CN112200767B - Point cloud data endpoint extraction method and device based on PCA - Google Patents
Point cloud data endpoint extraction method and device based on PCA Download PDFInfo
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Abstract
The method and the device are applied to the technical field of machine vision, can be used for 3D machine vision positioning and measuring problems in industrial production, have obvious advantages of calculation efficiency and stability compared with a bounding box-based or straight line extraction-based method under specific conditions, do not need parameter setting, have lower requirements on field technicians, and are beneficial to maintenance.
Description
Technical Field
The present disclosure relates to the field of machine vision, and in particular, to a method and an apparatus for extracting point cloud data endpoints based on PCA.
Background
In the industry, it is very common to use machine vision to detect the end point characteristics of an elongated workpiece, and there are two common concepts:
(1) Firstly, calculating a directed bounding box, then taking the surface centers of two surfaces which are far away as endpoints, wherein the method is only suitable for images with higher boundary quality, and in fact, a large number of laser point cloud images acquired in an industrial field all have complex edge problems, and particularly when a plurality of slender vertical surfaces are detected, the side edges easily interfere with the calculation of the bounding box to obviously expand the bounding box, so that endpoints cannot be found;
(2) Based on the method for solving the line segment characteristics, the method such as edge extraction, hough straight line detection, straight line fitting and the like is used for obtaining the target straight line first, then the end point is solved indirectly according to the straight line, the method is complex, the method belongs to the type of compound use of multiple methods, the scheme is strong in pertinence and poor in universality.
Disclosure of Invention
The method and the device for extracting the point cloud data end points based on the PCA can be used for the problems of 3D machine vision positioning and measurement in industrial production, and under specific conditions, the method has obvious advantages of calculation efficiency and stability compared with a method based on bounding boxes or linear extraction, parameter setting is not needed, requirements on field technicians are lower, and maintenance is facilitated.
The application adopts the following technical means for solving the technical problems:
the application provides a point cloud data endpoint extraction method based on PCA, which comprises the following steps:
acquiring image data, converting the image data into first 3D point cloud data, and forming three-axis column vectors X, Y, Z according to n points in the first 3D point cloud data;
calculating a covariance matrix A through the triaxial column vector, and performing SVD decomposition on the covariance matrix A, namely A=USV T Wherein U is a main vector matrix;
taking out the same-column main direction vector v from the main vector matrix U, wherein the main direction vector v is the main direction vector of the strip-shaped point cloud;
calculating any rigid transformation matrix M from said principal direction vector v to a single axis vector t, i.e. mv=t;
applying the first 3D point cloud data to a rigid body transformation matrix M for direction conversion, and obtaining second 3D point cloud data after the direction conversion, wherein triaxial column vectors X ', Y ', Z ' of the second 3D point cloud data;
carrying out endpoint calculation according to the triaxial column vectors X ', Y ', Z ' to obtain two endpoints e1 and e2;
and calculating the end point e1 and the end point e2 by adopting an inverse matrix of the rigid body transformation matrix M to obtain two required end points.
Further, the step of calculating the covariance matrix a by the triaxial column vector includes:
the covariance matrix
wherein ,p, q are any axis of the triaxial column vector, and i is one point in the axis among n points.
Further, the covariance matrix a is subjected to SVD decomposition, i.e. a=usv T The step of using U as a main vector matrix comprises the following steps:
the main vector matrix
Further, the step of extracting the same-column principal direction vector v from the principal vector matrix U includes:
the principal direction vector v= (u 11, u21, u 31) T 。
Further, the step of calculating the end points according to the triaxial column vectors X ', Y ', Z ' to obtain two end points e1 and e2 includes:
endpoint e1= (min (X '), mean (Y '), mean (Z '));
endpoint e2= (max (X '), mean (Y '), mean (Z ')).
Further, the media function may be replaced with an average function in the calculation process of the endpoint e1 and the endpoint e 2.
Further, the step of calculating any rigid body transformation matrix M from the principal direction vector v to a single axis vector t includes:
calculating the included angle between the main direction vector v and the uniaxial vector t
Calculating rotation axis vectors wherein />
The rotation matrix M is converted from the shaft angle representation by using a formula, thereby obtaining a rigid body transformation matrix M.
Further, the step of converting the formula into the rotation matrix M from the shaft angle representation includes:
rigid body transformation matrix
Further, the step of calculating any rigid body transformation matrix M from the principal direction vector v to a single axis vector t includes:
the uniaxial vector t may take any one of t= (1, 0), t= (0, 1, 0) and t= (0, 1).
