.

Description

LIDAR point cloud method under model line constraint

Technical field:

LIDAR point cloud method under model line constraint of the present invention, relates to photogrammetric technology field, belongs to the combination technology of technical field of mapping and image processing field.

Background technology:

LIDAR is the important means of city space acquisition of information, because city space target complexity is higher, the collection of LIDAR point cloud needs to scan from different visual angles extraterrestrial target usually, then is spliced by neighboring stations point cloud, thus realizes the expressed intact to extraterrestrial target.According to primitive, joining method mainly utilizes same place between LIDAR point cloud and line of the same name.There is not completely corresponding same place feature between some cloud in fact to be spliced, this makes same place merging features arithmetic accuracy be difficult to be guaranteed.Generally, straight line is senior geometric feature description symbol in LIDAR point cloud, and relative to point, straight line has stronger geometry Topological and geometrical constraint, can obtain higher splicing precision.Joining method based on straight line primitive generally uses the end points closest of the same name of homonymous line, then splicing parameter is solved according to the terminal point information of line correspondence, but owing to there is not completely corresponding same place feature between a cloud, the feature primitive used in this way is still point, and splicing precision is low.Therefore, make full use of the geometric topo-relationship between the linear feature of LIDAR point cloud and straight line, to high-precision LIDAR point cloud, there is important actual application value.

Summary of the invention:

The invention provides a kind of LIDAR point cloud method under model line constraint, the homonymous line on the LIDAR point cloud of datum station and survey station to be spliced is formed an overall topological structure by respectively, establishes model straight line collinearity condition equation.

The present invention adopts following technical scheme: a kind of LIDAR point cloud method under model line constraint, it comprises the steps

Steps A: extract homonymous line respectively on the LIDAR point cloud of datum station and survey station to be spliced;

Step B: by the homonymous line in steps A, sets up model straight line of the same name;

Step C: Modling model straight line collinearity condition equation, makes model straight line convergent-divergent to be spliced, rotates and move to and overlap with benchmark model straight line;

Step D: calculate splicing parameter.

Further, in described step B, the method for building up of model straight line is:

(B-1): on the LIDAR point cloud of survey station to be spliced, obtain any straight line l in model straight line, be expressed as: l=[0 M N O 0 M ₀n ₀o ₀], wherein, (M, N, O) and (M ₀, N ₀, O ₀) be respectively the direction vector of l and square vector;

(B-2): according to the method for step (1), the LIDAR point cloud of datum station obtains any straight line l ' in model straight line, is expressed as: l '=[0 M ' N ' O ' 0 M ₀' N ₀' O ₀'], wherein, (M ', N ', O ') and (M ₀', N ₀', O ₀') be respectively the direction vector of l ' and square vector.

Further, described step C comprises the steps

(C-1): Modling model straight line collinearity condition equation, namely spliced model straight line overlaps with the LIDAR point cloud straight line of corresponding datum station

l^{'} = q \cdot (l \cdot [\begin{matrix} I & 0 \\ 0 & λI \end{matrix}]) \cdot q^{- 1} - - - (1)

In formula, λ is zooming parameter; I is 4 dimension unit matrixs; Q=[q ₁q ₂q ₃q ₄q ₀₁q ₀₂q ₀₃q ₀₄]; 0 is 4 dimension 0 matrixes; q ^-1inverse for q;

(C-2): determine to splice initial parameter value

q ₁＝λ＝1，q ₂＝q ₃＝q ₄＝q ₀₁＝q ₀₂＝q ₀₃＝q ₀₄＝0；

(C-3): the l ' on formula (C-1) the equation left side is moved on on the right of equation, then launch to obtain

F_{1} = M (q_{1}^{2} + q_{2}^{2} - q_{3}^{2} - q_{4}^{2}) + 2 N (q_{2} q_{3} - q_{1} q_{4}) + 2 O (q_{1} q_{3} + q_{2} q_{4}) - M^{'} = 0

F_{2} = N (q_{1}^{2} - q_{2}^{2} + q_{3}^{2} - q_{4}^{2}) + 2 M (q_{2} q_{3} + q_{1} q_{4}) - 2 O (q_{1} q_{2} - q_{3} q_{4}) - N^{'} = 0

