Classifications

• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
  • G06T7/00—Image analysis
  • G06T7/30—Determination of transform parameters for the alignment of images, i.e. image registration
  • G06T7/35—Determination of transform parameters for the alignment of images, i.e. image registration using statistical methods
• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
  • G06T7/00—Image analysis
  • G06T7/80—Analysis of captured images to determine intrinsic or extrinsic camera parameters, i.e. camera calibration

Definitions

• the present invention relates generally to digital image processing techniques and in particular to a method and apparatus for calibrating a non-contact range sensor of the type used to obtain digital images of objects for the purpose of inspecting the objects for defects.
• Airfoils e.g. turbine blades
• digital data and images of the objects are inspected for deformation parameters such as platform orientation, contour cross-section, bow and twist along stacking axis, thickness and chord length at given cross-sections.
• CMMs coordinate measurement machines
• Non-contact full-field sensors scan the external surfaces of opaque objects using laser or white light. These sensors are capable of scanning the part quickly while obtaining large quantities of data. Examples of non contact sensors include sensors that are based on laser line grating and stereo triangulation; and based on single laser line scan plus rotating the part. Another non contact sensor is based on phased-shift Moire and white light.
• a method for calibrating a non contact range sensor comprises the steps of scanning the object to be inspected with the range sensor to obtain a range image of the object.
• the range image is registered with a reference image of the object to provide registered data . Normal deviations between the registered data and the reference image are computed. Noise is filtered from the normal deviations.
• a plurality of bias vectors and a covariance matrix are estimated and used to generate a lookup table comprising geometric correction factors.
• the range image of the object is compensated in accordance with the lookup table.
• Figure 1 is a flowchart of the method of the present invention, of calibrating a full-field non-contact range sensor
• Figure 2 is a perspective view of a plurality of projections of a bias vector disposed along the z-axis;
• Figure 3 is a perspective view of the x, y and z components of the bias vector illustrated in FIG.2.
• Figure 4 is a flowchart of one method of registering a range image of an object with a reference image of the object.
• sensor calibration is defined as the process of identifying bias errors in measurements obtained by the sensor such that later-obtained measurements can be compensated for the errors.
• the sensor is calibrated in a sequence of steps as follows.
• the sensor is employed to obtain a range image of an object to be inspected.
• the sensor scans the object as the object translates and rotates through its working volume.
• range data points are obtained.
• the data points are arranged in data sets, also referred to herein as a scanned image, and the data sets are registered to one or more reference data sets.
• Reference data comprises geometric ideal models of the object and is also referred to herein as a reference image.
• the scanned image and the reference image are registered to each other such that both are represented in a common coordinate system. Normal deviations are then computed from the scanned image to the registered image. Random noise, which describes precision, and bias error, which describes accuracy, are estimated from the normal deviations and stored in a lookup table.
• the look up table is employed for 3D geometric correction and multiple view integration of images obtained by the sensor.
• Step 42 of method 40 obtains a scanned image of an object to be inspected by translating the object on a translation stage, and rotating the object on a rotation stage along a plurality of directions throughout the 3 dimensional working volume of the object. This step is accomplished using typical scanning and digital imaging systems and techniques.
• a reference image comprising data points corresponding to the ideal shape of the object, and the scanned image of the actual object are registered.
• One method of obtaining a reference image with which to register the scanned image is to grind a planar object to achieve flatness.
• the object itself is measured using a more accurate sensor like a CMM, and the measurements stored as reference data.
• computer assisted drawing (CAD) data or other engineering or design specifications may be used to provide a reference image.
• one embodiment of the invention uses a Robust- Closest-Patch (RCP) algorithm in the registration process.
• the RCP algorithm is the subject of co-pending application SN 09/303,241 , entitled “Method and Apparatus for Image Registration", filed 4/30/99, and assigned to the assignee of the present invention and hereby incorporated by reference.
• RCP algorithm given an initial rigid pose, each scanned image data point is matched to its nearest data point on the reference image as indicated at 62 and 64 of FIG. 4.
• the RCP algorithm matches reference image data points and scanned image data points based on the current pose estimate, and then refines the pose estimate based on these matches.
• pose is solved by singular value decomposition (SVD) of a linear system in six parameters.
• SSVD singular value decomposition
• One embodiment of the invention employs, a linear and symmetric formulation of the rotation constraint using Rodrigues' formula rather than quaternions or orthonormal matrices. This is a simplified method of solving for pose.
