Cortical Dynamics of 3-D Vision and Figure-Ground Pop-Out

Air Force Office of Scientific Research (90-0175); Defense Advanced Research Projects Agency (90-0083); Office of Naval Research (N00014-91-J-4100

Neural Computing in Quaternion Algebra

兵庫県立大学201

Convolution and Correlation Based on Discrete Quaternion Fourier Transform

In this paper we present the generalized convolution and correlation for the two-dimensional discrete quaternion Fourier transforn (DQFT). We provide several new properties of the generalization. These results can be considered as the extensions of the correlation and convolution properties of real and complex Fourier transform to the DQFT domai

A survey of visual preprocessing and shape representation techniques

Many recent theories and methods proposed for visual preprocessing and shape representation are summarized. The survey brings together research from the fields of biology, psychology, computer science, electrical engineering, and most recently, neural networks. It was motivated by the need to preprocess images for a sparse distributed memory (SDM), but the techniques presented may also prove useful for applying other associative memories to visual pattern recognition. The material of this survey is divided into three sections: an overview of biological visual processing; methods of preprocessing (extracting parts of shape, texture, motion, and depth); and shape representation and recognition (form invariance, primitives and structural descriptions, and theories of attention)

Quaternion generative adversarial networks

Latest Generative Adversarial Networks (GANs) are gathering outstanding results through a large-scale training, thus employing models composed of millions of parameters requiring extensive computational capabilities. Building such huge models undermines their replicability and increases the training instability. Moreover, multi-channel data, such as images or audio, are usually processed by real-valued convolutional networks that flatten and concatenate the input, often losing intra-channel spatial relations. To address these issues related to complexity and information loss, we propose a family of quaternion-valued generative adversarial networks (QGANs). QGANs exploit the properties of quaternion algebra, e.g., the Hamilton product, that allows to process channels as a single entity and capture internal latent relations, while reducing by a factor of 4 the overall number of parameters. We show how to design QGANs and to extend the proposed approach even to advanced models. We compare the proposed QGANs with real-valued counterparts on several image generation benchmarks. Results show that QGANs are able to obtain better FID scores than real-valued GANs and to generate visually pleasing images. Furthermore, QGANs save up to 75% of the training parameters. We believe these results may pave the way to novel, more accessible, GANs capable of improving performance and saving computational resources

Convolution theorems associated with quaternion linear canonical transform and applications

Novel types of convolution operators for quaternion linear canonical transform (QLCT) are proposed. Type one and two are defined in the spatial and QLCT spectral domains, respectively. They are distinct in the quaternion space and are consistent once in complex or real space. Various types of convolution formulas are discussed. Consequently, the QLCT of the convolution of two quaternionic functions can be implemented by the product of their QLCTs, or the summation of the products of their QLCTs. As applications, correlation operators and theorems of the QLCT are derived. The proposed convolution formulas are used to solve Fredholm integral equations with special kernels. Some systems of second-order partial differential equations, which can be transformed into the second-order quaternion partial differential equations, can be solved by the convolution formulas as well. As a final point, we demonstrate that the convolution theorem facilitates the design of multiplicative filters