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Neural networks in the real domain have been studied for a long time and achieved promising results in many vision tasks for recent years. However, the extensions of the neural network models in other number fields and their potential applications are not fully-investigated yet. Focusing on color images, which can be naturally represented as quaternion matrices, we propose a quaternion convolutional neural network (QCNN) model to obtain more representative features. In particular, we re-design the basic modules like convolution layer and fullyconnected layer in the quaternion domain, which can be used to establish fully-quaternion convolutional neural networks. Moreover, these modules are compatible with almost all deep learning techniques and can be plugged into traditional CNNs easily. We test our QCNN models in both color image classification and denoising tasks. Experimental results show that they outperform the real-valued CNNs with same structures.

Abstract.A 3-dimensional finite element model is developed to simulate and analyze the temperature and degree of cure field of epoxy casting part during cure process. The present model based on general finite element software ABAQUS is verified by literature example and experimental data. The numerical results show good agreement with literature example and measured data, and are even more accurate than the simulation of literature. After modeling successfully, the influence of temperature cure cycle ramps have on the temperature and degree of cure gradient is investigated. Moreover, the effect of non-uniform temperature and degree of cure field within epoxy casting part on hardness is demonstrated. The present model provides an accurate and novel method that allows further insight into the process of cure for epoxy resin.

Traditional sparse image models treat color image pixel as a scalar, which represents color channels separately or concatenate color channels as a monochrome image. In this paper, we propose a vector sparse representation model for color images using quaternion matrix analysis. As a new tool for color image representation, its potential applications in several image-processing tasks are presented, including color image reconstruction, denoising, inpainting, and super-resolution. The proposed model represents the color image as a quaternion matrix, where a quaternion-based dictionary learning algorithm is presented using the K-quaternion singular value decomposition (QSVD) (generalized K-means clustering for QSVD) method. It conducts the sparse basis selection in quaternion space, which uniformly transforms the channel images to an orthogonal color space. In this new color space, it is significant that the inherent color structures can be completely preserved during vector reconstruction. Moreover, the proposed sparse model is more efficient comparing with the current sparse models for image restoration tasks due to lower redundancy between the atoms of different color channels. The experimental results demonstrate that the proposed sparse image model avoids the hue bias issue successfully and shows its potential as a general and powerful tool in color image analysis and processing domain.

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A good distance metric for the input data is crucial in many pattern recognition and machine learning applications. Past studies have demonstrated that learning a metric from labeled samples can significantly improve the performance of classification and clustering algorithms. In this paper, we investigate the problem of learning a distance metric that measures the semantic similarity of input data for regression problems. The particular application we consider is human age estimation. Our guiding principle for learning the distance metric is to preserve the local neighborhoods based on a specially designed distance as well as to maximize the distances between data that are not in the same neighborhood in the semantic space. Without any assumption about the structure and the distribution of the input data, we show that this can be done by using semidefinite programming. Furthermore, the low-level feature space can be mapped to the high-level semantic space by a linear transformation with very low computational cost. Experimental results on the publicly available FG-NET database show that 1) the learned metric correctly discovers the semantic structure of the data even when the amount of training data is small and 2) significant improvement over the traditional Euclidean metric for regression can be obtained using the learned metric. Most importantly, simple regression methods such as k nearest neighbors (kNN), combined with our learned metric, become quite competitive (and sometimes even superior) in terms of accuracy when compared with the state-of-the-art human age estimation approaches.

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