Quaternion Convolutional Neural Networks for Heterogeneous Image Processing

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

[1]  Deepak S. Turaga,et al.  No reference PSNR estimation for compressed pictures , 2002, Proceedings. International Conference on Image Processing.

[2]  Lucas Theis,et al.  Lossy Image Compression with Compressive Autoencoders , 2017, ICLR.

[3]  Nikos A. Aspragathos,et al.  A comparative study of three methods for robot kinematics , 1998, IEEE Trans. Syst. Man Cybern. Part B.

[4]  Luigi Fortuna,et al.  Neural networks for quaternion-valued function approximation , 1994, Proceedings of IEEE International Symposium on Circuits and Systems - ISCAS '94.

[5]  Anthony S. Maida,et al.  Deep Quaternion Networks , 2017, 2018 International Joint Conference on Neural Networks (IJCNN).

[6]  Eero P. Simoncelli,et al.  Image quality assessment: from error visibility to structural similarity , 2004, IEEE Transactions on Image Processing.

[7]  Eric Hamilton JPEG File Interchange Format , 2004 .

[8]  Yoon Kim,et al.  Convolutional Neural Networks for Sentence Classification , 2014, EMNLP.

[9]  Nobuyuki Matsui,et al.  Quaternion Neural Network and Its Application , 2003, KES.

[10]  Jean-Philippe Vert Large-Scale Machine Learning , 2020, Mining of Massive Datasets.

[11]  Jimmy Ba,et al.  Adam: A Method for Stochastic Optimization , 2014, ICLR.

[12]  Yoshua Bengio,et al.  Extracting and composing robust features with denoising autoencoders , 2008, ICML '08.

[13]  Ying Zhang,et al.  Quaternion Convolutional Neural Networks for End-to-End Automatic Speech Recognition , 2018, INTERSPEECH.

[14]  Titouan Parcollet,et al.  Quaternion Recurrent Neural Networks , 2018, ICLR.

[15]  Francesco Visin,et al.  A guide to convolution arithmetic for deep learning , 2016, ArXiv.

[16]  Titouan Parcollet,et al.  Quaternion Neural Networks for Spoken Language Understanding , 2016, 2016 IEEE Spoken Language Technology Workshop (SLT).

[17]  Dongpo Xu,et al.  Learning Algorithms in Quaternion Neural Networks Using GHR Calculus , 2017 .

[18]  Yi Xu,et al.  Quaternion Convolutional Neural Networks , 2018, ECCV.

[19]  Jian Sun,et al.  Deep Residual Learning for Image Recognition , 2015, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[20]  Giovanni Muscato,et al.  Multilayer Perceptrons to Approximate Quaternion Valued Functions , 1997, Neural Networks.

[21]  S. Sangwine Fourier transforms of colour images using quaternion or hypercomplex, numbers , 1996 .