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Estimation of visual axis during sleep has been attracting a considerable attention. A simultaneous measurement system composed of functional MRI and infrared-video has been developed to investigate a relationship between eye-movement and brain function during sleep. Although there are some methods for measuring visual axis of opening eyes from video images, they cannot be applied to estimate visual axis of closing eyes during sleep. This paper proposes a method based on artificial neural network (ANN) for estimating visual axes during sleep from infrared-video images. Also, this paper introduces a novel calibration method using MRI. The method takes structural MR images of the eyeball and detects the visual axes from the MR images. And, using the detected visual axes and the simultaneously taken infrared-video image, the ANN is trained. The experimental results showed that the proposed method detected visual axes of the right and the left eyes with errors of 1.32plusmn4.24 (RMSEplusmnSD) deg and 1.26plusmn4.20 deg, respectively.