• a typical M-estimator is employed to estimate both the rigid pose parameters and the error standard deviation to ensure robustness to gross errors in the data.
• step 66 The 3D rigid transformation that best aligns these matches is determined at step 66 and applied in step 68 of FIG. 4.
• the foregoing steps are repeated using the most recently estimated pose until convergence. Accordingly, registration step 44 of FIG. 1 solves for the translation direction and the axis of rotation by which the reference image may be represented in the scanned image coordinates.
• step 46 of FIG.1 normal deviations from registered data points to data points of the scanned image are found.
• an approximate normal distance between model data points, also referred to herein as patches, and data surface points is used, avoiding the need to estimate local surface normal and curvature from noisy data.
• one embodiment of the invention computes the raw error The raw error e, ; along the normal, n k , for the given direction D ⁇ , at the point q ⁇ according to the relationship :
• Random noise is filtered from the normal deviations using a Gaussian or mean filter.
• the projection b IJk of the bias vector b, j at each point is determined by:
• M is a small region surrounding the data point.
• FIG 2 illustrates a portion of the step 50 of estimating bias vectors.
• Bias values 56 are determined for a set of planes 58, from the plane 59 closest to the sensor, to the plane furthest from the sensor, along the z axis.
• a 3D geometric correction table is built by finding the projection of the bias vectors at regularly (evenly) spaced grid points p in the 3D volume of the object. To accomplish this the projections of the bias vectors found at each point q terme are down-sampled and interpolated.
• One embodiment of the invention employs Gaussian interpolation to interpolate the projections of the bias vectors.
• step 50 estimates bias vectors as a function of surface location and orientation based upon the projection of the bias vector along a plurality of normals, all projections stemming from the same grid point.
• the previous steps provide, for each direction D k , the normal to the planes n k , and the projections of the bias vector, b pk , at each grid point p.
• the following system of relationships are solved for each grid point p of the 3d working volume of the object to be inspected.
• N is the k x 3 matrix of the normal vectors
• v p is the k x 1 vector of the bias projections from gridpoint p.
• the system described above is solved by applying a typical singular value decomposition (SVD) algorithm when the rank of N is 3.
• SSVD singular value decomposition
• Figure 3 illustrates three components X, Y and Z of bias vector components in a 3D grid.
• a covariance matrix is estimated.
• the covariance matrix provides a model of the random noise and precision of the range sensor based on data points corrected for bias as described above. Principal eigenvalues and eigenvectors of the covariance matrix are found and analyzed to simplify the noise model. To accomplish this, the variance in normal direction n k at the grid point p is determined by the relationship:
• n' s the vector:
• s p which contains the terms of the covariance matrix S p , is estimated by forming the /ex 6 matrix as follows:
• the foregoing is solved using a typical least squares approach.
• An alternative embodiment of the invention employs an SVD or pseudo-inverse approach, as long as the rank of T p is at least 6.
• step 54 the calibration obtained by the process of the invention is verified using an independent data source relating to known features of the object.
• an independent data source relating to known features of the object.
• use of a corner artifact allows independent verification of the sensor calibration.
• sphere artifacts of different radii can be employed to reveal the effect of curvature on the 3D geometric correction and the sensor noise model.
• the method 40 can be used to implement on-site calibration checks and re-calibration procedures that can extend the working life of the sensor.
• calibration checks are performed at least at 8-hour intervals, and re-calibration procedures at least every week.
• the present invention can be embodied in the form of computer-implemented processes and apparatuses for practicing those processes.
• the present invention can also be embodied in the form of computer program code containing instructions embodied in tangible media, such as floppy diskettes, CD-ROMs, hard drives, or any other computer-readable storage medium, wherein, when the computer program code is loaded into and executed by a computer, the computer becomes an apparatus for practicing the invention.
• the present invention can also be embodied in the form of computer program code, for example, whether stored in a storage medium, loaded into and/or executed by a computer, or transmitted over some transmission medium, such as over electrical wiring or cabling, through fiber optics, or via electromagnetic radiation, wherein, when the computer program code is loaded into and executed by a computer, the computer becomes an apparatus for practicing the invention.
• computer program code segments configure the microprocessor to create specific logic circuits.

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• 1999
  • 1999-07-27 EP EP99935950A patent/EP1040449A1/de not_active Withdrawn
  • 1999-07-27 WO PCT/US1999/016941 patent/WO2000007146A1/en active Application Filing
  • 1999-07-27 JP JP2000562864A patent/JP2002521699A/ja active Pending

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