CN112465829A - Interactive point cloud segmentation method based on feedback control - Google Patents

Interactive point cloud segmentation method based on feedback control Download PDF

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CN112465829A
CN112465829A CN202011151636.8A CN202011151636A CN112465829A CN 112465829 A CN112465829 A CN 112465829A CN 202011151636 A CN202011151636 A CN 202011151636A CN 112465829 A CN112465829 A CN 112465829A
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CN112465829B (en
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何丽君
邓安
苏智勇
单梁
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Nanjing University of Science and Technology
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Abstract

The invention discloses an interactive point cloud segmentation method based on feedback control. The method comprises the following steps: determining a feedback state according to a point cloud segmentation principle based on region growth, and designing a feedback control framework and a mathematical concept expression thereof; processing the point cloud input by the user and diffusing the input effect; determining a control law of the estimated segmentation expression by utilizing a Lyapunov direct method according to user input and the estimated segmentation result expression, so that the estimated segmentation result tends to an ideal segmentation result; and determining a control law of an output segmentation expression by utilizing a Lyapunov direct method, so that the result of the output segmentation tracks and estimates a segmentation result, and a point cloud segmentation result expected by a user is obtained. The stability and the convergence of the interactive point cloud segmentation system are analyzed from the perspective of feedback control, the anti-interference capability of interactive segmentation is improved, and the user interaction is reduced; and the estimated segmentation result is adopted to estimate the ideal segmentation result of the user, so that the accuracy of interactive segmentation is improved.

Description

Interactive point cloud segmentation method based on feedback control
Technical Field
The invention relates to the technical field of computer vision and feedback control, in particular to an interactive point cloud segmentation method based on feedback control.
Background
In recent years, with the spread of hardware three-dimensional scanning apparatuses (laser scanners, depth scanners, Kinect, and the like), point cloud data can be easily acquired for different targets. In addition, with the increasing task demands of three-dimensional reconstruction, AR/VR, 3D printing and the like, the processing of point cloud data, especially point cloud segmentation, is receiving more extensive attention. Due to various characteristics of the point cloud data and the limitations of the automatic point cloud segmentation algorithm, the automatic point cloud segmentation often cannot achieve one-hundred-percent accuracy, and cannot completely meet the user requirements. Point cloud segmentation is mainly classified into the following categories according to whether an interaction stage is involved:
the automatic point cloud segmentation method mainly comprises a traditional segmentation method using a pure mathematical model and geometric reasoning and point cloud segmentation based on deep learning. The conventional segmentation methods are commonly used as follows: calculating the edge strength, and judging the edge by referring to a strength threshold; selecting seed points, and combining points with the same attribute in the adjacent neighborhood together to form a region; and performing model fitting on the point cloud data, and classifying the point cloud data according to mathematical models with different geometric shapes. The traditional segmentation method is restricted by geometry and difficult in parameter adjustment, and the segmentation result is uncontrollable. A segmentation method based on deep learning extracts features from the point cloud data and learns different classes of object types using deep learning/machine learning, and then classifies the acquired data using a result model. Although point cloud segmentation methods based on deep learning can provide better results, they have high requirements on a GPU, require a large amount of data for training a model, and are generally slow in operation speed. When the user is not satisfied with the segmentation result, the automatic point cloud segmentation method cannot carry out real-time interaction, and the segmentation result is corrected.
An interactive point cloud segmentation method generally adds foreground and background constraints by a user, and runs a segmentation algorithm on the basis of the foreground and background constraints. And if the segmentation result does not meet the requirement, continuously adding the constraint until a satisfactory result is obtained. A common method is a point cloud segmentation algorithm based on minimum Cut (Min-Cut), which can only divide data into foreground/background and cannot inherit the previous segmentation result; and the Lazy snapping marks foreground and background constraints, and a segmentation result obtained previously can be used as a new seed point for next segmentation, but the stability and the convergence of the whole system are not analyzed, and the adverse effect of excessive user input on the segmentation result is not considered.
