Quaternion Convolutional Neural Networks for Heterogeneous Image Processing

Abstract

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.Index Terms-Quaternion convolutional encoder-decoder, convolutional neural networks, heterogeneous image processing

A Quaternion-Valued Variational Autoencoder

“…These advantages are due to the properties of quaternion algebras, including the Hamilton product that is used in quaternion convolutions. This has recently paved the way to the development of novel deep quaternion neural networks [11,13,14], often tailored to specific applications, including theme identification in telephone conversation [15], 3D sound event localization and detection [16,17], heterogeneous image processing [18] and speech recognition [19]. Other properties of quaternion algebra that may be exploited in learning processes are related to the second-order statistics.…”

An Information-Theoretic Perspective on Proper Quaternion Variational Autoencoders

“…Another fundamental property of quaternion-valued learning is the Hamilton product, which has recently favored the proliferation of convolutional neural networks in the quaternion domain [ 35 , 36 , 37 , 38 ]. Due to their capabilities, quaternion-valued learning methods have been applied in several applications, including spoken language understanding [ 39 ], color image processing [ 40 , 41 ], 3D audio [ 42 , 43 ], speech recognition [ 44 ], image generation [ 45 ], quantum mechanics [ 46 ], risk diversification [ 47 ], gait data analysis [ 48 ].…”

A unified criterion for global exponential stability of quaternion‐valued neural networks with hybrid impulses

“…In order to directly process the three-dimensional data, quaternion-valued neural networks (QVNNs) are proposed as a result. 3 At present, QVNNs have been studied in many fields, such as image processing, 4 optimization control. 5 Quaternions, discovered by a British mathematician William Rowan Hamilton in 1843, were the first discovered noncommutative division algebra.…”

“…In order to directly process the three‐dimensional data, quaternion‐valued neural networks (QVNNs) are proposed as a result 3 . At present, QVNNs have been studied in many fields, such as image processing, 4 optimization control 5 …”