Jingmao Cui

Jingmao Cui, Donglai Tao, Linmi Tao et al.

The prevailing approach to embedding prior knowledge within convolutional layers typically includes the design of steerable kernels or their modulation using designated kernel banks. In this study, we introduce the Analytic Convolutional Layer (ACL), an innovative model-driven convolutional layer, which is a mosaic of analytical convolution kernels (ACKs) and traditional convolution kernels. ACKs are characterized by mathematical functions governed by analytic kernel parameters (AKPs) learned in training process. Learnable AKPs permit the adaptive update of incorporated knowledge to align with the features representation of data. Our extensive experiments demonstrate that the ACLs not only have a remarkable capacity for feature representation with a reduced number of parameters but also attain increased reliability through the analytical formulation of ACKs. Furthermore, ACLs offer a means for neural network interpretation, thereby paving the way for the intrinsic interpretability of neural network. The source code will be published in company with the paper.

Linmi Tao, Ruiyang Liu, Donglai Tao et al.

Numerical difference computation is one of the cores and indispensable in the modern digital era. Tao general difference (TGD) is a novel theory and approach to difference computation for discrete sequences and arrays in multidimensional space. Built on the solid theoretical foundation of the general difference in a finite interval, the TGD operators demonstrate exceptional signal processing capabilities in real-world applications. A novel smoothness property of a sequence is defined on the first- and second TGD. This property is used to denoise one-dimensional signals, where the noise is the non-smooth points in the sequence. Meanwhile, the center of the gradient in a finite interval can be accurately location via TGD calculation. This solves a traditional challenge in computer vision, which is the precise localization of image edges with noise robustness. Furthermore, the power of TGD operators extends to spatio-temporal edge detection in three-dimensional arrays, enabling the identification of kinetic edges in video data. These diverse applications highlight the properties of TGD in discrete domain and the significant promise of TGD for the computation across signal processing, image analysis, and video analytic.