In 2018, Zhu et al (Zhu L, Karasev P, Kolesov I, et al. guiding Image Segmentation on the Fly: Interactive Segmentation From a Feedback Control Perspective [ J ]// IEEE Transactions on Automatic control.2018) proposed an Image Segmentation method based on Feedback Control, designed user input and target Segmentation result From the Perspective of Feedback Control, given corresponding Control laws, and analyzed the influence of user input on the stability and convergence of the system. However, the method is applied to the field of image segmentation and is not suitable for 3D scenes.
Disclosure of Invention
The invention aims to provide an interactive point cloud segmentation method based on feedback control, which has strong robustness, high interaction efficiency and high accuracy.
The technical solution for realizing the purpose of the invention is as follows: an interactive point cloud segmentation method based on feedback control comprises the following steps:
step 1, determining a feedback state according to a point cloud segmentation principle based on region growth, designing a feedback control framework, and giving a mathematical concept expression of the feedback control framework;
step 2, processing the point cloud input by the user and diffusing the input effect;
step 3, determining a control law of the estimated segmentation expression by utilizing a Lyapunov direct method according to user input and the estimated segmentation result expression, so that the estimated segmentation result tends to an ideal segmentation result;
and 4, determining a control law of an output segmentation expression by utilizing a Lyapunov direct method, so that the result of the output segmentation tracks and estimates a segmentation result, and obtaining a point cloud segmentation result expected by a user.
Further, the step 1 of determining a feedback state according to a point cloud segmentation principle based on region growth, designing a feedback control framework, and providing a mathematical concept expression of the feedback control framework, specifically as follows:
step 1.1, analyzing a point cloud segmentation principle based on region growth;
step 1.2, providing a feedback state according to a principle, designing a feedback control framework, and providing a mathematical concept expression of the feedback control framework, wherein the mathematical concept expression specifically comprises the following steps:
according to the division basis of the region growing algorithm, taking a normal included angle theta between the current point and the seed point as a feedback state;
determining an input/output form of a feedback control system according to the feedback state, designing a feedback control framework, and giving a mathematical concept expression of the feedback control framework;
let the output segmentation result be theta and the estimated segmentation result be theta*The superscripts k-1 and k respectively represent input of k-1 and k times;
the mathematical concept expression of the feedback control framework is
Figure BDA0002741493510000021
Figure BDA0002741493510000022
Figure BDA0002741493510000023
Figure BDA0002741493510000024
In which ξk、
Figure BDA0002741493510000031
Respectively estimating errors between the segmentation result and the output segmentation result, estimating errors between the segmentation result and the user input effect during the kth user input;
Figure BDA0002741493510000032
is output divisionThe control law of (3) ensures that the output segmentation result can track the pre-estimated segmentation result;
Figure BDA0002741493510000033
the method is a control law of the pre-estimated segmentation, and ensures that the pre-estimated segmentation result can track the user input.
Further, the processing of the point cloud input by the user and the diffusion of the input effect in step 2 are specifically as follows:
searching for input point P by K-nearest neighbor method, i.e. KNNinputCalculating the normal angle theta between the adjacent point and the seed point, and when theta is smaller than the threshold value thetathWhen the input influence area is occupied by the adjacent point x;
if theta < thetathCurvature c < c of point xthAnd the Label (x) of the point x and the Label (P) of the input pointinput) At a different time,
Label(x)≠Label(Pinput) (6)
then place point x in the set of seed points; wherein c isthRepresents a curvature threshold;
sequentially taking seed points from the seed point set, searching adjacent points to obtain curvature c and normal included angle
Figure BDA0002741493510000034
Figure BDA0002741493510000035
Wherein
Figure BDA0002741493510000036
For the influence of the point x at the kth input, i.e. the ith pass point P during the diffusion of the kth input pointi kDiffusing the resulting neighborhood points x and Pi kThe normal included angle between them; point Pi kThe ith diffused seed point being the kth input point;
Figure BDA0002741493510000037
respectively point x and point Pi kThe normal vector of (a);
and circularly taking the seed points, searching the adjacent points, and judging the curvature and the normal included angle until the seed point set is empty.
