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This paper proposes a novel neural-network-based photometric stereo approach for 3D surface reconstruction. The neural network inputs are the pixel values of the 2D images to be reconstructed. The normal vectors of the surface can then be obtained from the weights of the neural network after supervised learning, where the illuminant direction does not have to be known in advance. Finally, the obtained normal vectors are applied to enforce integrability when reconstructing 3D objects. The experimental results demonstrate that the proposed neural-network-based photometric stereo approach can be successfully applied to objects generally, and perform 3D surface reconstruction better than some existing approaches.