CN115205462A - Three-dimensional reconstruction method aiming at light section type and based on semi-ordered point cloud - Google Patents

Abstract

The invention discloses a light section type three-dimensional reconstruction method based on semi-ordered point cloud, which comprises the following steps: step 1: defining a point cloud format; step 2: selecting a target object for scanning to obtain a semi-ordered point cloud; and step 3: analyzing the error source of the measurement data; and 4, step 4: detecting and extracting hole boundaries in the point cloud model; and 5: and repairing the point cloud holes based on the Bayes model. The method obtains the semi-ordered point cloud on the basis of the classical structured light triangulation method, has the flexibility of discrete point cloud and the regularity of the ordered point cloud, and is very suitable for high-precision three-dimensional reconstruction. Meanwhile, aiming at the semi-ordered point cloud, a Bayes probability model is established in the hole region, and the maximum likelihood parameter estimation is carried out on the region to be increased by combining the specific distribution of the point cloud, so that the local features and the global optimization can be comprehensively considered to the maximum extent.

Description

Three-dimensional reconstruction method aiming at light section type and based on semi-ordered point cloud

Technical Field

The invention relates to the technical field of three-dimensional reconstruction, in particular to a light section type three-dimensional reconstruction method based on semi-ordered point cloud.

Background

The three-dimensional reconstruction technology has wide application prospects in the fields of industry, construction industry, biomedical treatment, transportation, aerospace military industry and the like, wherein accurate acquisition of digital point cloud is a key link of three-dimensional reconstruction. The optical active non-contact three-dimensional point cloud acquisition method is usually used for high-precision reconstruction of complex targets due to high measurement precision and large effective information amount. At present, three-dimensional laser scanners with various principles are commonly used, a time of flight (TOF) method depends on time resolution, has higher requirements on equipment parameters, is expensive and is difficult to adapt to complex environments; the working range of an optical interferometry (such as a moire fringe method) mainly depends on the size of a reference grating, an object with a larger size cannot be reconstructed, and the measurement stability is poor; the phase measurement profilometry (also known as a grating projection method) has a small measurement range and strict measurement environment requirements, and is difficult to popularize in practical application. As a non-contact high-precision measurement method, the structured light triangulation method has the advantages of being free of abrasion, high in efficiency, high in precision, low in cost and the like, strong in environmental adaptability, high in measurement robustness, wide in application scene, and high in measurement precision which can reach the micron level, and therefore much attention is paid.

The traditional structured light trigonometry method can acquire coordinate information of a target contour in a current light plane by combining with a mature light stripe center line extraction algorithm, and complete three-dimensional information of a current covered scene can be acquired if a mobile device with a third degree of freedom is used as an auxiliary device. When the offset information of each cross section stack is measured, if the measured target is rigid or static, the measured target can be converted into displacement, and the accuracy of the point cloud obtained in the method is greatly influenced by the parameters and the performance of a light triangle system and a mobile device. When the detected target is non-rigid or dynamic, the information of two adjacent frames acquired by the method does not have strong spatial correlation, and the confidence coefficient of the result acquired by directly fitting the data is not high enough to complete the high-precision three-dimensional reconstruction of the scene.

In addition, the structured light imaging stripe under the condition of a single frame has a certain thickness, and the two-dimensional image covers information under multi-dimensional characteristics, such as light intensity distribution information in a certain direction, normal information of a boundary equation, gray value probability density function information and the like. If the information of a certain depth coordinate is obtained by using the center line mapping of the local area as in the conventional method, the information utilization degree is extremely low, and the topological information in the local area with higher confidence coefficient is difficult to establish.

In the practical application of point cloud, the hole phenomenon caused by point cloud deletion is often made due to self-mutual shielding caused by complex multiple parts in the target to be reconstructed, noise introduced by the measurement environment and the surface characteristics of the target, or inherent limitations such as incomplete scanning/dead zone and data loss of front-end equipment. These holes make the polygonal mesh obtained from real world objects exhibit defects that do not meet the algorithm design criteria, such as degraded elements, self-intersecting/overlapping portions, surface holes, etc., limiting the application scenarios of point clouds. In addition, the original point cloud obtained in a dynamic scene also has a hole phenomenon caused by data loss due to the reasons of high relative movement speed of a target object, limited functions or parameters of acquisition equipment, complex scene components and the like, so that the accuracy, uniformity and effectiveness of the point cloud are influenced, and the requirements of point cloud processing algorithms such as subsequent modeling and the like cannot be met. Meanwhile, when the point cloud model is deformed in a large scale, the model also has the phenomena of cracks and the like.