The application also provides a point cloud data endpoint extraction device based on PCA, which comprises:
an acquisition unit configured to acquire image data, convert the image data into first 3D point cloud data, and form three-axis column vectors X, Y, Z according to n points in the first 3D point cloud data;
a first calculation unit for calculating a covariance matrix a by the triaxial column vector and performing SVD decomposition on the covariance matrix a, i.e., a=usv T Wherein U is a main vector matrix;
the main vector confirming unit is used for taking out the same-column main direction vector v from the main vector matrix U, wherein the main direction vector v is the main direction vector of the strip-shaped point cloud;
a second calculation unit for calculating any rigid body transformation matrix M from the main direction vector v to the uniaxial vector t, i.e., mv=t;
the first conversion unit is used for applying the first 3D point cloud data to the rigid body transformation matrix M to perform direction conversion, and obtaining second 3D point cloud data after the conversion, wherein the triaxial column vectors X ', Y ', Z ' of the second 3D point cloud data;
the endpoint calculation unit is used for calculating endpoints according to the triaxial column vectors X ', Y ', Z ' to obtain two endpoints e1 and e2;
and the second conversion unit is used for calculating the endpoint e1 and the endpoint e2 by adopting the inverse matrix of the rigid body transformation matrix M to obtain two required endpoints.
The application provides a point cloud data endpoint extraction method and device based on PCA, which have the following beneficial effects:
according to the point cloud data endpoint extraction method based on PCA, image data are obtained and converted into the first image dataThe three-dimensional point cloud data is formed into three-axis column vectors X, Y, Z according to n points in the first 3D point cloud data; calculating a covariance matrix A through the triaxial column vector, and performing SVD decomposition on the covariance matrix A, namely A=USV T Wherein U is a main vector matrix; taking out the same-column main direction vector v from the main vector matrix U, wherein the main direction vector v is the main direction vector of the strip-shaped point cloud; calculating any rigid transformation matrix M from said principal direction vector v to a single axis vector t, i.e. mv=t; applying the first 3D point cloud data to a rigid body transformation matrix M for direction conversion, and obtaining second 3D point cloud data after the direction conversion, wherein triaxial column vectors X ', Y ', Z ' of the second 3D point cloud data; carrying out endpoint calculation according to the triaxial column vectors X ', Y ', Z ' to obtain two endpoints e1 and e2; the method has the advantages that the method has obvious calculation efficiency and stability advantages compared with a bounding box-based method or a straight line extraction-based method, parameter setting is not needed, requirements on field technicians are lower, and maintenance is facilitated.
Drawings
Fig. 1 is a flowchart illustrating an embodiment of a PCA-based point cloud data endpoint extraction method according to the present application;
fig. 2 is a block diagram illustrating an embodiment of a PCA-based point cloud data endpoint extraction apparatus of the present application.
The implementation, functional features and advantages of the present application will be further described with reference to the accompanying drawings in conjunction with the embodiments.
Detailed Description
It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the present application.
The technical solutions of the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is apparent that the described embodiments are only some embodiments of the present application, but not all embodiments. All other embodiments, which can be made by one of ordinary skill in the art based on the embodiments herein without making any inventive effort, are intended to be within the scope of the present application.
It is noted that the terms "comprising," "including," and "having," and any variations thereof, in the description and claims of the present application and in the foregoing figures, are intended to cover non-exclusive inclusions. For example, a process, method, system, article, or apparatus that comprises a list of steps or elements is not limited to only those listed steps or elements but may include other steps or elements not listed or inherent to such process, method, article, or apparatus. In the claims, specification, and drawings of this application, relational terms such as "first" and "second," and the like are used solely to distinguish one entity/operation/object from another entity/operation/object without necessarily requiring or implying any actual such relationship or order between such entities/operations/objects.
Reference herein to "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment may be included in at least one embodiment of the present application. The appearances of such phrases in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments. Those of skill in the art will explicitly and implicitly appreciate that the embodiments described herein may be combined with other embodiments.
