Continuous crystal based PET detectors have features of simple design, low cost, good energy resolution and high detection efficiency. Through single-end readout of scintillation light, direct three-dimensional (3D) position estimation could be another advantage that the continuous crystal detector would have. In this paper, we propose to use artificial neural networks to simultaneously estimate the plane coordinate and DOI coordinate of incident γ photons with detected scintillation light. Using our experimental setup with an '8 + 8' simplified signal readout scheme, the training data of perpendicular irradiation on the front surface and one side surface are obtained, and the plane (x, y) networks and DOI networks are trained and evaluated. The test results show that the artificial neural network for DOI estimation is as effective as for plane estimation. The performance of both estimators is presented by resolution and bias. Without bias correction, the resolution of the plane estimator is on average better than 2 mm and that of the DOI estimator is about 2 mm over the whole area of the detector. With bias correction, the resolution at the edge area for plane estimation or at the end of the block away from the readout PMT for DOI estimation becomes worse, as we expect. The comprehensive performance of the 3D positioning by a neural network is accessed by the experimental test data of oblique irradiations. To show the combined effect of the 3D positioning over the whole area of the detector, the 2D flood images of oblique irradiation are presented with and without bias correction.

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