Various classical point cloud hole repairing algorithms exist for discrete point clouds, but the algorithms have some defects, on one hand, part of the algorithms pay attention to universality, and the hole repairing problem is converted into a curved surface closing problem. This definitely makes the algorithm have high operation efficiency and robustness, and the repairing result is feasible and controllable, but the local detail characteristics are lost correspondingly, thereby reducing the overall fidelity effect of the data and the quality of the point cloud. On the other hand, the rest of algorithms focus more on processing the detailed features of the point cloud, and seek to restore missing data with higher confidence. Errors such as chaotic topology or self-intersecting patches are introduced during such operations, and adaptive adjustment or human intervention of algorithm parameters is also required. Meanwhile, the targets and implementation means pursued by the algorithms are not completely suitable for targets with semi-ordered point clouds, which have a dimension between that of scattered point clouds and ordered point clouds.

Therefore, the invention provides a light section type three-dimensional reconstruction method based on semi-ordered point cloud, and the semi-ordered point cloud is obtained on the basis of a classical structured light triangulation method, so that the flexibility of dispersing the point cloud and the regularity of the ordered point cloud are realized, and the method is very suitable for high-precision three-dimensional reconstruction. Meanwhile, aiming at the semi-ordered point cloud, a Bayes probability model is established in the hole area, and the maximum likelihood parameter estimation is carried out on the area to be increased by combining the specific distribution of the point cloud, so that the local characteristics and the global optimization can be comprehensively considered to the maximum extent.

Disclosure of Invention

In order to achieve the above object, the present invention provides a method for reconstructing a truncated semi-ordered point cloud based three-dimensional reconstruction method, comprising:

step 1: defining the point cloud format as:

x _i ,y _i ,z _i belonging to a point cloud p _i Three-dimensional coordinate information of the points; n is _i Represents p _i Normal information of points on the current frame plane;

represents p _i Normal information of the point and the point close to the two ends on the current moving shaft; i is _i Represents p _i Light intensity information of the dots; ID represents p _i The discrete attribute class to which the point belongs;

and 2, step: selecting a target object for scanning to obtain semi-ordered point cloud;

and step 3: analyzing the error source of the measurement data;

and 4, step 4: detecting and extracting hole boundaries in the point cloud model;

and 5: and repairing the point cloud holes based on the Bayes model.

Further, the step 2 comprises:

on the basis of a structured light trigonometry, adding normal vector information and light intensity information in light stripes in the discrete point cloud; when the laminated offset of each section can meet the condition that vector information covered by the laser stripes of two adjacent frames is not parallel on the current extension line, topological structure information under a preset confidence coefficient can be established in a unified world coordinate system by establishing a space-time field model in the thickness light stripes, and then the semi-ordered point cloud with the dimensionality between the discrete point cloud and the ordered point cloud is obtained.

Further, the error sources in the step 3 include: the method comprises the following steps of introducing random errors into the width, the collimation degree and the drift of structured light, introducing system errors in the building process of a light cutting system, and measuring random errors introduced by various noises in the environment.

Further, the light cutting system is calibrated by adopting a cross-point algorithm.

Further, the step 4 comprises:

step 4.1: selecting a point p in the semi-ordered point cloud _i Searching and generating a neighborhood point set T (p) in the point cloud model;

step 4.2: calculate the point p _i Solving the eigenvector corresponding to the minimum eigenvalue and the tangent plane normal vector of the covariance matrix;

step 4.3: projecting T (p) into a unit circle of the tangent plane to obtain a mapping point set T' (p);

step 4.4: determine the point p _i Whether the point is a pending point;

step 4.5: judging the point p according to the prior information in the point cloud model _i If the point is a hole boundary point, rejecting the point if the point does not meet the requirement;

step 4.6: returning to the step 4.1 until the circulation of all points to be judged is completed;

step 4.7: and (5) whether other boundary points exist in the neighborhood of each hole boundary point is checked again, and whether the neighborhood is a pseudo boundary point is judged.

Further, the step 4.4 includes:

calculating the maximum included angle theta between each point in the mapping point set T' (p) and the left and right side points _i Let θ _max ＝max{θ _i }; if theta _max If it is greater than the decision threshold, the point p _i Is a point to be detected; otherwise the point p _i Is the inner point.