F_{3} = O (q_{1}^{2} - q_{2}^{2} - q_{3}^{2} + q_{4}^{2}) - 2 M (q_{1} q_{3} + q_{2} q_{4}) + 2 N (q_{1} q_{2} + q_{3} q_{4}) - O^{'} = 0

\begin{matrix} F_{4} = λ M_{0} (q_{1}^{2} + q_{2}^{2} - q_{3}^{2} - q_{4}^{2}) + 2 λ N_{0} (q_{2} q_{3} - q_{1} q_{4}) + 2 M (q_{1} q_{01} + q_{2} q_{02} \\ - q_{3} q_{03} - q_{4} q_{04}) - 2 N (q_{1} q_{04} + q_{01} q_{4} - q_{2} q_{03} - q_{02} q_{3}) + 2 O (q_{1} q_{03} \\ + q_{01} q_{3} + q_{2} q_{04} + q_{02} q_{4}) + 2 λ O_{0} (q_{1} q_{3} + q_{2} q_{4}) - M_{0}^{'} = 0 \end{matrix} - - - (2)

\begin{matrix} F_{5} = λ N_{0} (q_{1}^{2} - q_{2}^{2} + q_{3}^{2} - q_{4}^{2}) + 2 λ M_{0} (q_{2} q_{3} + q_{1} q_{4}) + 2 N (q_{1} q_{01} - q_{2} q_{02} \\ + q_{3} q_{03} - q_{4} q_{04}) + 2 M (q_{1} q_{04} + q_{01} q_{4} + q_{2} q_{03} + q_{02} q_{3}) - 2 O (q_{1} q_{02} + \\ q_{01} q_{2} - q_{3} q_{04} - q_{03} q_{4}) - 2 λ O_{0} (q_{1} q_{2} - q_{3} q_{4}) - N_{0}^{'} = 0 \end{matrix}

\begin{matrix} F_{6} = λ O_{0} (q_{1}^{2} - q_{2}^{2} - q_{3}^{2} + q_{4}^{2}) + 2 λ M_{0} (q_{1} q_{3} - q_{2} q_{4}) + 2 O (q_{1} q_{01} - q_{2} q_{02} \\ - q_{3} q_{03} + q_{4} q_{04}) - 2 M (q_{1} q_{03} + q_{01} q_{3} - q_{2} q_{04} - q_{02} q_{4}) + 2 N (q_{1} q_{02} + \\ q_{01} q_{2} + q_{3} q_{04} + q_{03} q_{4}) + 2 λ N_{0} (q_{1} q_{2} + q_{3} q_{4}) - O_{0}^{'} = 0 \end{matrix}

(C-4): formula (C-2) is expanded to once item by Taylor's formula at q and λ:

F ₁＝F ₁₀+a ₁₁dq ₁+a ₁₂dq ₂+a ₁₃dq ₃+a ₁₄dq ₄+a ₁₅dq ₀₁+a ₁₆dq ₀₂+a ₁₇dq ₀₃+a ₁₈dq ₀₄+a ₁₉dλ

F ₂＝F ₂₀+a ₂₁dq ₁+a ₂₂dq ₂+a ₂₃dq ₃+a ₂₄dq ₄+a ₂₅dq ₀₁+a ₂₆q ₀₂+a ₂₇dq ₀₃+a ₂₈dq ₀₄+a ₂₉dλ

F ₃＝F ₃₀+a ₃₁dq ₁+a ₃₂dq ₂+a ₃₃dq ₃+a ₃₄dq ₄+a ₃₅dq ₀₁+a ₃₆dq ₀₂+a ₃₇dq ₀₃+a ₃₈dq ₀₄+a ₃₉dλ

(3)

F ₄＝F ₄₀+a ₄₁dq ₁+a ₄₂dq ₂+a ₄₃dq ₃+a ₄₄dq ₄+a ₄₅dq ₀₁+a ₄₆dq ₀₂+a ₄₇dq ₀₃+a ₄₈dq ₀₄+a ₄₉dλ

F ₅＝F ₅₀+a ₅₁dq ₁+a ₅₂dq ₂+a ₅₃dq ₃+a ₅₄dq ₄+a ₅₅dq ₀₁+a ₅₆dq ₀₂+a ₅₇dq ₀₃+a ₅₈dq ₀₄+a ₅₉dλ

