JPH04124779A - Three-dimensional shaped symmetry plane extracting device - Google Patents

Abstract

PURPOSE:To input both shape information and a shape as a whole by detecting a cell with a peak value with the aid of a symmetry plane parameter which is determined by two points and performing the application of the symmetry plane while taking the parameter value as an initial value. CONSTITUTION:In an input picture storage part 101, one eye of binocular vision is replaced by a slit light projector, and the depth in the direction of line of sight is measured. From a local symmetrical parameter extraction part 102, a symmetrical point, a symmetry plane normal, and a distance from an origin to a plane are outputted. In a symmetry plane parameter space storage part 103, the regular division of a unit spherical surface is performed to obtain parameter space regularly divided into cells with the same space and shape against the unit normal direction. In a symmetry plane parameter voting part 104, the symmetry plane normal and the distance from the origin obtained in the extraction part 102 are voted to the parameter space of the storage part 103. A symmetry plane parameter accurate measuring estimation part 106 performs accurate parameter estimation by repeating M estimation method, and all the symmetry plane parameter in the distance picture can be accurately extracted from the distance picture of one view point.

Description

[Detailed description of the invention] [Industrial application field] This invention recognizes three-dimensional objects from distance images.

Alternatively, the present invention relates to a three-dimensional shape symmetry plane extraction device that extracts a symmetry plane used for determining the posture of a three-dimensional object or describing the characteristics of a distance image in acquiring a three-dimensional shape model from a distance image.

[Conventional technology]

A description of symmetry extraction is given in 1984, Th
e+international journal of
robotics research.

νo1.3. No, 3. pp, 36-60'Sm
oothed local symmetries
d their jmp1ementaL'ron J
There are many others, but they are related to two-dimensional shapes. In addition, the method for extracting the symmetry plane of a three-dimensional shape is
1989, IEICE 5 Pattern Recognition and Understanding Study Group Research Report, PRU89-81 “On ident
making symmetry of a thre
e-di++ technical object from
It is written in ``its octree''.

(1) Extraction from a distance M image of one viewpoint cannot be performed, and all data (octree representation) of the target three-dimensional shape is required. (2) A symmetric SJfM segmentation is assumed. There was a problem.

[Problem to be solved by the invention]

Ordinary distance image (3D shape) input devices can only acquire shape information from one viewpoint, and even when integrating distance images from multiple viewpoints in a controlled environment, the 3D shape is , it is difficult to input the entire shape completely. Furthermore, when performing object recognition, there are many situations in which the operator must deal with scenes in which multiple three-dimensional objects overlap. This kind of muko 5
The scope of application of the method based on assumptions (C]) and (2) is significantly limited.

The purpose of this invention is to avoid the limitations of 9 or more, assume a distance image (and gray scale image) of one viewpoint as input data (+'), and do not assume segmentation of a 1 (2°) symmetric area. It works very effectively under the following two assumptions:
An object of the present invention is to provide an apparatus for extracting a plane of symmetry of a three-dimensional shape.

[Means for Solving the Problems] In the symmetry plane extraction device for a three-dimensional shape according to the present invention, based on the idea of Hough transform, the symmetry plane is regularly divided into cells of approximately uniform shape representing the range that the symmetry plane parameters can take. (tess
(elate) Prepare a parameter space. First 1
The symmetry between any two points in the image is checked, and if the symmetry condition is satisfied, the symmetry plane parameters determined from those two points are voted into the corresponding cell in the parameter space. Next, a cell in which the number of votes has a peak value (extreme value) is detected in the parameter space, and a plane of symmetry is fitted using the 1M estimation method using the parameter value represented by that cell as an initial value. This is defined as every detected peak value t
I will do this regarding this.

In this invention, we utilize the fact that among the symmetry plane parameter values assumed from any two points, the symmetry plane parameter values representing the most prominent symmetry plane form clusters in the parameter space. , the peak value in the parameter space representing the symmetry plane is taken as a candidate location for the symmetry plane parameter. This is the commonly used principle of Hough transform. However, in the Hough transform, a method for determining the cell size in the parameter space has not been established, and it is difficult to achieve both high accuracy and suppression of false peaks. That is, there is a problem that as the cells become larger, the accuracy deteriorates, and as the cells become smaller, false peaks are more likely to occur. Therefore, assuming such uncertainty, symmetry plane fitting is performed using the 1M estimation method using all peak values in the parameter space as initial values. The M estimation method is a method that converges to the best parameter estimate in a hill-climbing manner by repeatedly executing the 1-weighted least squares method. As a result, a plurality of peak values originating from the same plane of symmetry converge to the same parameter value, and the converged variable make value becomes extremely precise. In addition, both the Hough transform and M estimation method used in 1 and above are methods that work effectively even when there is data other than the target data, or when the data itself is incomplete, so as a result, multiple It works effectively even when an object exists and when only a direct image can be obtained from one viewpoint.