Further, the step 3 of determining the control law of the estimated segmentation expression by using the lyapunov direct method according to the user input and the estimated segmentation result expression makes the estimated segmentation result tend to an ideal segmentation result, which is specifically as follows:
step 3.1, designing a Lyapunov function V according to a Lyapunov stability analysis method1I.e. the total label error of the ideal segmentation and input:
Figure BDA0002741493510000038
wherein P represents a collection of points in the point cloud; x represents a point in the point cloud, and x belongs to P;
Figure BDA0002741493510000039
to predict the error of the segmentation result and the user input effect;
step 3.2, designing the formula (2) according to the second Lyapunov method
Figure BDA0002741493510000041
The specific expression of (1);
Figure BDA0002741493510000042
should satisfy V1Negative semi-definite requirement to make the pre-estimated segmentation result track the user input
Figure BDA0002741493510000043
Wherein alpha represents a weight coefficient of the error of the estimated segmentation result and the user input effect in the control law G;
if it is desired to make V1Negative half constant, due to
Figure BDA0002741493510000044
And (3) proving that:
Figure BDA0002741493510000045
wherein V1(k+1)、V1(k) And respectively representing the total label error of the ideal segmentation and input after the k +1 th iteration and the k th iteration.
Further, the control law of the output segmentation expression is determined by using the lyapunov direct method in the step 4, so that the result of the output segmentation tracks the pre-estimated segmentation result to obtain the point cloud segmentation result expected by the user, and the specific method is as follows:
step 4.1, designing a Lyapunov function V according to a Lyapunov stability analysis method2I.e. the total tag error of the output segmentation and the estimated segmentation:
Figure BDA0002741493510000051
step 4.2, designing the formula (1) according to the second Lyapunov method
Figure BDA0002741493510000052
The specific expression of (a) is,
Figure BDA0002741493510000053
should satisfy V2Negative semi-definite requirement, so that the output segmentation result tends to the estimated segmentation result
Figure BDA0002741493510000054
If it is desired to make V2Negative half constant, due to
Figure BDA0002741493510000055
Wherein beta represents the output and estimated segmentation point cloudsThe weight coefficient of the error of (3) in the control law F;
and (3) proving that:
Figure BDA0002741493510000056
wherein V2(k+1)、V2(k) And respectively representing the total label errors of the output segmentation and the estimated segmentation after the (k + 1) th iteration and the k-th iteration.
Compared with the prior art, the invention has the following remarkable advantages: (1) the stability and the convergence of the interactive point cloud segmentation system are analyzed from the feedback control angle, the theoretical basis of the stable convergence of the system is provided, the anti-interference capability of the interactive point cloud segmentation is improved, and the user interaction is effectively reduced; (2) the method provides the estimation of the ideal segmentation result of the user by the pre-estimated segmentation result, provides a target for outputting the segmentation result, and improves the accuracy of the interactive point cloud segmentation.
Drawings
FIG. 1 is a flow chart of the interactive point cloud segmentation method based on feedback control according to the present invention.
Fig. 2 is a structural framework diagram of the feedback control model of the present invention.
Detailed Description
With reference to fig. 1-2, the interactive point cloud segmentation method based on feedback control of the invention specifically comprises the following steps:
step 1, determining a feedback state according to a point cloud segmentation principle based on region growth, designing a feedback control framework, and giving a mathematical concept expression of the feedback control framework;
step 2, processing the point cloud input by the user and diffusing the input effect;
step 3, determining a control law of the estimated segmentation expression by utilizing a Lyapunov direct method according to user input and the estimated segmentation result expression, so that the estimated segmentation result can tend to an ideal segmentation result;
and 4, determining a control law of the output segmentation expression by using the Lyapunov direct method, so that the output segmentation result can track the estimated segmentation result to obtain a point cloud segmentation result expected by a user.
As a specific example, in step 1, a feedback state is determined according to a point cloud segmentation principle based on region growing, a feedback control framework is designed, and a mathematical concept expression of the feedback control framework is given, which specifically includes the following steps:
step 1.1, analyzing a point cloud segmentation principle based on region growth;
step 1.2, providing a feedback state according to a principle, designing a feedback control framework, and providing a mathematical concept expression of the feedback control framework, wherein the mathematical concept expression specifically comprises the following steps:
according to the division basis of the region growing algorithm, taking a normal included angle theta between the current point and the seed point as a feedback state;
and determining the input and output form of the feedback control system according to the feedback state, designing a feedback control framework, and giving a mathematical concept expression of the feedback control framework.