F ₆＝F ₆₀+a ₆₁dq ₁+a ₆₂dq ₂+a ₆₃dq ₃+a ₆₄dq ₄+a ₆₅dq ₀₁+a ₆₆dq ₀₂+a ₆₇dq ₀₃+a ₆₈dq ₀₄+a ₆₉dλ

In formula:

a ₁₁＝2Mq ₁+2Oq ₃-2Nq ₄a ₁₂＝2Mq ₂+2Nq ₃+2Oq ₄

a ₁₃＝2Oq ₁+2Nq ₂-2Mq ₃a ₁₄＝-2Nq ₁+2Oq ₂-2Mq ₄

a ₁₅＝a ₁₆＝a ₁₇＝a ₁₈＝a ₁₉＝0

a ₂₁＝2Nq ₁-2Oq ₂+2Mq ₄a ₂₂＝-2Nq ₂-2Oq ₁+2Mq ₃

a ₂₃＝2Nq ₃+2Oq ₄+2Mq ₂a ₂₄＝-2Nq ₄+2Oq ₃+2Mq ₁

a ₂₅＝a ₂₆＝a ₂₇＝a ₂₈＝a ₂₉＝0

a ₃₁＝2Oq ₁+2Nq ₂-2Mq ₃a ₃₂＝-2Oq ₂+2Nq ₁+2Mq ₄

a ₃₃＝2Nq ₄-2Oq ₃-2Mq ₁a ₃₄＝2Oq ₄+2Nq ₃+2Mq ₂

a ₃₅＝a ₃₆＝a ₃₇＝a ₃₈＝a ₃₉＝0

a ₄₁＝2Mq ₀₁+2λM ₀q ₁-2Nq ₀₄-2λN ₀q ₄+2Oq ₀₃+2λO ₀q ₃

a ₄₂＝+2Mq ₀₂+2λM ₀q ₂-2Nq ₀₃+2λN ₀q ₃+2Oq ₀₄+2λO ₀q ₄

a ₄₃＝-2Mq ₀₃-2λM ₀q ₃+2Nq ₀₂+2λN ₀q ₂+2Oq ₀₁+2λO ₀q ₁

a ₄₄＝-2Mq ₀₄-2λM ₀q ₄-2Nq ₀₁-2λN ₀q ₁+2Oq ₀₂+2λO ₀q ₂

a ₄₅＝a ₁₁,a ₄₆＝a ₁₂,a ₄₇＝a ₁₃,a ₄₈＝a ₁₄

a_{49} = M_{0} (q_{1}^{2} + q_{2}^{2} - q_{3}^{2} - q_{4}^{2}) + 2 N_{0} (q_{2} q_{3} - q_{1} q_{4}) + 2 O_{0} (q_{1} q_{3} + q_{2} q_{4})

a ₅₁＝2Mq ₀₄+2λM ₀q ₄+2Nq ₀₁+2λN ₀q ₁-2Oq ₀₂-2λO ₀q ₂

a ₅₂＝2Mq ₀₃+2λM ₀q ₃-2Nq ₀₂-2λN ₀q ₂-2Oq ₀₁-2λO ₀q ₁

a ₅₃＝2Mq ₀₂+2λM ₀q ₂+2Nq ₀₃+2λN ₀q ₃+2Oq ₀₄+2λO ₀q ₄

a ₅₄＝2Mq ₀₁+2λM ₀q ₁-2Nq ₀₄-2λN ₀q ₄+2Oq ₀₃+2λO ₀q ₃

a ₅₅＝a ₂₁,a ₅₆＝a ₂₂,a ₅₇＝a ₂₃,a ₅₈＝a ₂₄

a_{59} = N_{0} (q_{1}^{2} - q_{2}^{2} + q_{3}^{2} - q_{4}^{2}) + 2 M_{0} (q_{2} q_{3} + q_{1} q_{4}) - 2 O_{0} (q_{1} q_{3} - q_{2} q_{4})