〔Example〕

FIG. 1 shows a configuration diagram of an embodiment of the present invention.

Reference numeral 101 in FIG. 1 is a manual image storage unit, which inputs a distance image, which is a direct image, and a projected binary image.

and one normal image is stored.

102 is a 9-local symmetric parameter extractor, which extracts any 2
This is the part that estimates local symmetry plane parameters based on points. Reference numeral 103 denotes a symmetry plane parameter space storage unit, which stores a symmetry plane parameter space regularly divided into cells having a uniform shape. Each cell represents 1M1O values of a symmetry plane parameter and is provided with a counter representing the number of votes for that symmetry plane parameter. 104 is a symmetry plane parameter voting unit which increases the counter of the corresponding cell in the symmetry plane parameter space storage unit 103 by 1 for each local symmetry plane parameter extracted by the two local symmetry parameter extraction unit 102 by '-5. let 105 is a peak value detection unit, and among the counters of each cell of the symmetry plane parameter space square product unit 103,
A cell whose value takes the maximum value is detected, and the parameter value represented by that cell is output. Reference numeral 106 is a symmetrical plane precision estimating unit which calculates the symmetrical plane variation t-5 value detected by the peak value detecting unit 105 as an initial value and the Y-t value extracted by the local symmetrical parameter extracting unit 102. This moon! Te N1
Estimation method ↓ There is a part that precisely fits the plane of symmetry, and this output becomes the positioning needle output.

The force image storage unit 101 in FIG. 1: Well, three types of force images are accumulated.

First, distance images taken from a certain viewpoint are stored.
Suppose that the dimensional array is scaled. A distance image is an image in which each pixel is assigned a three-dimensional coordinate value corresponding to the viewing direction; 1987 Proc, of 1
international conference o
nComputervision, pp, 657-
661.7RanF, e imaging system
mutiliziB nematic 1iquid
It can be obtained using the device described in Crystal Mask J. In this device, one eye in binocular stereoscopic vision is replaced with a slit light projector, and the depth in the viewing direction is measured using the principle of triangulation.

FIG. 2 is a diagram showing the viewing direction for a certain pixel and the three-dimensional coordinates assigned to that pixel. 201 is the U-axis of the image coordinate system, 202: V-axis 203 is the X-axis of the three-dimensional space coordinate system, 204 is the y-axis 205 is the Z-axis, and 206 is the punctuation distance. 207: This is the line of sight for the pixel 208, and the three-dimensional coordinates stored in one pixel 208 are the line of sight 20
7 and the surface 209 in three-dimensional space.

Next, a 2-dimensional array is prepared in which 2 (24M images of arrow projection (object 1. O is assigned to the background) of 3-dimensional objects taken from the same viewpoint are stored. 2 (I! Both images 2 distance images In a human-powered device, the f: & pale image, which is acquired simultaneously with the distance image, can be acquired by applying threshold processing, etc.). On the other hand, Kyodo System Development Co., Ltd. 7 image processing subroutine rsPIDER, subroutine name BDF
Using the method described in I, 2, etc., it is possible to trace the circular needle of the projected image and find the 2-dimensional coordinates and 2-dimensional normal in the 1-image coordinate system for each contour point. .

In BDFL2, an 8-connected series of 1 pixel adjacent to 0 pixel of a binary image is sequentially traced and used as a boundary line series.

Furthermore, the two-dimensional array in which the normal images are stored is outdated. The normal image is 3 for the corresponding viewing direction.
This is an image in which the normal direction of the dimensional surface is assigned to each pixel, and for each pixel of the distance image, a local window centered at 1 pixel is set, and the The normal direction corresponding to each pixel can be obtained by fitting the surface to the three-dimensional point.

The locally symmetric parameter extraction unit 102 in FIG. 1 will be explained. The two-dimensional coordinates of the contour point of the projected binary image are (u, V)
, the two-dimensional normal (nu, nv).

If the busy point distance at the time of photographing is f, the three-dimensional coordinate of one contour point is
, is
nv)/m). Here, r is 3 from the center of the lens.
The distance to the dimensional coordinates m = *'f''+u''n, 2+v''nv''. 3
In the dimensional coordinates, there is one degree of freedom r in the line of sight direction, but with respect to the three-dimensional normal, the degree of freedom is uniquely determined without existence Q.

For the 3-dimensional coordinates X1 and 3-dimensional normal n1 of the ri point,
The three-dimensional coordinates of one point in the distance image and normal image are N
2. If the three-dimensional normal is n2, the condition for these two points to be symmetrical is expressed by the following equation.