Let the output division result be thetakThe segmentation result is estimated as
Figure BDA0002741493510000061
Where k represents the number of inputs over k.
The mathematical concept expression of the feedback control framework is
Figure BDA0002741493510000062
Figure BDA0002741493510000063
Figure BDA0002741493510000064
Figure BDA0002741493510000065
In which ξk、
Figure BDA0002741493510000066
Respectively estimating errors between the segmentation result and the output segmentation result, estimating errors between the segmentation result and the user input effect during the kth user input;
Figure BDA0002741493510000067
the method is a control law for outputting segmentation, and ensures that the output segmentation result can track and predict the segmentation result;
Figure BDA0002741493510000068
the method is a control law of pre-estimated segmentation, and ensures that a pre-estimated segmentation result can track user input;
as a specific example, the processing of the user input and the diffusion of the input effect in step 2 are specifically as follows:
searching for an input point P by the K-nearest neighbor (KNN)inputCalculating the normal angle theta between the adjacent point and the seed point, and when theta is smaller than the threshold value thetathWhen the input influence area is occupied by the adjacent point x;
if theta < thetathCurvature c < c of point xthAnd the label of point x is different from the label of the input point,
Label(x)≠Label(Pinput) (6)
then place point x in the set of seed points; wherein c isthRepresents a curvature threshold;
sequentially taking seed points from the seed point set, searching adjacent points to obtain curvature c and normal included angle
Figure BDA0002741493510000071
Figure BDA0002741493510000072
Wherein
Figure BDA0002741493510000073
For the influence of the point x at the kth input, i.e. the ith pass point P during the diffusion of the kth input pointi kDiffusing the resulting neighborhood points x and Pi kNormal angle therebetween, point Pi kThe ith diffused seed point being the kth input point;
Figure BDA0002741493510000074
respectively point x and point Pi kThe normal vector of (a);
and circularly taking the seed points, searching the adjacent points, and judging the curvature and the normal included angle until the seed point set is empty.
As a specific example, in step 3, according to the user input and the estimated segmentation result expression, the control law of the estimated segmentation expression is determined by using the lyapunov direct method, so that the estimated segmentation result may tend to an ideal segmentation result, which is specifically as follows:
step 3.1, designing a Lyapunov function V according to a Lyapunov stability analysis method1I.e. the total label error of the ideal segmentation and input:
Figure BDA0002741493510000075
wherein P represents a collection of points in the point cloud; x represents a point in the point cloud, and x belongs to P;
Figure BDA0002741493510000076
to predict the error of the segmentation result and the user input effect;
step 3.2, designing the formula (2) according to the second Lyapunov method
Figure BDA0002741493510000077
The specific expression of (1).
Figure BDA0002741493510000078
Should satisfy V1And the requirement of negative and semi-definite ensures that the estimated segmentation result can track the input of the user. Is provided with
Figure BDA0002741493510000079
If it is desired to make V1Negative half constant, due to
Figure BDA0002741493510000081
Wherein alpha represents a weight coefficient of the error of the estimated segmentation result and the user input effect in the control law G;
and (3) proving that:
Figure BDA0002741493510000082
wherein V1(k+1)、V1(k) Respectively representing the total label error of the ideal segmentation and input after the k +1 th iteration and the k th iteration;
as a specific example, the control law of the output segmentation expression determined by the lyapunov direct method in step 4 enables the output segmentation result to track the estimated segmentation result to obtain the point cloud segmentation result desired by the user, which is specifically as follows:
step 4.1, designing a Lyapunov function V according to a Lyapunov stability analysis method2I.e. the total tag error of the output segmentation and the estimated segmentation:
Figure BDA0002741493510000083
step 4.2, designing the formula (1) according to the second Lyapunov method
Figure BDA0002741493510000084
The specific expression of (1).