a ₆₁＝-2Mq ₀₃-2λM ₀q ₃+2Nq ₀₂+2λN ₀q ₂+2Oq ₀₁+2λO ₀q ₁

a ₆₂＝2Mq ₀₄+2λM ₀q ₄+2Nq ₀₁+2λN ₀q ₁-2Oq ₀₂-2λO ₀q ₂

a ₆₃＝-2Mq ₀₁-2λM ₀q ₁+2Nq ₀₄+2λN ₀q ₄-2Oq ₀₃-2λO ₀q ₃

a ₆₄＝2Mq ₀₂+2λM ₀q ₂+2Nq ₀₃+2λN ₀q ₃+2Oq ₀₄+2λO ₀q ₄

a ₆₅＝a ₃₁,a ₆₆＝a ₃₂,a ₆₇＝a ₃₃,a ₆₈＝a ₃₄

a_{69} = O_{0} (q_{1}^{2} - q_{2}^{2} - q_{3}^{2} + q_{4}^{2}) - 2 M_{0} (q_{1} q_{3} - q_{2} q_{4}) + 2 N_{0} (q_{1} q_{2} + q_{3} q_{4})

F ₁₀, F ₂₀, F ₃₀, F ₄₀, F ₅₀, F ₆₀the approximate value being respectively q and λ brings the F that formula (C-3) and formula (C-4) obtain into ₁~ F ₆approximate value; Dq ₁, dq ₂, dq ₃, dq ₄, dq ₀₁, dq ₀₂, dq ₀₃, dq ₀₄, d λ is respectively the correction of each splicing parameter.

The present invention has following beneficial effect: the LIDAR point cloud method under model line constraint of the present invention is compared with traditional LIDAR based on straight line point cloud method, can by zooming parameter Unified Solution, give full play to the geometrical constraint of straight line, the geometry intensity of stereoscopic model can be strengthened, thus improve the precision of LIDAR point cloud.

Embodiment:

LIDAR point cloud method under model line constraint of the present invention comprises the steps:

Step D: calculate splicing parameter.

Wherein: in step B, the method for building up of model straight line is:

Wherein step step C is as follows:

(C-1): Modling model straight line collinearity condition equation, namely spliced model straight line overlaps with the LIDAR point cloud straight line of corresponding datum station:

l^{'} = q \cdot (l \cdot [\begin{matrix} I & 0 \\ 0 & λI \end{matrix}]) \cdot q^{- 1} - - - (1)

In formula, λ is zooming parameter; I is 4 dimension unit matrixs; Q=[q ₁q ₂q ₃q ₄q ₀₁q ₀₂q ₀₃q ₀₄]; 0 is 4 dimension 0 matrixes; q ^-1inverse for q.

(C-2): determine to splice initial parameter value.

q ₁＝λ＝1，q ₂＝q ₃＝q ₄＝q ₀₁＝q ₀₂＝q ₀₃＝q ₀₄＝0。

(C-3): the l ' on formula (C-1) the equation left side is moved on on the right of equation, then launch to obtain:

F_{1} = M (q_{1}^{2} + q_{2}^{2} - q_{3}^{2} - q_{4}^{2}) + 2 N (q_{2} q_{3} - q_{1} q_{4}) + 2 O (q_{1} q_{3} + q_{2} q_{4}) - M^{'} = 0

F_{2} = N (q_{1}^{2} - q_{2}^{2} + q_{3}^{2} - q_{4}^{2}) + 2 M (q_{2} q_{3} + q_{1} q_{4}) - 2 O (q_{1} q_{2} - q_{3} q_{4}) - N^{'} = 0

F_{3} = O (q_{1}^{2} - q_{2}^{2} - q_{3}^{2} + q_{4}^{2}) - 2 M (q_{1} q_{3} + q_{2} q_{4}) + 2 N (q_{1} q_{2} + q_{3} q_{4}) - O^{'} = 0

\begin{matrix} F_{4} = λ M_{0} (q_{1}^{2} + q_{2}^{2} - q_{3}^{2} - q_{4}^{2}) + 2 λ N_{0} (q_{2} q_{3} - q_{1} q_{4}) + 2 M (q_{1} q_{01} + q_{2} q_{02} \\ - q_{3} q_{03} - q_{4} q_{04}) - 2 N (q_{1} q_{04} + q_{01} q_{4} - q_{2} q_{03} - q_{02} q_{3}) + 2 O (q_{1} q_{03} \\ + q_{01} q_{3} + q_{2} q_{04} + q_{02} q_{4}) + 2 λ O_{0} (q_{1} q_{3} + q_{2} q_{4}) - M_{0}^{'} = 0 \end{matrix} - - - (2)