(n half nz) ・ (x, -xz) = O(1,
)(ru,”nz) −λ (x, −x, )
(2) From the second equation (1), r can be determined, and the presence or absence of symmetry can be determined from the equation (2). The condition of equation (2) is determined by a linear equation with the threshold value set to δ.

Symmetry point X determined by these two points.

The drawing method WAn@ is expressed by a linear equation.

If there is symmetry between the pair of two points, then the symmetry of the cross-sectional shape obtained by cutting the range image by the plane determined by the two points and the center of the lens (the origin of three-dimensional spatial coordinates). Sir 1 is determined.

The 2D position on the image of the two points is ul, ul is the 3D position in the 2D (device U), the image projection (i.e., 2D position) of the 3D (ffl device) is P(xJ), and the cross-sectional shape is The deviation from symmetry, diff, is defined by the following equation.

Here, 5=(xs-x(tu,+(1-t)uz))
・NS.

If the value calculated by discretely approximating the integral in the above equation is within a certain threshold value, it is determined that symmetry exists in the cross-sectional shape between the two points.

The equation of the plane passing through the point of symmetry X and determined by the normal n is expressed by a quadratic equation assuming that the coordinate system is set as shown in FIG. 2 and the center of the lens is the origin.

n X X + ny y+ n E Z = ρ(7
) where rhs= (nx, ny, nx)
It is.

Also, ρ-n, xs represents the distance from the origin to the plane.

From the local symmetry parameter extraction unit 102, the symmetry point XS,
Symmetry plane normal n, , and distance ρ from the origin to the plane
is output.

The symmetry plane parameter space storage unit 103 shown in FIG. 1 will be explained. The plane of symmetry can be expressed by a unit normal hector n and a distance ρ from the origin, as shown in (7) 2. A parameter space representing the unit normal nS of the plane of symmetry and the distance ρ from the origin can be constructed as follows.

When the starting point of the unit vector coincides with the center of the unit method, the ending point of the unit vector will be on the unit sphere, so the unit vector has a one-to-one correspondence with the unit sphere.

Prentice-)fall, INC, rcomp
As described in Uter Visiorl pp, 492493, by following the method of configuring a geodesic dome, it is possible to perform regular tessellation of the unit sphere, with approximately equal intervals in the unit normal direction,
In addition, a parameter space regularly divided into uniformly shaped cells can be prepared.

An example is shown in Fig. 3, where 301 is one cell (surface).
The normal vector at one point 302 becomes the normal vector representing that cell. That is, all normal directions within one cell 301 are represented by normal hectors having the direction of point 302. moreover.

A one-dimensional array representing the distance ρ from the origin of the plane of symmetry is prepared for each cell of the geodesic dome. As a result, for one symmetry plane parameter, a regularly divided parameter space having cells of approximately uniform shape can be prepared. Each cell is equipped with a counter representing the number of votes for the plane parameter representing that cell.

The symmetry plane parameter voting section 104 shown in FIG. 1 will be explained. The symmetry plane normal ns and the distance ρ from the origin obtained in the local symmetry baranota extraction unit 102 in FIG. The symmetry plane parameter voting section 104 increments by one the counter of the cell whose representative value is closest among the cells in the parameter space for each parameter value extracted by the one-local symmetry parameter extraction section 102.

The peak value detection section) 05 in FIG. 1 will be explained. In this part, the counter value of each cell in the parameter space is
Extract all parameter values of cells that have local maximum values. To determine the local maximum value, the counter values of adjacent cells are compared, and if the counter value is not smaller than the counter value of any adjacent cell, the local maximum value is determined.

For example, the definition of ``adjacent cells'' can be as follows. Cells that share a side in a regularly divided cell based on a geodesic dome, and are one-dimensional arrays representing the distance ρ from the origin. It is assumed that the cells have the same representative value, or the cells belong to the same cell in regular division based on the geodesic dome, and are interlocked in a one-dimensional array representing the distance ρ from the lens center of the plane of symmetry.

The symmetry plane parameter precise estimator 106 shown in FIG. 1 will be explained. The symmetry plane parameter precision estimating unit 106 is a part that performs precise estimation of symmetry plane parameters using the M estimation method.

The 1M estimation method will be briefly explained. Details are described in 1, for example, University of Tokyo Press, "Experimental Data Analysis by Least Squares Method J pp, 163-176. In ordinary least squares fitting, all data are
Assume that it is due to only one model and that its errors are normally distributed. However, if a certain data set is attributed to more than one model, that assumption does not hold. In the symmetry plane detection process, this corresponds to the case where two or more symmetry planes exist in the data. In general, there are many symmetries in two images, so it is not appropriate to use the ordinary least squares method.The 0M estimation method performs fitting in such cases. Consider a model that includes multiple parameters.1 Now, assume that certain estimated values of those parameters are given. Here, the weight for each given data is determined depending on the residual. That is, data with a large residual error is considered to be data that does not originate from the model to which it is applied, and its weight is reduced in order to reduce its influence. Furthermore, the weight is increased for data with small residuals. The function that determines this weight W is, for example, a Gaussian function with a residual of 2, w=g (
z ; σ). Here, g(x;σ)
is a Gaussian function with standard deviation σ. All data are weighted in this manner and a one-weighted least squares method is performed to obtain new parameter estimates. Next↓ko,
For each data based on the new parameter estimates,
The weights are determined again using the above procedure and the one least squares method is executed. The M estimation method is a method of performing precise parameter estimation by repeating this process.