Figure BDA0002741493510000085
Should satisfy V2The negative and semi-definite requirements make the output segmentation result tend to the pre-estimated segmentation result. Is provided with
Figure BDA0002741493510000091
If it is desired to make V2Negative half constant, due to
Figure BDA0002741493510000092
Wherein beta represents the weight coefficient of the error of the output segmentation point cloud and the estimated segmentation point cloud in the control law F.
And (3) proving that:
Figure BDA0002741493510000093
wherein V2(k+1)、V2(k) And (4) representing the total label error of the output segmentation and the estimated segmentation after the (k + 1) th iteration and the k-th iteration.
The stability and convergence of the interactive point cloud segmentation system are analyzed from the perspective of feedback control, the theoretical basis of stable convergence of the system is provided, the anti-interference capability of the interactive point cloud segmentation is improved, and the user interaction is effectively reduced; the method provides the estimation of the ideal segmentation result of the user by the pre-estimated segmentation result, provides a target for outputting the segmentation result, and improves the accuracy of the interactive point cloud segmentation.

Claims (5)

1. An interactive point cloud segmentation method based on feedback control is characterized by comprising the following steps:
step 1, determining a feedback state according to a point cloud segmentation principle based on region growth, designing a feedback control framework, and giving a mathematical concept expression of the feedback control framework;
step 2, processing the point cloud input by the user and diffusing the input effect;
step 3, determining a control law of the estimated segmentation expression by utilizing a Lyapunov direct method according to user input and the estimated segmentation result expression, so that the estimated segmentation result tends to an ideal segmentation result;
and 4, determining a control law of an output segmentation expression by utilizing a Lyapunov direct method, so that the result of the output segmentation tracks and estimates a segmentation result, and obtaining a point cloud segmentation result expected by a user.
2. The interactive point cloud segmentation method based on feedback control as claimed in claim 1, wherein the step 1 is to determine the feedback state according to the point cloud segmentation principle based on region growing, design the feedback control framework, and provide the mathematical concept expression of the feedback control framework as follows:
step 1.1, analyzing a point cloud segmentation principle based on region growth;
step 1.2, providing a feedback state according to a principle, designing a feedback control framework, and providing a mathematical concept expression of the feedback control framework, wherein the mathematical concept expression specifically comprises the following steps:
according to the division basis of the region growing algorithm, taking a normal included angle theta between the current point and the seed point as a feedback state;
determining an input/output form of a feedback control system according to the feedback state, designing a feedback control framework, and giving a mathematical concept expression of the feedback control framework;
let the output segmentation result be theta and the estimated segmentation result be theta*The superscripts k-1 and k respectively represent input of k-1 and k times;
the mathematical concept expression of the feedback control framework is
Figure FDA0002741493500000011
Figure FDA0002741493500000012
Figure FDA0002741493500000013
Figure FDA0002741493500000014
In which ξk、
Figure FDA0002741493500000015
Respectively estimating errors between the segmentation result and the output segmentation result, estimating errors between the segmentation result and the user input effect during the kth user input;
Figure FDA0002741493500000016
the method is a control law for outputting segmentation, and ensures that the output segmentation result can track and predict the segmentation result;
Figure FDA0002741493500000017
the method is a control law of the pre-estimated segmentation, and ensures that the pre-estimated segmentation result can track the user input.
3. The interactive point cloud segmentation method based on feedback control as claimed in claim 1, wherein the point cloud inputted by the user is processed and the input effect is diffused in step 2, specifically as follows:
searching for input point P by K-nearest neighbor method, i.e. KNNinputCalculating the normal angle theta between the adjacent point and the seed point, and when theta is smaller than the threshold value thetathWhen the input influence area is occupied by the adjacent point x;
if theta < thetathCurvature c < c of point xthAnd the Label (x) of the point x and the Label (P) of the input pointinput) At a different time,
Label(x)≠Label(Pinput) (6)
then place point x in the set of seed points; wherein c isthRepresents a curvature threshold;
sequentially taking seed points from the seed point set, searching adjacent points to obtain curvature c and normal included angle
Figure FDA0002741493500000021
Figure FDA0002741493500000022
Wherein
Figure FDA0002741493500000023
For the influence of the point x at the kth input, i.e. the ith pass point P during the diffusion of the kth input pointi kDiffusing the resulting neighborhood points x and Pi kThe normal included angle between them; point Pi kThe ith diffused seed point being the kth input point;
Figure FDA0002741493500000024
respectively point x and point Pi kThe normal vector of (a);
and circularly taking the seed points, searching the adjacent points, and judging the curvature and the normal included angle until the seed point set is empty.
