Quaternion Convolutional Neural Networks for Heterogeneous Image Processing

Convolutional neural networks (CNN) have recently achieved state-of-the-art in various applications. In the case of image recognition, an ideal has to learn independently of the training data, both local dependencies the three components (R, G, B) of a pixel, and the global relations edges or shapes, making it efficient with small or heterogeneous. Quaternion-valued convolutional neural networks (QCNN) solved this by introducing multidimensional algebra to CNN. This paper proposes explore the fundamental reason of the success of QCNN over CNN, by the impact of the Hamilton product on a color image task performed from a gray-scale only training. By learning both internal and external relations and with less parameters real valued convolutional encoder-decoder (CAE), quaternion convolutional-decoders (QCAE) perfectly reconstructed unseen color images while CAE worst and gray-scale versions.