Further, the step 5 comprises:

step 5.1: setting a real value set O and a measured value set M of an object or a scene to be reconstructed, wherein the measured value set M is generated by the real value set O and comprises a statistical error, and the model is described as P (M | O);

step 5.2: assuming that the measurement process is an unbiased estimation, the measurement process is described by a statistical concept under the Bayes' law, and the probability that the reconstruction set is exactly the true set O after the measurement value set M is given is as follows:

step 5.3: determining the corresponding set O with P (O | M) maximized:

step 5.4: determining point clouds obtained during a measurement

In the above description, M points all have a mapping relationship with one point in the measurement value set M:

wherein, measuring point m _i Is from the origin point o _i By coincidence probability density p _i (o _i + Δ x) measurement error;

step 5.5: in the light cutting systemThe error of (2) is mainly Gaussian distribution and each error is mutually independent, and points are reconstructed

Is in accordance with p _i (m _i -Δx)：

Step 5.6: the set prior set consists of density prior, riemann manifold prior and discrete attribute feature prior which are independent of each other:

wherein Z is a normalization constant representing the integral of all other factors in the set; w (O) is a window function, the range to be repaired in the point cloud model is framed, and the target function can be integrated.

Further, the density prior is defined as:

defining an unequal probability random potential p in the framed area _dist Characterized by a local maximum at the desired point within the proportional neighborhood radius:

wherein N is _δ (x) Represents all the sets of points contained within set O within radius δ of point x; the radius delta is obtained by iterative calculation of the expansion area of the current hole to be repaired; and N is increased progressively according to the positive correlation of the singularity of the original point cloud model.

Further, the riemann manifold prior is defined as:

the distribution problem of the original point cloud is converted into an unconstrained optimization problem of the sum of a plurality of component functions on the Riemannian manifold:

wherein, L is a complete Riemann manifold, and the function fi is a convex function defined on L;

definition of T _p L is the tangent space of the manifold L at the point p, TL = $ U _p∈M T _p L represents the tangent cluster of the manifold L, χ (L) represents the vector field space on the manifold L; then the following is defined by the extension:

(1) Defining a T for each p ∈ L _p Inner product g (p) = on L<,·〉 _p Then, call g = ∑<·,·> _p } _p∈L ＝{g(p)} _p∈L For a Riemann metric on the manifold L, we call (L, g) a Riemann manifold, and g ∈ T ^0,2 L is a second order covariant tensor field;

(2) Is provided with

Is a Levi-Civita contact on the Riemann manifold (L, g), gamma: [ a, b ]]→ L is the smooth curve in the Riemannian manifold (L, g), then

A geodesic curvature vector called γ, where γ' (t) represents the derivative of γ at t; if it is

Then, the curve gamma is called as the geodesic line in the manifold L;

(3) If (L, g) is a smooth Riemann manifold, given p ∈ L, v ∈ T _p L, then there is a unique geodesic γ _v :[a,b]→ L is gamma _v (a) = p and γ' _v (a) = v; wherein when gamma: [ a, b ]]| γ' | is a constant when → L is a geodesic line; γ is a regular geodesic line if and only if |' | = 1;

the flow of the Riemannian manifold up-increment sub-gradient algorithm is as follows:

a) Arbitrary point x ₀ E.l, while letting k =0;

b) Optimizing an objective functionChemical examination: if it is

Stopping iteration; otherwise order psi _0,k ＝x _k I =1, go to the next step;

satisfies alpha _k >A dot column of 0;

e) Calculating psi according to the above steps c) and d) until i = m _m,k Let it equal x _k+1 ；

Let k = k +1 and return to step b) for optimization check.

Further, the discrete attribute feature is defined a priori as:

determining whether a point belongs to the types of a region, a boundary and an angular point, wherein the region is defined as a smooth connection curved surface, the boundary is defined as a boundary line between curved surfaces, and the angular point is defined as n or more than 2 boundary intersections; wherein, the first and the second end of the pipe are connected with each other,

(1) The point cloud model comprises a neighboring area within a certain radius including the discrete characteristic points, which is called a special area;

(2) The point cloud model is divided into independent and uncoupled smooth areas by boundary lines, and the areas do not contain discrete feature points and are called as common areas; the boundary points belong to two adjacent areas;

(3) In the special area: the probability of the boundary increases with the curvature of the local neighborhood; the probability of the corner point depends on the number of boundary intersections in the neighborhood;

(4) The angular points only exist in the intersection of two or more boundary lines in the neighborhood with a certain radius specially, and the probability distribution of the angular points meets the requirement of a regression line after the boundary lines are optimized to be the same;

(5) The neighborhoods defined in the density priors and the Riemann manifold priors are limited to the same neighborhood in the process, and the attributes are not divided additionally.

