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Solving Sylvester equation is a common algebraic problem in mathematics and control theory. Different from the traditional fixed-parameter recurrent neural networks, such as gradient-based recurrent neural networks or Zhang neural networks, a novel varying-parameter recurrent neural network, [called varying-parameter convergent-differential neural network (VP-CDNN)] is proposed in this paper for obtaining the online solution to the time-varying Sylvester equation. With time passing by, this kind of new varying-parameter neural network can achieve super-exponential performance. Computer simulation comparisons between the fixed-parameter neural networks and the proposed VP-CDNN via using different kinds of activation functions demonstrate that the proposed VP-CDNN has better convergence and robustness properties.

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In this paper, we address the problem of indoor semantic segmentation by incorporating the depth information into the convolutional neural network and conditional random field of a neural network architecture. The architecture combines a RGB-D fully convolutional neural network (DFCN) with a depth-sensitive fully-connected conditional random field (DCRF). In the DFCN module, the depth information is incorporated into the early layers using a fusion structure which is followed by several dilated convolution layers for contextual reasoning. Later in the DCRF module, a depth-sensitive fully-connected conditional random field (DCRF) is proposed and combined with the previous DFCN output to refine the preliminary result. Comparative experiments show that the proposed DFCN-DCRF architecture achieves competitive performance compared with state-of-the-art methods.