Referring to fig. 1, a flow chart of a method for extracting point cloud data end points based on PCA in an embodiment of the present application is shown;
a point cloud data endpoint extraction method based on PCA comprises the following steps:
s1, acquiring image data, converting the image data into first 3D point cloud data, and forming three-axis column vectors X, Y, Z according to n points in the first 3D point cloud data;
s2, calculating a covariance matrix A through three-axis column vectors, and carrying out SVD decomposition on the covariance matrix A, namely A=USV T Wherein U is a main vector matrix;
s3, taking out the same-column main direction vector v from the main vector matrix U, wherein the main direction vector v is the main direction vector of the strip-shaped point cloud;
s4, calculating any rigid transformation matrix M from the main direction vector v to the uniaxial vector t, i.e., mv=t;
s5, applying the first 3D point cloud data to a rigid body transformation matrix M for direction conversion, and obtaining second 3D point cloud data after the direction conversion, wherein three-axis column vectors X ', Y ', Z ' of the second 3D point cloud data;
s6, carrying out endpoint calculation according to the triaxial column vectors X ', Y ', Z ' to obtain two endpoints e1 and e2;
and S7, calculating the end point e1 and the end point e2 by adopting an inverse matrix of the rigid body transformation matrix M to obtain two required end points.
In particular, the method comprises the steps of,
the image data described above includes 2.5D images and 3D images.
In one embodiment, the step of calculating the covariance matrix a from the triaxial column vectors includes:
covariance matrix
wherein ,p, q are any axis of the triaxial column vector, and i is one point in the axis among n points.
In one embodiment, covariance matrix a is subjected to SVD decomposition, i.e., a=usv T The step of using U as a main vector matrix comprises the following steps:
principal vector matrix
In one embodiment, the step of extracting the same-column principal direction vector v from the principal vector matrix U includes:
principal direction vector v= (u 11, u21, u 31) T 。
In one embodiment, the step of calculating the end points according to the triaxial column vectors X ', Y ', Z ' to obtain two end points e1 and e2 includes:
endpoint e1= (min (X '), mean (Y '), mean (Z '));
endpoint e2= (max (X '), mean (Y '), mean (Z ')).
Specifically, the media function may be replaced by an average function in the calculation process of the endpoint e1 and the endpoint e 2.
In one embodiment, the transformation matrix M may be solved in any of a plurality of ways. A new solution is proposed herein, the step of calculating any rigid transformation matrix M from a principal direction vector v to a single axis vector t, comprising:
calculating the included angle between the main direction vector v and the uniaxial vector t
Calculating rotation axis vectors wherein />
The rotation matrix M is converted from the shaft angle representation by using a formula, thereby obtaining a rigid body transformation matrix M.
The rigid body transformation matrix
In one embodiment, the step of computing any rigid body transformation matrix M from the principal direction vector v to the uniaxial vector t comprises:
the uniaxial vector t may take any one of t= (1, 0), t= (0, 1, 0) and t= (0, 1).
Referring to fig. 2, which is a block diagram of a point cloud data endpoint extraction device based on PCA according to the present application, the point cloud data endpoint extraction device based on PCA includes:
an acquisition unit 1 for acquiring image data, converting the image data into first 3D point cloud data, and forming three-axis column vectors X, Y, Z according to n points in the first 3D point cloud data;
a first calculation unit 2 for calculating a covariance matrix a by three-axis column vectors and performing SVD decomposition on the covariance matrix a, i.e., a=usv T Wherein U is a main vector matrix;
the main vector confirmation unit 3 is used for taking out the main direction vector v in the same column from the main vector matrix U, wherein the main direction vector v is the main direction vector of the strip point cloud;
a second calculation unit 4 for calculating any rigid body transformation matrix M from the main direction vector v to the uniaxial vector t, i.e., mv=t;
the first conversion unit 5 is configured to apply the first 3D point cloud data to the rigid transformation matrix M for performing direction conversion, and obtain second 3D point cloud data after the direction conversion, where the triaxial column vectors X ', Y ', Z ' of the second 3D point cloud data;
an endpoint calculation unit 6 for calculating endpoints according to the triaxial column vectors X ', Y ', Z ', to obtain two endpoints e1 and e2;
and the second conversion unit 7 is used for calculating the endpoint e1 and the endpoint e2 by adopting an inverse matrix of the rigid transformation matrix M to obtain two required endpoints.
Although embodiments of the present application have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made therein without departing from the principles and spirit of the application, the scope of which is defined in the appended claims and their equivalents.