Compared with the prior art, the invention has the beneficial effects that: the Bayes hole region repairing algorithm for the semi-ordered point cloud is provided for the first time, and the algorithm has a series of advantages in detail/structure retention, robustness, accuracy, robustness and the like. Especially, the self characteristics of the semi-ordered point cloud are combined, the existing parameters are adopted as much as possible in the hole boundary detection and priori knowledge optimization process, the low-efficiency calculation process in the similar method is greatly reduced, and the problems of topology definition errors, self-intersection disorder and the like caused by complicated processing flows are not needed to be worried about. In addition, due to the introduction of three types of prior functions, the feasibility and controllability of the algorithm in a universal environment are guaranteed, the combination of global optimization and local characteristics is comprehensively considered, and the fault tolerance rate and the noise tolerance of the algorithm and the high structure quality of a repair result are further improved.

The conception, specific structure and technical effects of the present invention will be further described in conjunction with the accompanying drawings to fully understand the purpose, characteristics and effects of the present invention.

Drawings

FIG. 1 is a block diagram of a high precision optical cutting system of the present invention;

FIG. 2 is a point cloud hole and algorithm repair result of a 3D printed rabbit ear actually measured by the invention;

fig. 3 is a flow chart of the algorithm principle of the present invention.

Detailed Description

The technical contents of the preferred embodiments of the present invention will be made clear and easily understood by referring to the drawings attached to the specification. The present invention may be embodied in many different forms of embodiments and the scope of the invention is not limited to the embodiments set forth herein.

In the drawings, structurally identical elements are represented by like reference numerals, and structurally or functionally similar elements are represented by like reference numerals throughout the several views. The size and thickness of each component shown in the drawings are arbitrarily illustrated, and the present invention is not limited to the size and thickness of each component. The thickness of the components may be exaggerated where appropriate in the figures to improve clarity.

The invention provides a light-section type three-dimensional reconstruction method based on semi-ordered point clouds, which is used for obtaining the semi-ordered point clouds and then applying a Bayes hole region repairing algorithm to the semi-ordered point clouds. On the basis of a classical structured light trigonometry, high-dimensional information such as normal vector information, light intensity information and the like in the light stripes is added into the discrete point cloud. When the offset of each section stack can meet the condition that vector information covered by two adjacent frames of laser stripes is not parallel on a current extension line, a space-time field model is established in the thickness stripes, topological structure information under a preset confidence coefficient can be established in a unified world coordinate system, and a result with the dimensionality between classical discrete point cloud and ordered point cloud is obtained and is called as semi-ordered point cloud. The space-time field model comprises coupling time and space parameters such as normal direction, sampling time, probability density distribution function, gray distribution and other parameter indexes in two adjacent frames of data, so that the two frames of data are not independent. Generally, establishing a corresponding simultaneous relationship in a certain coordinate axis can be called semi-ordered. For the confidence, for example, a discrete point cloud may be corresponding to a confidence of 0, an ordered point cloud may be corresponding to a confidence of 1, and a semi-ordered point cloud may be obtained if the confidence is between the two. The semi-ordered point cloud has the flexibility of discrete point cloud and the regularity of the ordered point cloud, and is very suitable for high-precision three-dimensional reconstruction. The semi-ordered point cloud can provide a specific certain axial downward normal vector set and other information with higher dimensionality, and improves the information utilization degree and the confidence coefficient. The semi-ordered point cloud obtained by the light section system can provide a specific normal vector set in a certain axial direction and other information with higher dimensionality. Aiming at the semi-ordered point cloud, a Bayesian probability model is established in the hole region, and the maximum likelihood parameter estimation is carried out on the region to be increased by combining the specific distribution of the point cloud. The core is that local features and global optimization can be comprehensively considered to the maximum extent by means of a Bayesian probability model and three types of prior knowledge of targeted density, riemann manifold and discrete attributes.

As shown in fig. 1, the three-dimensional reconstruction method of the present invention is implemented based on a light sectioning system. The main components of the light cutting system include a laser light source (line or plane), a triangulation imaging system, a scanning mechanism, and the like. The moving mode of the light cutting system can be adjusted into translation, self-rotation, pitching scanning or multi-degree-of-freedom combination and the like according to the using scene. Preferably, the laser source is an SL-660-130-RS-A-60 line structure light source of OSELA, the triangulation system is se:Sup>A MARS-1230-23U3C camerse:Sup>A of DAHENG IMAGING or se:Sup>A V1228-MPY2 lens of computer, and the scanning mechanism is an LDY-3-300 axis motorized translation stage of Hitachi electronic technology, guangzhou.

