A Gaussian process and image registration based stitching method for high dynamic range measurement of precision surfaces

Abstract

Please cite this article as: Liu MY, Cheung CF, Cheng CH, Su R, Leach R.K.A Gaussian process and image registration based stitching method for high dynamic range measurement of precision surfaces.Precision Engineering http://dx.doi.org/10. 1016/j.precisioneng.2017.04.017 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. A Gaussian Highlights： It makes use of Gaussian process to model the sub-aperture measurement datasets to obtain the mean surface for registration, which is a novel method as comparing to traditional filtering methods, and provides better registration accuracy. Image registration and z shift method are used to simplify the 6 degrees of freedom 3D point cloud registration to a 3 degrees of freedom registration. Edge intensity data fusion method is used to fuse the overlapped region to provide a better transition between two datasets. It provides a novel stitching solution for a wide range of optical measurement instruments for achieving high dynamic range optical measurement of precision surfaces Abstract: Optical instruments are widely used for precision surface measurement. However, the dynamic range of optical instruments, in terms of measurement area and resolution, is limited by the characteristics of the imaging and the detection systems. If a large area with a high resolution is required, multiple measurements need to be conducted and the resulting datasets needs to be stitched together. Traditional stitching methods use six degrees of freedom for the registration of the overlapped regions, which can result in high computational complexity. Moreover, measurement error increases with increasing measurement data. In this paper, a stitching method, based on a Gaussian process, image registration and edge intensity data fusion, is presented. Firstly, the stitched datasets are modelled by using a Gaussian process so as to determine the mean of each stitched tile. Secondly, the datasets are projected to a base plane. In this way, the three-dimensional datasets are transformed to two-dimensional (2D) images. The images are registered by using an (x, y) translation to simplify the complexity. By using a high precision linear stage that is integral to the measurement instrument, the rotational error becomes insignificant and the cumulative rotational error can be eliminated. The translational error can be compensated by the image registration process. The z direction registration is performed by a least-squares error algorithm and the (x, y, z) translational information is determined. Finally, the overlapped regions of the measurement datasets are fused together by the edge intensity ...

Gaussian process machine learning-based surface extrapolation method for improvement of the edge effect in surface filtering

“…Currently, the calculation of Gaussian process machine learning requires long computation time especially when the dataset is large. Although the data size in the present study was limited to several hundreds × several hundreds and there was no need for special handling to reduce the data size, it would be difficult to deal with an extremely large dataset such as those in the high dynamic range measurements [35,40]. One solution to this is to first down-sample the original dataset to a reasonable dimension and then conduct the Gaussian process calculation for surface extrapolation.…”

“…The measurement process contains noise governed by Gaussian distribution and the original measured surface can be determined by [35,36],…”

“…Moreover, the sub-micron level accuracy requirement for precision surfaces is difficult to achieve. Recently, Gaussian process has gained research interest [34,35] for data modelling regarding the measurement of precision freeform surfaces with high accuracy. The measurement process contains measurement noise which is governed by Gaussian distribution and hence the measurement process is essentially a Gaussian process.…”

Any-degrees-of-freedom (anyDOF) registration for the characterization of freeform surfaces

“…The most widely used is probably the iterative closest points (ICP) method developed by Besl and McKay [6] and Zhang [7], from which several variants have been developed [8]. Other frequently used methods include the least square method [9], the intrinsic feature-based method [10], and methods based on image registration [11]. Most of these methods perform surface transformation in all six degrees of freedom (DOF), which in most cases provides accurate alignment of the measured and designed surfaces.…”

A self-calibration rotational stitching method for precision measurement of revolving surfaces

“…The stitching method is applied at the software level, independent of the instrument hardware setup. Several studies have focused on planar stitching, such as sub-aperture stitching interferometry for relatively flat surfaces [7,8], and spherical and aspherical surfaces [9,10]. Some studies have explored the measurement of revolving surfaces -specifically cylindrical surfaces.…”