Claims (8)
1. The PCA-based point cloud data endpoint extraction method is characterized by comprising the following steps of:
acquiring image data, converting the image data into first 3D point cloud data, and forming three-axis column vectors X, Y, Z according to n points in the first 3D point cloud data;
calculating a covariance matrix A through the triaxial column vector, and performing SVD decomposition on the covariance matrix A, namely A=USV T Wherein U is a main vector matrix;
taking out the same-column main direction vector v from the main vector matrix U, wherein the main direction vector v is the main direction vector of the strip-shaped point cloud;
calculating any rigid transformation matrix M from said principal direction vector v to a single axis vector t, i.e. mv=t;
applying the first 3D point cloud data to a rigid body transformation matrix M for direction conversion, and obtaining second 3D point cloud data after the direction conversion, wherein triaxial column vectors X ', Y ', Z ' of the second 3D point cloud data;
carrying out endpoint calculation according to the triaxial column vectors X ', Y ', Z ' to obtain two endpoints e1 and e2;
calculating an endpoint e1 and an endpoint e2 by adopting an inverse matrix of the rigid transformation matrix M to obtain two required endpoints;
the step of calculating the end points according to the triaxial column vectors X ', Y ', Z ' to obtain two end points e1 and e2 includes:
endpoint e1= (min (X '), mean (Y '), mean (Z '));
endpoint e2= (max (X '), mean (Y '), mean (Z '));
the step of calculating any rigid body transformation matrix M from said principal direction vector v to a single axis vector t comprises:
the uniaxial vector t may take any one of t= (1, 0), t= (0, 1, 0) and t= (0, 1).
2. The PCA-based point cloud data endpoint extraction method of claim 1, wherein the step of calculating a covariance matrix a by the tri-axial column vectors comprises:
the covariance matrix
wherein ,p, q are any axis of the triaxial column vector, and i is one point in the axis among n points.
3. The PCA-based point cloud data endpoint extraction method of claim 1, wherein the subjecting the covariance matrix a to SVD decomposition, i.e., a = USV T The step of using U as a main vector matrix comprises the following steps:
the main vector matrix
4. A method of PCA-based point cloud data endpoint extraction according to claim 3, wherein the step of extracting the co-columnar principal direction vector v from the principal vector matrix U comprises:
the principal direction vector v= (u 11, u21, u 31) T 。
5. The PCA-based point cloud data endpoint extraction method of claim 1, wherein the media function is replaced with an average function during the computation of the endpoint e1 and the endpoint e 2.
6. The PCA-based point cloud data endpoint extraction method of claim 1, wherein the step of computing any rigid body transformation matrix M from the principal direction vector v to a single axis vector t, comprises:
calculating the included angle between the main direction vector v and the uniaxial vector t
Calculating rotation axis vectors wherein />
The rotation matrix M is converted from the shaft angle representation by using a formula, thereby obtaining a rigid body transformation matrix M.
7. The PCA-based point cloud data endpoint extraction method of claim 6, wherein the step of the formula scaling the rotation matrix M from an axis angle representation, comprising:
rigid body transformation matrix
8. A PCA-based point cloud data endpoint extraction apparatus, comprising:
an acquisition unit configured to acquire image data, convert the image data into first 3D point cloud data, and form three-axis column vectors X, Y, Z according to n points in the first 3D point cloud data;
a first calculation unit for calculating a covariance matrix a by the triaxial column vector and performing SVD decomposition on the covariance matrix a, i.e., a=usv T Wherein U is a main vector matrix;
the main vector confirming unit is used for taking out the same-column main direction vector v from the main vector matrix U, wherein the main direction vector v is the main direction vector of the strip-shaped point cloud;
a second calculation unit for calculating any rigid body transformation matrix M from the main direction vector v to the uniaxial vector t, i.e., mv=t;
the first conversion unit is used for applying the first 3D point cloud data to the rigid body transformation matrix M to perform direction conversion, and obtaining second 3D point cloud data after the conversion, wherein the triaxial column vectors X ', Y ', Z ' of the second 3D point cloud data;
the endpoint calculation unit is used for calculating endpoints according to the triaxial column vectors X ', Y ', Z ' to obtain two endpoints e1 and e2;
the second conversion unit is used for calculating the endpoint e1 and the endpoint e2 by adopting the inverse matrix of the rigid body transformation matrix M to obtain two required endpoints;
the step of calculating the end points according to the triaxial column vectors X ', Y ', Z ' to obtain two end points e1 and e2 includes:
endpoint e1= (min (X '), mean (Y '), mean (Z '));
endpoint e2= (max (X '), mean (Y '), mean (Z '));
the step of calculating any rigid body transformation matrix M from said principal direction vector v to a single axis vector t comprises:
the uniaxial vector t may take any one of t= (1, 0), t= (0, 1, 0) and t= (0, 1).
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