JP2896283B2 - Device for calculating misalignment between data of multiple three-dimensional shape data - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an apparatus for calculating a positional shift between data of a plurality of three-dimensional shape data, and more particularly, to image communication,
It is used to generate virtual space by graphics, shape modeling for CG and CAD, stereoscopic display field of video conference, and even when a robot equipped with a range sensor estimates the posture of an object. ,
The present invention relates to an apparatus for calculating a positional shift between data of a plurality of three-dimensional shape data, which calculates a positional shift between data of a plurality of three-dimensional shape data.

[0002]

2. Description of the Related Art As a method for measuring the three-dimensional shape of an object, there is known a light cutting method in which a structured light such as a laser beam or slit light is illuminated on the object, and the shape of the illuminated portion is measured to obtain the object shape. ing. In addition, when measuring the shape, since a drop always occurs, the table on which the object to be measured is placed is moved, the range sensor is moved, the data of the missing part is measured using a mirror, and these are combined. There is a way. Further, there is a method of manually combining data obtained by replacing an object.

[0003]

By the way, in a real-life communication conference or the like, it is necessary to arrange arbitrary objects in a virtual space. However, these object shapes are not missing even when viewed from any direction. Required. However, when the shape of an object is measured, a missing portion always occurs. Therefore, it is necessary to estimate or supplement the shape of the missing portion, or to paste another measurement result in which the portion is measured. To combine different measurement results, move the table on which the object is placed or move the measurement device to associate multiple measurement values obtained by measuring the object from more directions Then, the amount of displacement between data must be calculated.

However, in the conventional method of associating local features, a method of dividing the surface into regions based on range data or a method of obtaining feature points based on the curvature of the surface is used. In some cases, stable area division cannot be performed, and when the data density is low, unstable calculations are required to extract data features, for example, feature points cannot be obtained with high accuracy. Further, if the measurement direction changes significantly, it becomes impossible to cope with the change, so that a large number of data having a small change in the direction is required.

[0005] In particular, there is no application example in which an object is replaced for the purpose of measuring the bottom surface of an object that cannot be measured only by moving a measuring device or a table on which the object is placed. Relied on human hands.

Therefore, a main object of the present invention is to calculate the amount of displacement between a plurality of ranges in which the measurement directions obtained by replacing an object are significantly different, so that the object surface is smooth and the surface cannot be stably divided into regions. Even in such a case, it is an object to provide a device for calculating a positional shift between data of a plurality of three-dimensional shape data so that a corresponding part between the data can be obtained stably.

[0007]

SUMMARY OF THE INVENTION The present invention is a position shift calculating apparatus for calculating a position shift between respective data from a plurality of three-dimensional data measured by a shape measuring unit, wherein the position shift is calculated by the shape measuring unit. A convex hull calculating means for calculating each convex hull from a plurality of data; and selecting a representative surface of the convex hull from the small faces constituting the calculated convex hull surface using the stability of the small face of the convex hull as a selection criterion. A representative plane selecting unit and a unit for obtaining a coordinate transformation operator for superimposing data by associating the representative planes of the selected measurement data with each other are configured.

[0008] More preferably, among the facets constituting the convex hull surface, a facet which is close to the center of the object and which is large and has the same direction is selected so as not to overlap.

More preferably, a coordinate transformation operator is obtained by using the direction of the corresponding facet and the normal direction component of the position of the center of gravity of the facet among the measurement data.

[0010]

According to the present invention, there is provided an apparatus for calculating a positional deviation between data,
Each convex hull is calculated from the plurality of data measured by the shape measuring unit, and the representative surface of the convex hull is determined based on the stability of the small surface of the convex hull from the calculated small surface constituting the convex hull surface. A coordinate conversion operator for superimposing the selected data is determined by associating the representative surfaces of the selected measurement data with each other.

[0011]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Before describing an embodiment of the present invention, the principle of the present invention will be described. In the present invention, the portion where the shape could not be measured by one measurement (especially,
Replace the object to obtain the data of the bottom surface of the object and re-measure, and construct the surface of the convex hull of each of the obtained data (the smallest shell that contains all the measured data points inside) Then, several pieces are selected from the small surfaces to be replaced, and the amount of displacement when the replacement is performed is calculated using the feature amounts. In this calculation, in order to select a small surface used for data correspondence from among the small surfaces constituting the convex hull surface, it is preferable to select a large surface close to the center of the object from the small surfaces. In addition, it is effective to prevent redundant selection of facets having substantially the same direction, and it is preferable to perform the selection based on the stability of each facet as described later. Then, the correspondence of each convex hull surface can be obtained based on the direction of the facet. Further, when calculating the positional deviation based on the correspondence between the respective small surfaces, it is preferable to use only the direction of the corresponding small surface and the normal direction component of the center of gravity position of the small surface.