4. The interactive point cloud segmentation method based on feedback control as claimed in claim 2, wherein the control law of the estimated segmentation expression is determined by the Lyapunov direct method according to the user input and the estimated segmentation result expression in step 3, so that the estimated segmentation result can tend to an ideal segmentation result, specifically as follows:
step 3.1, designing a Lyapunov function V according to a Lyapunov stability analysis method1I.e. the total label error of the ideal segmentation and input:
Figure FDA0002741493500000025
wherein P represents a collection of points in the point cloud; x represents a point in the point cloud, and x belongs to P;
Figure FDA0002741493500000026
for estimating segmentation result and user inputError in effect;
step 3.2, designing the formula (2) according to the second Lyapunov method
Figure FDA0002741493500000027
The specific expression of (1);
Figure FDA0002741493500000031
should satisfy V1Negative semi-definite requirement to make the pre-estimated segmentation result track the user input
Figure FDA0002741493500000032
Wherein alpha represents a weight coefficient of the error of the estimated segmentation result and the user input effect in the control law G;
if it is desired to make V1Negative half constant, due to
Figure FDA0002741493500000033
And (3) proving that:
Figure FDA0002741493500000034
wherein V1(k+1)、V1(k) And respectively representing the total label error of the ideal segmentation and input after the k +1 th iteration and the k th iteration.
5. The interactive point cloud segmentation method based on feedback control as claimed in claim 4, wherein the control law of the output segmentation expression is determined by the Lyapunov direct method in step 4, so that the result of the output segmentation tracks the pre-estimated segmentation result to obtain the point cloud segmentation result desired by the user, and the method specifically comprises the following steps:
step 4.1, designing a Lyapunov function V according to a Lyapunov stability analysis method2I.e. total tag errors of output segmentation and estimated segmentationDifference:
Figure FDA0002741493500000035
step 4.2, designing the formula (1) according to the second Lyapunov method
Figure FDA0002741493500000041
The specific expression of (a) is,
Figure FDA0002741493500000042
should satisfy V2Negative semi-definite requirement, so that the output segmentation result tends to the estimated segmentation result
Figure FDA0002741493500000043
If it is desired to make V2Negative half constant, due to
Figure FDA0002741493500000044
Wherein beta represents the weight coefficient of the error of the output segmentation point cloud and the estimated segmentation point cloud in the control law F;
and (3) proving that:
Figure FDA0002741493500000045
wherein V2(k+1)、V2(k) And respectively representing the total label errors of the output segmentation and the estimated segmentation after the (k + 1) th iteration and the k-th iteration.
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CN110110802A (en) * 2019-05-14 2019-08-09 南京林业大学 Airborne laser point cloud classification method based on high-order condition random field
CN110969624A (en) * 2019-11-07 2020-04-07 哈尔滨工程大学 Laser radar three-dimensional point cloud segmentation method
CN111352420A (en) * 2020-03-03 2020-06-30 厦门大学 High-precision positioning and target alignment control method for laser navigation AGV

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109634291A (en) * 2018-11-27 2019-04-16 浙江工业大学 A kind of rigid aircraft posture restraint tracking and controlling method based on modified obstacle liapunov function
CN110110802A (en) * 2019-05-14 2019-08-09 南京林业大学 Airborne laser point cloud classification method based on high-order condition random field
CN110969624A (en) * 2019-11-07 2020-04-07 哈尔滨工程大学 Laser radar three-dimensional point cloud segmentation method
CN111352420A (en) * 2020-03-03 2020-06-30 厦门大学 High-precision positioning and target alignment control method for laser navigation AGV

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