\begin{matrix} F_{5} = λ N_{0} (q_{1}^{2} - q_{2}^{2} + q_{3}^{2} - q_{4}^{2}) + 2 λ M_{0} (q_{2} q_{3} + q_{1} q_{4}) + 2 N (q_{1} q_{01} - q_{2} q_{02} \\ + q_{3} q_{03} - q_{4} q_{04}) + 2 M (q_{1} q_{04} + q_{01} q_{4} + q_{2} q_{03} + q_{02} q_{3}) - 2 O (q_{1} q_{02} + \\ q_{01} q_{2} - q_{3} q_{04} - q_{03} q_{4}) - 2 λ O_{0} (q_{1} q_{2} - q_{3} q_{4}) - N_{0}^{'} = 0 \end{matrix}

\begin{matrix} F_{6} = λ O_{0} (q_{1}^{2} - q_{2}^{2} - q_{3}^{2} + q_{4}^{2}) + 2 λ M_{0} (q_{1} q_{3} - q_{2} q_{4}) + 2 O (q_{1} q_{01} - q_{2} q_{02} \\ - q_{3} q_{03} + q_{4} q_{04}) - 2 M (q_{1} q_{03} + q_{01} q_{3} - q_{2} q_{04} - q_{02} q_{4}) + 2 N (q_{1} q_{02} + \\ q_{01} q_{2} + q_{3} q_{04} + q_{03} q_{4}) + 2 λ N_{0} (q_{1} q_{2} + q_{3} q_{4}) - O_{0}^{'} = 0 \end{matrix}

(C-4): formula (C-2) is expanded to once item by Taylor's formula at q and λ:

(3)

In formula:

a ₁₁＝2Mq ₁+2Oq ₃-2Nq ₄a ₁₂＝2Mq ₂+2Nq ₃+2Oq ₄

a ₁₃＝2Oq ₁+2Nq ₂-2Mq ₃a ₁₄＝-2Nq ₁+2Oq ₂-2Mq ₄

a ₁₅＝a ₁₆＝a ₁₇＝a ₁₈＝a ₁₉＝0

a ₂₁＝2Nq ₁-2Oq ₂+2Mq ₄a ₂₂＝-2Nq ₂-2Oq ₁+2Mq ₃

a ₂₃＝2Nq ₃+2Oq ₄+2Mq ₂a ₂₄＝-2Nq ₄+2Oq ₃+2Mq ₁

a ₂₅＝a ₂₆＝a ₂₇＝a ₂₈＝a ₂₉＝0

a ₃₁＝2Oq ₁+2Nq ₂-2Mq ₃a ₃₂＝-2Oq ₂+2Nq ₁+2Mq ₄

a ₃₃＝2Nq ₄-2Oq ₃-2Mq ₁a ₃₄＝2Oq ₄+2Nq ₃+2Mq ₂

a ₃₅＝a ₃₆＝a ₃₇＝a ₃₈＝a ₃₉＝0

a ₄₅＝a ₁₁,a ₄₆＝a ₁₂,a ₄₇＝a ₁₃,a ₄₈＝a ₁₄

a_{49} = M_{0} (q_{1}^{2} + q_{2}^{2} - q_{3}^{2} - q_{4}^{2}) + 2 N_{0} (q_{2} q_{3} - q_{1} q_{4}) + 2 O_{0} (q_{1} q_{3} + q_{2} q_{4})

a ₅₅＝a ₂₁,a ₅₆＝a ₂₂,a ₅₇＝a ₂₃,a ₅₈＝a ₂₄

a_{59} = N_{0} (q_{1}^{2} - q_{2}^{2} + q_{3}^{2} - q_{4}^{2}) + 2 M_{0} (q_{2} q_{3} + q_{1} q_{4}) - 2 O_{0} (q_{1} q_{3} - q_{2} q_{4})

a ₆₅＝a ₃₁,a ₆₆＝a ₃₂,a ₆₇＝a ₃₃,a ₆₈＝a ₃₄

a_{69} = O_{0} (q_{1}^{2} - q_{2}^{2} - q_{3}^{2} + q_{4}^{2}) - 2 M_{0} (q_{1} q_{3} - q_{2} q_{4}) + 2 N_{0} (q_{1} q_{2} + q_{3} q_{4})

(C-5): row write error equation and method, normal equation is separated.