As described above, when the range data association method using several small faces selected from the convex hull surface is used, it is possible to effectively utilize the features of the convex portions of the object, which are unlikely to lose data. Therefore, it is possible to avoid the influence of the concave portion of the object, which is the main cause of the data loss. Due to the structure of the range finder, if light shines on the part to be measured and this part cannot be seen from the camera, data will be lost. For this reason, if there is a concave portion of the object, the portion may be blocked by the convex portion and measurement may not be performed. This omission is
This occurs in a concave portion of an object. On the other hand, since such data loss hardly occurs in the convex portion of the object, it is easy to take a correspondence based on the data of the convex portion, and erroneous correspondence does not occur.

The convex hull of the actual object shape and the convex hull of the data point are slightly different due to the measurement error. Comparing with, the endpoints that make up the surface obtained from the data points are the points that have the largest error in the direction outside the object among the measurement points distributed near the endpoints of the convex hull of the actual shape. Become. Therefore, since the error of the component in the normal direction of the position of each end point is a constant value that can be easily estimated, the direction of the surface is determined by a plurality of end points having substantially the same error in almost the same direction, so that the convex hull surface is formed. If a small face with a large area is selected as a representative point from among the small faces to be set, the end points are far apart, so that the influence of the position error of the end point on the calculation of the small face direction is small, and the small face direction is small. The error can be further reduced.

Further, the error in the direction of the surface can be estimated from the distribution of the end points of the facet. Further, the error of the component in the normal direction of the position of the center of gravity of the facet can be estimated very accurately. Therefore, in the calculation method based on the local feature, the error of the data greatly affects, whereas in the method using the convex hull, the error can be easily corrected. Further, since the influence of the error in the direction of the representative surface increases as the distance from the representative surface increases, the influence of the error in the direction of the representative surface can be further reduced by estimating the displacement using a surface close to the center of the object. In addition, in order to obtain the correspondence of each facet based on the direction of the facet, it is preferable that facets having almost the same direction cannot be selected as the representative face at the same time. These conditions are satisfied, and it is convenient to calculate the correspondence and to calculate the displacement.

FIG. 1 is a schematic block diagram of one embodiment of the present invention. First, a configuration of an embodiment of the present invention will be described with reference to FIG. The shape measuring unit 10 measures the shape of the object in the posture 1, and the data of each measured point of the measured object shape is given to the convex hull calculating unit 11, and the convex hull of the data point is calculated. The calculated convex hull is the stability calculation unit 1
The stability is calculated for each of the small surfaces constituting the convex hull surface, and is provided to the representative surface selection unit 13. The representative surface selection unit 13 selects M small surfaces for each convex hull in the order of stability.

Similarly, a shape measuring unit 20, a convex hull calculating unit 21, a stability calculating unit 22, and a representative surface selecting unit 23 are provided to measure the shape of the object in posture 2.

The representative surfaces selected by the representative surface selecting units 13 and 23 are given to a representative surface associating unit 14, where the selected small surfaces are associated with each other. Then, the rotation amount calculation unit 15 calculates the rotation movement amount for alignment by using the least squares method using the respective surfaces whose corresponding surfaces are known. Further, the parallel movement amount calculating section 16 obtains a parallel movement amount for alignment by using the least squares method using the respective surfaces, and obtains a data displacement amount based on the rotation movement amount and the parallel movement amount.

FIG. 2 is a diagram showing an example of the data points of the object shape obtained by the shape measuring unit, FIG. 3 is a diagram showing an example of the convex hull calculated by the convex hull calculating unit, and FIG. FIG. 5 is a diagram for explaining a stability calculating method by a stability calculating unit; FIG. 5 is a diagram for explaining association of surfaces by a representative surface associating unit; FIG. 6 is an angle at which small surfaces are associated; In particular, the figure shows the minimum value of the sum of squares of the error of the angle between the corresponding facets when N pieces of the number M of the selected facets are corresponded.

