Quaternion Convolutional Neural Networks for Heterogeneous Image\n Processing

Abstract

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