The three-dimensional reconstruction method comprises the following steps:

step 1: defining the point cloud format as:

x _i ,y _i ,z _i belonging to a point cloud p _i Three-dimensional coordinate information of the points; n is _i Represents p _i Normal information of points on the current frame plane;

represents p _i Normal information of the point and the points close to the two ends on the current moving shaft; i is _i Represents p _i Light intensity information of the dots; ID represents p _i The discrete attribute class to which the point belongs. The targets tested are diverse. When the target is static/rigid/simple, discrete attributes such as boundaries, coupling edges, corner points, vertexes and the like can be visually defined. However, in the case of dynamic/non-rigid/complex targets, the definition of the discrete attributes depends on the high-dimensional features of the point cloud data, and the dimensions are not fixed and are not limited to specific representation forms.

And 2, step: selecting a target object for scanning to obtain a semi-ordered point cloud;

and 3, step 3: analysis of the error sources of the measurement data: a) Random errors introduced by the characteristics of the structured light width, the collimation degree, the drift and the like; b) Systematic errors (changes of dynamic or static parameters) introduced in the process of building the light cutting system; c) Random errors introduced by various types of noise in the environment are measured. Therefore, the system is calibrated by adopting a cross-point algorithm, and the measurement precision of the system is 28 μm after being verified by a 0-grade measuring block. The cross-point algorithm may adopt an algorithm described in chinese patent publication CN 110470239A.

And 4, step 4: detecting and extracting hole boundaries in the semi-ordered point cloud model;

and 5: and repairing the point cloud hole based on the Bayes model.

Further, as shown in fig. 2 and 3, step 4 specifically includes:

step 4.1: selecting a point p in the point cloud _i Searching in the model and generating a neighborhood point set T (p) of the model;

step 4.2: calculate the point p _i Solving the eigenvector corresponding to the minimum eigenvalue and the tangent plane normal vector of the covariance matrix;

step 4.3: projecting T (p) into a unit circle of the tangent plane to obtain a mapping point set T' (p);

step 4.4: judging the point p _i Is a pending point or an interior point.

Calculating the maximum included angle theta between each point in T' (p) and the left and right points _i Let θ _max ＝max{θ _i }. If theta _max Greater than the decision threshold, then p _i Is a point to be detected; otherwise p _i Is an interior point;

step 4.5: judging p according to each prior information (based on shape, breakpoint, sampling space and other information) in the point cloud model _i If the point is a hole boundary point, rejecting the point if the point does not meet the requirement;

step 4.6: returning to the step 4.1 until the circulation of all points to be judged is completed;

step 4.7: and (5) rechecking whether other boundary points exist in the neighborhood of each hole boundary point, and judging whether the neighborhood is a pseudo boundary point.

Further, step 5, classifying the boundary points and the window functions, establishing a Bayesian model, introducing three types of prior knowledge of density, riemannian manifold and discrete characteristic attributes, and performing maximum likelihood estimation and reconstruction on the region to be increased to complete hole repair. The method specifically comprises the following steps:

step 5.1: a set of true values O and a set of measured values M are set for the object or scene to be reconstructed, where M is generated by O and includes a statistical error describing the model as P (M | O).Generate one

Where n is the number of original points, m is the number of measurement points, ω _O ,ω _M 、

And

the concept of space is characterized.

Step 5.2: assuming that the measurement process is unbiased estimation, describing the measurement process by a statistical concept under Bayes' law, and taking the probability that the reconstruction set is exactly the real set O after the measurement set M is given as:

p (M): reconstructing a probability of a set being M; p (O): probability of reconstructing the set as O; omega _O The interval is bayesian estimated.

Step 5.3: determining the corresponding set O with P (O | M) maximized:

step 5.4: determining a point cloud obtained during a measurement

In (n > M), M points all have a mapping relation with one point in the measurement value set M:

wherein, measuring point m _i Is from the origin point o _i By coincidence probability density p _i (o _i + Δ x) of the measurement error ofAnd (4) producing.

Step 5.5: the errors in the light cutting system are mainly Gaussian distribution and are mutually independent, and points are reconstructed

Is in accordance with p _i (m _i -Δx)：

Step 5.6: the set prior consists of three main components: the density prior, the Riemann manifold prior and the discrete attribute feature prior are independent of each other:

where Z is a normalization constant representing the integral of all other factors in the set. w (O) is a window function, the range to be repaired in the point cloud model is framed, and the target function can be accumulated; p is a radical of _density (O) Density prior function, p, representing set of true values O _riemann (O) Riemann manifold prior function, p, representing a set of true values O _discrete (O) represents a discrete attribute feature prior function of the set of real values O.

Three types of prior functions are defined and formed as follows:

density prior function: ideally (the original point cloud is scanned and recorded by a light-section system in a known motion direction, or a certain flag bit is present in the point cloud data), the expected position value of each point in the point cloud is predictable, and a sampling space is directly set according to the resolution of a single-frame imaging plane (XOZ plane) of structured light at a certain time, so that the complete mapping of the sampling space is equal to the resolution of an imaging device, and the complete points of the frame data of the point cloud model on each sampling interval on a projection plane perpendicular to the moving direction should be consistent. Meanwhile, the time-space intervals of several adjacent frames in the third moving direction (Y axis) have strong similarity, that is, the interval distances tend to be consistent.