Next, a specific operation of one embodiment of the present invention will be described with reference to FIGS. The shape measuring unit 10 measures the object shape in posture 1 as shown in FIG. 5A, and the shape measuring unit 20 measures the object shape in posture 2 as shown in FIG. The output is provided to the convex hull calculation units 11 and 12. Here, as shown in FIG. 2, for example, data points of the object shape are regularly output irrespective of the object shape, so that the data is output densely in the convex portion and the data is missing in the concave portion. is there. The convex hull calculators 11 and 21 calculate the convex hull based on these data. As shown in FIG. 3, the convex hull is represented by a small triangle at the convex part of the object shape shown in FIG. 2, and is represented by a relatively large triangle at the part covering the concave part of the object.

The stability calculators 12 and 22 calculate the stability for each of the small surfaces constituting the convex hull surface. The representative surface associating unit 14 calculates S as described later. In the calculation of S, the calculation amount increases when surfaces having extremely small direction differences are selected as the representative surface in an overlapping manner. When the representative plane is selected, overlapping is avoided. The stability of the facet of the convex hull surface as used herein means that l _ij is the center of the convex hull (the center of gravity calculated assuming that the internal mass distribution of the convex hull is uniform, G shown in FIG. 4) and the convex hull surface Of the facet C _{i to} the side E _ij , p _ij is the distance from the orthographic projection of the center G on C _i to E _ij , and becomes a positive value when the orthographic projection is inside C _i , When it takes a negative value when it is outside, the stability F _i is obtained by the following equation (1).

[0021]

(Equation 1)

[0022] Because never object out roll be tilted object is placed base to sin [theta = F _i when the facet C _i put an object down on a flat surface, the stability of this F _i Call.

The representative surface selection units 13 and 23 select M small surfaces for each convex hull in the order of stability. FIG. 5A shows the convex hulls of the data measured in the posture 1 arranged in descending order of stability, and FIG. 5B shows the convex hulls of the data measured in the posture 2. An example of a facet is shown.

The representative surface associating unit 14 associates the selected small surfaces with each other in the following procedure. That is, as shown in FIG. 5A, the representative planes selected from the convex hull facets of each data of posture 1 are respectively represented by C
_11, ..., C _1N and then, 5 representative surface culled from convex hull facets of each data posture 2 shown in (b), respectively C _21,
..., _C2N . FIG connecting a straight line shown in 5 the corresponding dihedral _{C 1i, C 1j, C 2i} , respectively the angle C _2j theta _{1ij,
Assuming} θ _2ij , the sum of the squares of all combinations of the two surfaces is obtained from the following equation (2).

[0025]

(Equation 2)

It is considered that the response that minimizes S is the optimal response for the N plane, and S at this time is defined as _SN . When several surfaces are selected from the constituent surfaces of the convex hull, if a surface having a very close direction is not selected, the number of subsequent calculations is reduced.

The maximum N that can be dealt with without including erroneous correspondences
Is determined as follows. When out of the M sub-surface correctly N corresponding can take is, S _N takes a value close to 0, but when erroneous corresponding not the N corresponding including can not be taken, S _N is very large . Thus, when we seek S _N by increasing the N by 1, it is possible to determine the number N of the most significant sub-surface the correct correspondence take out the M small surface. M can be appropriately determined in consideration of the amount of calculation for obtaining S and the speed of the computer.

[0028] With reference to FIG. 5, when the M will be described when the 8, when N is the case of 5, associating as indicated by the straight line of FIG. 5, respectively from the posture 1 and posture 2, S ₅
Becomes 0.002. When N is set to 6, S ₆ becomes 0.4, and it can be easily detected that an erroneous correspondence is included. FIG.
Uses the same measurements as in FIG.
_Is obtained by changing S _N from to 11.

Next, each rotation amount calculation section 15 was found small surfaces corresponding to each other the N small surface C ₁₁ shown in FIG. 1,
, C _1N , C ₂₁ ,..., C _2N are used to determine the amount of rotational movement for alignment by the least squares method. C by rotation
_11, ..., C _1N normalized normals n _21, ..., n _2N is C _21, ..., the normal n ₁₁ of C _2N, ..., most approaches rotates each n _1N is the next second (3 ) Is the rotation matrix R represented by the equation.

[0030]

(Equation 3)

[0031] This two different directions when the correspondence with singular value decomposition of the correlation matrix ^{_{C = Σ i n 1i n t}} 2i is the only, C = VΛU ^t and SVD orthogonal matrix U, V Is given by the following equation (4).

[0032]

(Equation 4)

In the portion for calculating the sum, when the residuals of the normal vectors are multiplied by the inverse of the sum of the covariance matrices of the occurrence probabilities of the errors of the normal vectors of each posture, the error accuracy is considered. Can be estimated the amount of rotational movement that has been entered.

