Classifications

• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
  • G06T7/00—Image analysis
  • G06T7/70—Determining position or orientation of objects or cameras

Definitions

• the present invention relates to a method for the reconstruction and recovery of the three-dimensional shape of an imaged object in a gauge measurement system, and more specifically, to a robust and accurate method for estimating the motion of an measured object mounted on a rotary stage.
• a gauge measurement system such as a non-contact optical measurement system or coordinate measuring machine (CMM)
• CCM coordinate measuring machine
• a rotary stage or platform is a mounting apparatus which is constrained to permit only movement about a single axis.
• Multiple views or contact measurements of the object are obtained by imaging or contacting the object at different poses.
• a calibration process is then utilized to provide a means to coherently merge the data taken at those views or measurements (recorded in local coordinate systems) into a single global coordinate system.
• the axis of rotation is fixed such that any object mounted to the rotary stage or platform is constrained to rotate about the same identified axis.
• the precision and robustness of any rotational axis estimation scheme depends upon the amount of uncorrelated (useful) data input to the system. Accordingly, there is a need for a method to accurately estimate the axis of rotation for a rotary stage or platform from multiple views or measurements of an object which provides an increase in the amount of data input to the system.
• the present invention provides a method for determining the axis of rotation of an object mounted to a rotary stage or platform in a gauge measurement system by estimating a transformation between multiple views or measurements of the object obtained at different poses.
• Figure 1 is a perspective view of a calibration object mounted on a rotary stage at a first orientation
• Figure 2 is a perspective view of the calibration object of Figure 1 at a second orientation
• Figure 3 is a perspective view of the calibration object of Figure 1 at a third orientation
• Figure 4 is a first coordinate system representation of the rotary stage axis of rotation
• Figure 5 is a second coordinate system representation of the rotary stage axis of rotation
• Figure 6 is a representation of a coordinate transformation in three- dimensional space.
• the present invention provides a method for determining the axis of rotation of a rotary stage or platform using a known calibration object and a robust registration scheme.
• a Robust Closest Patch (RCP) scheme is utilized to estimate the transformation between multiple poses of the object being measured.
• RCP Robust Closest Patch
• ICP iterative closest patch
• the known calibration object is designed in conjunction with the type of sensor undergoing calibration. Specifically, when mounted on the rotary stage or platform 10, a large area of the calibration object 12 must be visible to a camera based sensor or accessible to a contact based sensor in a wide range of poses or positions, without being occluded.
• the calibration object 12 is preferably centered at the suited-point of the sensor and should be large enough to cover the working volume of the sensor, as the accuracy of the calibration will increase with the average arm length of the calibration object 12, as measured from the center of rotation. To avoid reducing available information identifying the pose of the calibration object 12, it is preferred that the calibration object 12 not be round, and include a multiple number of large facets to avoid aliasing effects. Further, the facets are either visible to a camera based sensor or accessible to a contact sensor.
• Each pose of the calibration object 12 in a sequence is defined as P-i,
• the angle of rotation is preferably selected to be small enough to enforce a small amount of overlap between succeeding poses of the calibration object 12. From the data for P k and P k -i, the transformation ⁇ can be estimated independently using the RCP algorithm or any other registration scheme.
• the transformation ⁇ as a rigid body transform, can be decomposed into a rotation R around the origin point, and a translation T:
• ⁇ is the direction of the axis of rotation
• ⁇ is the angle of rotation
• t is the translation vector
• the direction of the axis of rotation is extracted from the estimated rotation by computing the quaternion equivalent of the rotation matrix.
• a point in an (/ ' , j, k) coordinate system such as the camera coordinate system, can be transformed into a (u, v, ⁇ ) coordinate system wherein the ⁇ -axis is parallel to the axis of rotation of the rotary stage 10.
• the center of rotation i.e. any point on the rotation axis, is determined as an invariant point, written using matrix notation as:
• the center of rotation in the rotated space is given coordinates ⁇ ', such that:
• A is the rotation from the coordinate system C to C.
• A is the rotation from the coordinate system C to C.
• a quaternion argument it is possible to compute A such that a point in the (/, j, k) coordinate system can be transformed into the (u, v, ⁇ ) coordinate system.
• Equation (4) can be rewritten in matrix form as:
• condition cos ⁇ ⁇ 1 is utilized to avoid the identity transform which is a particular rotation that does not yield any axis of rotation.
• the rotary stage or platform 10 is likely to be imperfect, hence the parameter t z is exploited to check the planarity of the motion of the rotary stage or platform, and any f z ⁇ 0 it is set to zero.
• Eqn. 3 can be solved for the coordinates of point ⁇ on the axis of rotation AR. Since the direction of the axis of rotation AR is also known, the rotary stage is completely defined mathematically.
• the transformation is represented as a matrix with coordinate points represented as vectors.
• the direction of the axis of rotation AR and the point T on the axis of rotation AR are invariant to the various parts of the transformation process.
• the direction of the axis of rotation AR is an eigenvector corresponding to an eigenvalue of +1.0 of the rotation R since it is invariant to the rotation.
• the point T on the axis of rotation AR is invariant to the transformation, and thus is an eigenvector corresponding to an eigenvalue of +1.0 of the [ R
• An alternative formulation is that there must be two eigenvectors of [R

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• 2002
  • 2002-04-16 US US10/063,362 patent/US6615503B1/en not_active Expired - Lifetime
• 2003
  • 2003-04-16 JP JP2005518207A patent/JP4445472B2/ja not_active Expired - Fee Related
  • 2003-04-16 CN CNB038084554A patent/CN1303572C/zh not_active Expired - Fee Related
  • 2003-04-16 DE DE60331641T patent/DE60331641D1/de not_active Expired - Lifetime
  • 2003-04-16 WO PCT/US2003/011658 patent/WO2003090172A2/en active Application Filing
  • 2003-04-16 EP EP03721688A patent/EP1497794B1/en not_active Expired - Fee Related

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