V＝AX+F (4)

Wherein:

V＝[v ₁,v ₂,v ₃,v ₄,v ₅,v ₆] ^T

A = [\begin{matrix} a_{11} & a_{12} & a_{13} & a_{14} & a_{15} & a_{16} & a_{17} & a_{18} & a_{19} \\ a_{21} & a_{22} & a_{23} & a_{24} & a_{25} & a_{26} & a_{27} & a_{28} & a_{29} \\ a_{31} & a_{32} & a_{33} & a_{34} & a_{35} & a_{36} & a_{37} & a_{38} & a_{39} \\ a_{41} & a_{42} & a_{43} & a_{44} & a_{45} & a_{46} & a_{47} & a_{48} & a_{49} \\ a_{51} & a_{52} & a_{53} & a_{54} & a_{55} & a_{56} & a_{57} & a_{58} & a_{59} \\ a_{61} & a_{62} & a_{63} & a_{64} & a_{65} & a_{66} & a_{67} & a_{68} & a_{69} \end{matrix}]

X＝[dq ₁dq ₂dq ₃dq ₄dq ₀₁dq ₀₂dq ₀₃dq ₀₄dλ] ^T

F＝[F ₁₀F ₂₀F ₃₀F ₄₀F ₅₀F ₆₀] ^T

N is had to homonymous line in hypothesized model straight line, can the error equation of a row formula (4) to often pair of homonymous line.

(C-6): according to the principle of least square:

X＝-(A ^TA) ^-1A ^TF (5)

X is the correction of splicing parameter undetermined.

(C-7): upgrade splicing parameter.

By splicing parameter approximate value and the splicing parameter correction sum that calculates of last iteration as new splicing parameter approximate value, when solving the X=[dq obtained ₁dq ₂dq ₃dq ₄dq ₀₁dq ₀₂dq ₀₃dq ₀₄d λ] ^tbe less than setting 10 ^-6shi Jixu step (C-7); Otherwise return step (C-3).

(C-8): calculate splicing parameter.

Final splicing parameter is substituted into following formula (C-5), formula (C-6) and formula (C-7), to splicing parameter.

The translation parameters formula of splicing is as follows:

Dx＝2(q ₁q ₀₂-q ₂q ₀₁+q ₃q ₀₄-q ₄q ₀₃)

Dy＝2(q ₁q ₀₃-q ₂q ₀₄-q ₃q ₀₁+q ₄q ₀₂) (6)

Dz＝2(q ₁q ₀₄+q ₂q ₀₃-q ₃q ₀₂-q ₄q ₀₁)

The rotational transformation matrix M formula of splicing is as follows:

M = [\begin{matrix} {q_{1}}^{2} + {q_{2}}^{2} - {q_{3}}^{2} - {q_{4}}^{2} & 2 (q_{2} q_{3} - q_{1} q_{4}) & 2 (q_{2} q_{4} - q_{1} q_{3}) \\ 2 (q_{2} q_{3} + q_{1} q_{4}) & {q_{1}}^{2} - {q_{2}}^{2} + {q_{3}}^{2} - {q_{4}}^{2} & 2 (q_{3} q_{4} + q_{1} q_{2}) \\ 2 (q_{2} q_{4} + q_{1} q_{3}) & 2 (q_{3} q_{4} - q_{1} q_{2}) & {q_{1}}^{2} - {q_{2}}^{2} - {q_{3}}^{2} + {q_{4}}^{2} \end{matrix}] - - - (7)

ω＝-M ₂₃(8)

κ＝artan(M ₂₁/Μ ₂₂)

In formula, M _i,j(i=1,2,3, j=1,2,3) representing matrix M _3,3i-th row jth row element.