At this time, an appropriate method for setting the initial value of the parameter estimate is required, and in the present invention, the initial value of the parameter estimate is obtained by Hough transform.

In the symmetry plane parameter precision estimating unit 106 in FIG. ,X!,n!,
”', X a, n n l as data 1M
Accurately estimate symmetry plane parameters using an estimation method.

The peak value detection unit 105 outputs the normal "5-(nx-ny, nx) of the cell with the maximum number of votes and the distance ρ from the origin as the initial value of the estimated value of the symmetry plane parameter. This plane of symmetry is expressed by the following formula % Formula % Here, the coordinate transformation of the pair of symmetry point and normal line output from the 1-local symmetry parameter extraction unit 102 is performed so that the two axis directions coincide with the initial value normal direction. This is to enable the use of normal data when estimating symmetry plane parameters.The initial symmetry plane after coordinate transformation is expressed by the following equation.

2-ρ (9) Also, the plane of symmetry estimated by fitting the data is expressed by the following equation.

z=ax→−b y 1c Qffla,
b and c are parameters to be estimated.

Among the pairs of symmetric points and normals after coordinate transformation, the normal data is expressed as (AJ, B,, 1) in accordance with the 00th expression method. The optimal symmetry plane is estimated by repeatedly performing the comparison of the following formula.

ΣWi, J(w+(Z, a, X, -blYJ-c7
) 2,000wz ((ai Aj”+(b, -B J)2)
)→min 00 Here, from equation (9), the initial value of the parameter estimate is ao ""0. bo=O,
It is Co-D.

(X,,Y,,ZJ), (A,,Bj,1) is 3
The three-dimensional position and normal direction of each symmetry plane element +”l and W
.

The weight parameter l for the three-dimensional position and normal direction represents the number of repetitions, and (a,,b,,c,).

The estimated values of the i-th symmetry plane parameters are shown. Further, the weight Wi+j for each data (symmetrical point and normal line &ll) is determined by a 9th order equation.

Wl, J= g (errorl, =)
(IZ1ffJ Here, g(x) is a Gaussian function, d+ffJ is the deviation from symmetry of each symmetry plane element, and error, j
is calculated using the following formula.

errorI+j"=lI'+(Zj at-+Xj
-bi-+Yj C1-1)t+11g((at-+
J) 2+(bH-+ J)”) OE The above iteration is converged by (a;, br-Ct) or 2
This is repeated until the number of repetitions i reaches a certain number of times. Finally, for the estimated value.

An inverse transformation of the coordinate transformation performed before estimation is performed.

The above processing is performed for all initial values of symmetry plane parameters output from the peak value detection section.

〔Effect of the invention〕

As explained above, according to the present invention, two planes of symmetry are extracted based on a distance image.

First, all local symmetry parameters assumed from two points in one image are voted on in a parameter space that is regularly divided into roughly uniform cells representing possible symmetry planes, and the symmetry plane parameter that has the maximum number of votes is determined. By extracting a value, using it as an initial value, and fitting a plane of symmetry using the M-estimation method, and then doing this to all local maximum values.

This method has the advantage that all symmetry plane parameters present in a distance image can be precisely extracted even from a distance image from a single viewpoint or even when multiple objects overlap.

[Brief explanation of drawings]

FIG. 1 is a block diagram of one embodiment of the present invention, and FIGS. 2 and 3 are diagrams for explaining the embodiment. 101 is an input image storage unit, 102 is a local symmetry parameter extraction unit, 103 is a symmetry plane parameter space storage unit, 104
The symmetry plane parameter voting section 105 is a peak value detection section, 1
06 is a symmetry plane parameter precision estimator.

Claims (1)

[Claims] In the process of extracting a plane of symmetry from a distance image in which each pixel stores the three-dimensional coordinate value of the surface along the corresponding line of sight, The parameters of the plane of symmetry are voted on in the parameter space representing the plane, and the parameter value with the maximum number of votes is taken out as the initial value. 1. A symmetry plane extraction device for a three-dimensional shape, characterized in that a symmetry plane parameter is precisely estimated by a method of repeatedly performing a weighted least squares method in which effective weights are adjusted using a weighted least squares method.