When the actual situation of the point cloud does not directly support the operation, the sampling space is optimized by evaluating the expected distance between adjacent points, and the density theory of the semi-ordered point cloud is expanded to a common point cloud model. Defining an unequal probability random potential p in the framed area _dist Characterized by a local maximum at the desired point within the proportional neighborhood radius:

wherein, N _δ (x) Representing all the sets of points contained within the set O within the radius δ of point x. The radius delta is obtained by iterative calculation of the expansion area of the current hole to be repaired. N can be increased progressively according to the positive correlation of the singularity of the original point cloud model, and is preferably 6 generally.

Riemann manifold prior function: the distribution problem of the original point cloud is converted into an unconstrained optimization problem of the sum of a plurality of component functions on the Riemannian manifold:

where L is a complete riemann manifold and function fi is a convex function defined on L. Due to the unidirectionality and the closure of the curved surface to be reconstructed by the point cloud, the incremental sub-gradient algorithm on the Riemannian manifold must be converged on the convex set.

Meanwhile, the present invention defines T _p L is the tangent space of the manifold L at the point p, TL = $ U _p∈M T _p L denotes the tangent cluster of manifold L, and χ (L) denotes the vector field space on L. Then it is defined as follows:

(1) Defining a T for each p ∈ L _p Inner product g (p) = (r,) on L> _p Then, call g = ∑<·,·> _p } _p∈L ＝{g(p)} _p∈L For a Riemann metric on manifold L, we call (L, g) a Riemann manifold, and g ∈ T ^0,2 L is the second order covariant tensor field.

(2) Is provided with

Is a Levi-Civita link on Riemann manifold (L, g), gamma: [ a, b ]]→ L is a smooth curve in Riemann manifold (L, g), then

A geodesic curvature vector (or acceleration) called γ, where γ' (t) represents the derivative of γ at t. If it is

The curve gamma is called the geodesic in L.

(3) If (L, g) is a smooth Riemannian manifold, given p ∈ L, v ∈ T _p L, then there is a unique geodesic γ _v :[a,b]→ L is gamma _v (a) = p and γ' _v (a) = v. Wherein when gamma: [ a, b ]]→ where L is a geodesic line, | γ' | is a constant; γ is a regular geodesic line if and only if | γ' | = 1.

The flow of the Riemannian manifold up-increment sub-gradient algorithm is as follows:

f) Arbitrary point x ₀ E.l, while letting k =0;

g) Performing optimization test on the objective function: if it is

The iteration is stopped; otherwise let psi _0,k ＝x _k I =1, go to the next step;

satisfies alpha _k >A dot column of 0;

j) Calculating psi according to the above steps c) and d) until i = m _m,k Let it equal x _k+1 ；

k) Let k = k +1 and return to step b) for optimization check.

Discrete attribute prior function: the invention uses the mode of acquiring original data by a light cutting system to endow each point in the point cloud with an additional discrete attribute mark: and determining whether a point belongs to the types of a region (smooth connection curved surface), a boundary (boundary line between curved surfaces) and an angular point (n is more than or equal to 2 boundary intersections). Wherein we make the following definitions:

(1) The adjacent area in a certain radius containing the discrete characteristic points in the point cloud model is called as a special area;

(2) The point cloud model is divided into independent and uncoupled smooth areas by each boundary line, and the areas do not contain discrete feature points and are called common areas. The boundary points belong to two adjacent areas;

(3) In the special area: the probability of boundary definition grows with the curvature of the local neighborhood; the probability of corner definition depends on the number of boundary intersections in the neighborhood;

(4) The angular point can only exist at the intersection of two or more boundary lines in the neighborhood with a certain radius specially, and the probability distribution of the angular point meets the requirement of a regression line after the boundary lines are optimized and identical with each other;

(5) The neighborhoods defined in the density prior function and the Riemann manifold prior function are limited to the same neighborhood in the process, and the attribute is not divided additionally.

In order to bias the feature retaining local detail in the hole repairing process, the invention builds the optimization process of discrete features on other prior function estimation. I.e., iteratively estimating the probabilities of discrete and continuous attribute assignments, the global continuous estimation results of the first two stages should be used. Considering that the smoothing effect contradicts the estimation of the edge probability, the influence of the curvature prior penalty term in the process should be set to zero. After the optimized convergence, the probability as the edge point is assigned to the high curvature point again.

