A Study on Robust SEM Photometric Stereo Using Two BSE Detectors

This thesis presents a novel robust SEM photometric stereo method using two backscattered electron detectors. Robustness is one of the most important factors for practical applications. Although SEM photometric stereo has gained a lot of attention and been extensively studied, the robustness remains a very interesting challenge. Among ill factors, we realize that shadowing and noise problems are almost inherent in SEM photometric stereo. In particular, the shadowing effects generally give rise to significant errors in the reconstructed shapes. The present work is thereby devoted to developing SEM photometric stereo so that it can automatically handle such ill factors. For dealing with shadowing effects, we introduce a shadowing compensation model though modeling image intensities in both cases of absence and presence of shadowing based mainly on angle distribution of backscattered electrons. This model relates the underlying shadowless image to the observed one by the corresponding detection ratio. The detection ratio has modeled the shadowing generation process by means of shadowing angles, which reflects the amount of occluded backscattered electrons. One advantage of the shadowing compensation model is that it is no need for us to treat the regions with shadowing errors separately from those without such errors, because the shadowless case is the special case of shadowing. Therefore, in contrast to some other approaches, the proposed method does not require an image segmentation process to extract shadowing regions, which is substantially difficult to implement automatically. The model has already provided an important cue to eliminate shadowing errors by means of inferring the shadowless images from the observed one if the shadowing angles can be obtained. With the shadowing compensation model and gradient estimation equation, we formulate the proposed robust shape reconstruction into a constrained optimization problem via a variational approach. The objective functional consists of two terms. One is the fidelity term that is to guarantee the gradient of reconstructed shape should be consistent with the gradient data. In particular, the gradient data are evaluated from shadowless images so as to eliminate shadowing errors. In addition, shadowless images are related to the corresponding observed ones through our shadowing compensation ∗Doctoral Thesis, Division of Systems Science and Informatics, Graduate School of Information Science and Technology, Hokkaido University, SSI-DT79115040, March 25, 2014.