Next, the parallel movement amount calculating section 16 corresponding small endoplasmic surfaces found was the N each C ₁₁ to each other, ...,
Using C _1N , C ₂₁ ,..., C _2N , the amount of parallel movement for alignment is obtained by the least square method. Parallel to the calculation of the amount of movement, the surface density of the small faces of the center of gravity (facets after translation is constant considered
Ete using the distance calculated centroid) and the distance between the corresponding small faces, and a small surface after translation and its corresponding small faces of the center of gravity. When the post-rotation center-of-gravity positions Rr ₂₁ ,..., Rr _2N approach r ₁₁ ,..., R _1N , respectively, the post-rotation normal direction Rn _{2i is changed} to n _2i and the post-rotation center of gravity position Rr _2i. Is represented as r _2i , the optimal translation amount x is a vector represented by the equation (5).

[0035]

(Equation 5)

[0036] detΣ _i, when ^{_{j n ji n ji t ≠ 0}} , the amount of parallel movement x is calculated by the equation (6).

[0037]

(Equation 6)

By multiplying each term by the accuracy E _ij of the estimation error of the center of gravity of the facet when calculating the sum, the translation amount can be estimated in consideration of the error accuracy.

According to the above-described embodiment, it is possible to calculate the amount of displacement between a plurality of shape data. In the example shown in FIG. 1, the present invention is applied to the case where the shape of two postures is measured. However, the present invention is not limited to this. To the representative surface associating unit 17 to calculate the positional deviation of each posture.

[0040]

According to the present invention, a plurality of measured 3
Each convex hull is calculated from the dimensional data, a representative surface of the convex hull is selected from the small surfaces constituting the convex hull surface using the stability of the small surface of the convex hull as a selection criterion. By obtaining a coordinate conversion operator for superimposing data by associating the representative planes, it is possible to associate data having greatly different measurement directions. Therefore, it is possible to easily identify objects having different postures. In addition, the missing portion at the bottom of the object, which cannot be measured unless the object is replaced, can be easily supplemented without manual intervention. Therefore, it is possible to obtain shape data that is required in a realistic communication conference or the like and is not missing even when viewed from any direction. Further, by associating data using the convex hull surface of the data point set, the association can be made with almost no influence of measurement error, measurement accuracy, and measurement density.

Further, even when the object surface is smooth or the data density is sparse, the feature of the shape can be easily and stably extracted, and the displacement between the data can be accurately calculated. . Furthermore, since there is no need to irregularly move a sensor or a measuring table in accordance with the shape of the object to be measured by using a robot or the like, shape data without omission can be measured with a simple measuring device.

[Brief description of the drawings]

FIG. 1 is a schematic block diagram of one embodiment of the present invention.

FIG. 2 is a diagram illustrating an example of data points of an object shape obtained by a shape measuring unit.

FIG. 3 is a diagram illustrating an example of a convex hull calculated by a convex hull calculating unit.

FIG. 4 is a diagram for explaining a stability calculation method by a stability calculation unit.

5 is a diagram for explaining the correspondence of the small surface of representatives face associating unit.

FIG. 6 is a diagram showing an allowable error of an angle when associating small surfaces.

[Explanation of symbols]

 10, 20 Shape measurement unit 11, 21 Convex hull calculation unit 12, 22 Stability calculation unit 13, 23 Representative surface selection unit 14 Representative surface association unit 15 Rotation amount calculation unit 16 Parallel movement amount calculation unit

Claims (3)

(57) [Claims] An apparatus for calculating a positional shift between respective data from a plurality of three-dimensional data in a shape measuring unit, wherein each convexity is calculated from a plurality of data measured by the shape measuring unit. A convex hull calculating means for calculating the hull, a representative face for selecting a representative face of the convex hull from the facets constituting the convex hull surface calculated by the convex hull calculating means, with the stability of the small face of the convex hull being used as a selection criterion. Selection means, and means for obtaining a coordinate operator for superimposing data by associating the representative planes of the respective measurement data selected by the representative plane selection means with each other. Data displacement calculator. 2. The representative surface selecting means selects, among the small surfaces constituting the convex hull surface, large small surfaces close to the center of the object and having the same direction so as not to overlap. The apparatus for calculating a positional shift between data of a plurality of three-dimensional shape data according to claim 1, characterized in that: 3. The means for determining the coordinate conversion operator comprises: using a corresponding normal direction component of the direction of the facet and the center of gravity of the facet in the measurement data. 2. The apparatus according to claim 1, wherein the data is calculated.