And estimating normal vectors of all points in the point cloud model by using a covariance matrix method, thereby ensuring the correctness of the repaired model. Meanwhile, in order to avoid a priori information change caused by sampling conditions, the invention uses geometric definition, a set of 20-40 points with the diameter epsilon is determined, and a local coordinate system is established in the set by PCA, namely all the points are sparse height fields in the n direction.

Wherein, N _δ (x) Representing all the sets of points contained within the set O within the radius γ of the point x. Gamma is typically 3-4 times the average distance (density) between points; g _i Is a Gaussian density function; n is _i Normal to each target point estimated by the covariance matrix method; o _t Is the current target point to be estimated.

The method converts the hole repairing problem in the point cloud model into the problem of maximum likelihood estimation according to the training sample under the Bayes framework. The prior information of the conditional probability density is combined with the self characteristics of the point cloud, and is subdivided into three prior functions, and a local fitting model is used for approximating the point cloud model, so that the accuracy and the confidence coefficient of an estimation result are improved.

The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations could be devised by those skilled in the art in light of the present teachings without departing from the inventive concepts. Therefore, the technical solutions available to those skilled in the art through logic analysis, reasoning and limited experiments based on the prior art according to the concept of the present invention should be within the scope of protection defined by the claims.

Claims (10)

1. A three-dimensional reconstruction method based on semi-ordered point cloud aiming at optical sectioning is characterized by comprising the following steps:

step 1: defining the point cloud format as:

x _i ，y _i ，z _i belonging to p in the point cloud _i Three-dimensional coordinate information of the points; n is _i Represents p _i Normal information of points on the current frame plane;

represents p _i Normal information of the point and the point close to the two ends on the current moving shaft; i is _i Represents p _i Light intensity information of the dots; ID represents p _i The discrete attribute class to which the point belongs;

step 2: selecting a target object for scanning to obtain a semi-ordered point cloud;

and 3, step 3: analyzing the error source of the measurement data;

and 4, step 4: detecting and extracting hole boundaries in the point cloud model;

and 5: and repairing the point cloud holes based on a Bayesian probability model.

2. The three-dimensional reconstruction method of claim 1, wherein said step 2 comprises:

on the basis of a structured light trigonometry method, adding normal vector information and light intensity information in light stripes in a discrete point cloud; when the offset of each cross section stack can meet the condition that vector information covered by two adjacent frames of laser stripes is not parallel on the current extension line, a space-time field model is established in the thickness light stripes, so that topological structure information under a preset confidence coefficient can be established in a unified world coordinate system, and the semi-ordered point cloud with the dimensionality between the discrete point cloud and the ordered point cloud is obtained.

3. The three-dimensional reconstruction method of claim 1 wherein said sources of error in said step 3 comprise: the method comprises the following steps of introducing random errors into the width, the collimation degree and the drift of structured light, introducing system errors in the building process of a light cutting system, and measuring random errors introduced by various noises in the environment.

4. A method of three-dimensional reconstruction as set forth in claim 3 wherein the light sectioning system is calibrated using a cross-point algorithm.

5. The three-dimensional reconstruction method of claim 1, wherein said step 4 comprises:

step 4.1: selecting instituteA point p in the semi-ordered point cloud _i Searching and generating a neighborhood point set T (p) in the point cloud model;

step 4.2: calculate the point p _i Solving the eigenvector corresponding to the minimum eigenvalue of the covariance matrix and the tangent plane normal vector;

step 4.3: projecting T (p) into a unit circle of the tangent plane to obtain a mapping point set T' (p);

step 4.4: judging the point p _i Whether the point is a pending point;

step 4.5: judging the point p according to the prior information in the point cloud model _i If the point is a hole boundary point, rejecting the point if the point does not meet the requirement;

step 4.6: returning to the step 4.1 until the circulation of all points to be judged is completed;

step 4.7: and (5) rechecking whether other boundary points exist in the neighborhood of each hole boundary point, and judging whether the neighborhood is a pseudo boundary point.

6. The three-dimensional reconstruction method of claim 5, wherein said step 4.4 comprises:

calculating the maximum included angle theta between each point in the mapping point set T' (p) and the left and right side points _i Let θ let _max ＝max{θ _i }; if theta _max If it is greater than the decision threshold, the point p _i Is a point to be detected; otherwise the point p _i Is the inner point.