LIDAR point cloud method under model line constraint of the present invention is described below by a specific embodiment:

LIDAR point cloud is carried out according to certain building object point cloud that the LMS-Z420 series of ground LIDAR equipment of Austrian Riegl company collects, scanner type is pulsed, laser emission frequency is 27000 points per second, range is 2m-1000m, scanning accuracy is 10mm (in 100 meters of distances), sweep velocity is that vertical direction 1-20 line is per second, horizontal direction 0.01 ° ~ 15 ° is per second, scanning angle is vertical direction 0 ° ~ 80 °, horizontal direction 0 ° ~ 360 °, angular resolution is vertical direction 0.002 °, horizontal direction 0.0025 °.From the LIDAR point cloud of datum station and survey station to be spliced, respectively extract 4 straight lines respectively, direction vector and the square vector of datum station homonymous line are as shown in table 1, and direction vector and the square vector of survey station homonymous line subject to registration are as shown in table 2, l ₁and l ₁', l ₂and l ₂', l ₃and l ₃', l ₄and l ₄' be respectively straight line of the same name.

Table 1 survey station model subject to registration straight line

Table 2 datum station model straight line

According to the model straight line in table 1 and table 2, utilize joining method of the present invention, splicing parameter can be solved: X _s=23.011m, Y _sfor 29.391m, Z _sfor-2.317m, be 12.593 °, ω is 1.063 °, and κ is 28.898 °, λ=0.9998.Splicing precision is 2.0mm, reaches the requirement of high-precision three-dimensional mapping.

The above is only the preferred embodiment of the present invention, it should be pointed out that for those skilled in the art, can also make some improvement under the premise without departing from the principles of the invention, and these improvement also should be considered as protection scope of the present invention.

Claims

1. the LIDAR point cloud method under model line constraint, is characterized in that: comprise the steps

Step D: calculate splicing parameter.

2. the LIDAR point cloud method under model line constraint as claimed in claim 1, is characterized in that: in described step B, the method for building up of model straight line is:

(B-2): according to the method for step (1), the LIDAR point cloud of datum station obtains any straight line l ' in model straight line, is expressed as: l '=[0 M ' N ' O ' 0 M ' ₀n ' ₀o ' ₀], wherein, (M ', N ', O ') and (M ' ₀, N ' ₀, O ' ₀) be respectively the direction vector of l ' and square vector.

3. the LIDAR point cloud method under model line constraint as claimed in claim 1, is characterized in that: described step C comprises the steps

l^{'} = q \cdot (l \cdot [\begin{matrix} I & 0 \\ 0 & λI \end{matrix}]) \cdot q^{- 1} - - - (1)

(C-2): determine to splice initial parameter value

F_{1} = M (q_{1}^{2} + q_{2}^{2} - q_{3}^{2} - q_{4}^{2}) + 2 N (q_{2} q_{3} - q_{1} q_{4}) + 2 O (q_{1} q_{3} + q_{2} q_{4}) - M^{'} = 0

F_{2} = N (q_{1}^{2} - q_{2}^{2} + q_{3}^{2} - q_{4}^{2}) + 2 M (q_{2} q_{3} + q_{1} q_{4}) - 2 O (q_{1} q_{2} - q_{3} q_{4}) - N^{'} = 0

F_{3} = O (q_{1}^{2} - q_{2}^{2} - q_{3}^{2} + q_{4}^{2}) - 2 M (q_{1} q_{3} - q_{2} q_{4}) + 2 N (q_{1} q_{2} + q_{3} q_{4}) - O^{'} = 0

\begin{matrix} F_{4} = {λM}_{0} (q_{1}^{2} + q_{2}^{2} - q_{3}^{2} - q_{4}^{2}) + {2 λN}_{0} (q_{2} q_{3} - q_{1} q_{4}) + 2 M (q_{1} q_{01} + q_{2} q_{02} \\ - q_{3} q_{03} - q_{4} q_{04}) - 2 N (q_{1} q_{04} + q_{01} q_{4} - q_{2} q_{03} - q_{02} q_{3}) + 2 O (q_{1} q_{03} \\ + q_{01} q_{3} + q_{2} q_{04} + q_{02} q_{4}) + {2 λO}_{0} (q_{1} q_{3} + q_{2} q_{4}) - M_{0}^{'} = 0 \end{matrix} - - - (2)

