Autocalibration method for scanning electron microscope using affine camera model
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ORIGINAL PAPER
Autocalibration method for scanning electron microscope using affine camera model Andrey V. Kudryavtsev1 · Valérian Guelpa1 Peter Sturm2 · Nadine Le Fort-Piat1
· Patrick Rougeot1 · Olivier Lehmann1 · Sounkalo Dembélé1 ·
Received: 14 December 2018 / Revised: 6 February 2020 / Accepted: 29 July 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This paper deals with the task of autocalibration of scanning electron microscope (SEM), which is a technique allowing to compute camera motion and intrinsic parameters. In contrast to classical calibration, which implies the use of a calibration object and is known to be a tedious and rigid operation, auto- or selfcalibration is performed directly on the images acquired for the visual task. As autocalibration represents an optimization problem, all the steps contributing to the success of the algorithm are presented: formulation of the cost function incorporating metric constraints, definition of bounds, regularization, and optimization algorithm. The presented method allows full estimation of camera matrices for all views in the sequence. It was validated on virtual images as well as on real SEM images (pollen grains, cutting tools, etc.). The results show a good convergence range and low execution time, notably compared to classical methods, and even more in the context of the calibration of SEM. Keywords Autocalibration · SEM · Affine camera · Global optimization
1 Introduction The use of vision in robotics currently requires camera calibration, i.e., the knowledge of its motion (extrinsic parameters) and model (intrinsic parameters). In the present work, the aim is to achieve calibration of a scanning electron microscope (SEM) directly from images of a specimen (like pollen grains presented in Fig. 1). For SEM, the perspective effects can be neglected and the affine camera model is considered [1,2]. But even if this subject is well studied, the calibration can be very complex due to the following reasons. First, in most cases it requires a calibration object. It often means a special step of fabrication, which can be very expensive and time-consuming especially
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Valérian Guelpa [email protected] Sounkalo Dembélé [email protected]
1
FEMTO-ST, AS2M, Université Bourgogne Franche-Comté, Université de Franche-Comté/CNRS/ENSMM, Besançon, France
2
LJK, Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, Grenoble, France
when working with SEM as, at microscale, the calibration object is of micrometric size. Moreover, it is very difficult to guarantee the quality of its fabrication, which has a profound impact on the accuracy of further image processing. Secondly, the classic calibration [3] needs to be done offline, which can be very restrictive in some applications where the calibration object cannot be placed in front of the camera once the operation started. Thirdly, which includes partially the second point, there is a problem of maintainability of calibration parameters. In order to re-calibrate a camera,
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