7. The three-dimensional reconstruction method of claim 1, wherein said step 5 comprises:

step 5.1: setting a real value set O and a measured value set M of an object or a scene to be reconstructed, wherein the measured value set M is generated by the real value set O and comprises a statistical error, and the model is described as P (M | O);

step 5.2: assuming that the measurement process is an unbiased estimation, describing the measurement process by a statistical concept under bayes' law, and taking the probability that a reconstructed set is exactly the true set O after the measurement value set M is given as:

step 5.3: determining the corresponding set O with P (O | M) maximized:

step 5.4: determining a point cloud obtained during a measurement

In the above method, M points all have a mapping relation with one point in the measurement value set M:

wherein, measuring point m _i Is from the origin point o _i By coincidence probability density p _i (o _i + Δ x) measurement error;

step 5.5: the errors in the light cutting system are mainly Gaussian distribution and are mutually independent, and points are reconstructed

Is in accordance with p _i (m _i -Δx)：

Step 5.6: the set prior set consists of density prior, riemann manifold prior and discrete attribute feature prior which are independent of each other:

wherein Z is a normalization constant representing the integral of all other factors in the set; w (O) is a window function, the range to be repaired in the point cloud model is framed, and the target function can be integrated.

8. The three-dimensional reconstruction method of claim 7 wherein the density prior is defined as:

defining an unequal probability random potential p in the framed area _dist Characterized by a local maximum at the desired point within the proportional neighborhood radius:

wherein, N _δ (x) Represents all the sets of points contained within set O within radius δ of point x; the radius delta is obtained by iterative calculation of the expansion area of the current hole to be repaired; and N is increased progressively according to the positive correlation of the singularity of the original point cloud model.

9. The three-dimensional reconstruction method of claim 7 wherein the Riemann manifold prior is defined as:

the distribution problem of the original point cloud is converted into an unconstrained optimization problem of the sum of a plurality of component functions on the Riemannian manifold:

wherein, L is a complete Riemann manifold, and the function fi is a convex function defined on L;

definition of T _p L is the tangent space of the manifold L at the point p, TL = $ U _p∈M T _p L represents the tangent cluster of the manifold L, χ (L) represents the vector field space on the manifold L; then it is defined as follows:

(1) Defining a T for each p e L _p Inner product g (p) = on L<·，·> _p Then, call g =:<·，·> _p } _p∈L ＝{g(p)} _p∈L for a Riemann metric on the manifold L, we call (L, g) a Riemann manifold, and g ∈ T ^0，2 L is a second order covariant tensor field;

(2) Is provided with

For Levi-Civita contact on the Riemann manifold (L, g), Y: [ a, b ]]→ L is the smooth curve in the Riemannian manifold (L, g), then

A geodesic curvature vector called γ, where γ' (t) represents the derivative of γ at t; if it is

Then, the curve gamma is called as the geodesic line in the manifold L;

(3) If (L, g) is a smooth Riemann manifold, given p ∈ L, v ∈ T _p L, then there is a unique geodesic γ _v ：[a，b]→ L so that gamma _v (a) = p and γ' _v (a) = v; wherein, when Y: [ a, b ]]When → L is a geodesic line, | | γ' | | is a constant; if and only if | | γ' | =1, γ is a normal geodesic;

the flow of the Riemannian manifold up-increment sub-gradient algorithm is as follows:

a) Arbitrary point x ₀ E.l, while letting k =0;

b) Performing optimization test on the objective function: if it is

The iteration is stopped; otherwise let psi _0，k ＝x _k I =1, go to the next step;

satisfies alpha _k Rows of dots > 0;

e) Calculating to obtain psi when i = m according to the steps c) and d) above _m，k Let it equal x _k+1 ；

Let k = k +1 and return to step b) for optimization check.

10. The three-dimensional reconstruction method of claim 7 wherein the discrete-attribute feature is defined a priori as:

determining whether a point belongs to the types of a region, a boundary and an angular point, wherein the region is defined as a smooth connection curved surface, the boundary is defined as a boundary line between curved surfaces, and the angular point is defined as n or more than 2 boundary intersections; wherein the content of the first and second substances,

(1) The adjacent area in a certain radius containing the discrete characteristic points in the point cloud model is called as a special area;

(2) The point cloud model is divided into independent and uncoupled smooth areas by boundary lines, and the areas do not contain discrete feature points and are called as common areas; the boundary points belong to two adjacent areas;

(3) In the special area: the probability of the boundary grows with the curvature of the local neighborhood; the probability of the corner point depends on the number of boundary intersections in the neighborhood;

(4) The angular points only exist in the intersection of two or more boundary lines in the neighborhood with a certain radius specially, and the probability distribution of the angular points meets the requirement of a regression line after the boundary lines are optimized to be the same;

(5) The neighborhoods defined in the density priors and the Riemann manifold priors are limited to the same neighborhood in the process, and the attributes are not divided additionally.

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