\begin{matrix} F_{5} = {λN}_{0} (q_{1}^{2} - q_{2}^{2} + q_{3}^{2} - q_{4}^{2}) + {2 λM}_{0} (q_{2} q_{3} + q_{1} q_{4}) + 2 N (q_{1} q_{01} - q_{2} q_{02}) \\ + q_{3} q_{03} - q_{4} q_{04}) + 2 M (q_{1} q_{04} + q_{01} q_{4} + q_{2} q_{03} + q_{02} q_{3}) - 2 O (q_{1} q_{02} + \\ q_{01} q_{2} - q_{3} q_{04} - q_{03} q_{4}) {2 λO}_{0} (q_{1} q_{2} - q_{3} q_{4}) - N_{0}^{'} = 0 \end{matrix}

\begin{matrix} F_{6} = {λO}_{0} (q_{1}^{2} - q_{2}^{2} - q_{3}^{2} + q_{4}^{2}) - {2 λM}_{0} (q_{1} q_{3} - q_{2} q_{4}) + 2 O (q_{1} q_{01} - q_{2} q_{02}) \\ - q_{3} q_{03} + q_{4} q_{04}) - 2 M (q_{1} q_{03} + q_{01} q_{3} - q_{2} q_{04} - q_{02} q_{4}) + 2 N (q_{1} q_{02} + \\ q_{01} q_{2} + q_{3} q_{04} + q_{03} q_{4}) + {2 λN}_{0} (q_{1} q_{2} + q_{3} q_{4}) - O_{0}^{'} = 0 \end{matrix}

(C-4): formula (C-2) is expanded to once item by Taylor's formula at q and λ:

(3)

In formula:

a ₁₁＝2Mq ₁+2Oq ₃-2Nq ₄a ₁₂＝2Mq ₂+2Nq ₃+2Oq ₄

a ₁₃＝2Oq ₁+2Nq ₂-2Mq ₃a ₁₄＝-2Nq ₁+2Oq ₂-2Mq ₄

a ₁₅＝a ₁₆＝a ₁₇＝a ₁₈＝a ₁₉＝0

a ₂₁＝2Nq ₁-2Oq ₂+2Mq ₄a ₂₂＝-2Nq ₂-2Oq ₁+2Mq ₃

a ₂₃＝2Nq ₃+2Oq ₄+2Mq ₂a ₂₄＝-2Nq ₄+2Oq ₃+2Mq ₁

a ₂₅＝a ₂₆＝a ₂₇＝a ₂₈＝a ₂₉＝0

a ₃₁＝2Oq ₁+2Nq ₂-2Mq ₃a ₃₂＝-2Oq ₂+2Nq ₁+2Mq ₄

a ₃₃＝2Nq ₄-2Oq ₃-2Mq ₁a ₃₄＝2Oq ₄+2Nq ₃+2Mq ₂

a ₃₅＝a ₃₆＝a ₃₇＝a ₃₈＝a ₃₉＝0

a ₄₅＝a ₁₁,a ₄₆＝a ₁₂,a ₄₇＝a ₁₃,a ₄₈＝a ₁₄

a_{49} = M_{0} (q_{1}^{2} + q_{2}^{2} - q_{3}^{2} - q_{4}^{2}) + {2 N}_{0} (q_{2} q_{3} - q_{1} q_{4}) + {2 O}_{0} (q_{1} q_{3} + q_{2} q_{4})

a ₅₅＝a ₂₁,a ₅₆＝a ₂₂,a ₅₇＝a ₂₃,a ₅₈＝a ₂₄

a_{59} = N_{0} (q_{1}^{2} - q_{2}^{2} + q_{3}^{2} - q_{4}^{2}) + {2 M}_{0} (q_{2} q_{3} + q_{1} q_{4}) + {2 O}_{0} (q_{1} q_{2} - q_{3} q_{4})

a ₆₅＝a ₃₁,a ₆₆＝a ₃₂,a ₆₇＝a ₃₃,a ₆₈＝a ₃₄

a_{69} = O_{0} (q_{1}^{2} - q_{2}^{2} - q_{3}^{2} + q_{4}^{2}) - {2 M}_{0} (q_{1} q_{3} - q_{2} q_{4}) + {2 N}_{0} (q_{1} q_{2} + q_{3} q_{4})