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We present a new approach to localize extensive facial landmarks with a coarse-to-fine convolutional network cascade. Deep convolutional neural networks (DCNN) have been successfully utilized in facial landmark localization for two-fold advantages: 1) geometric constraints among facial points are implicitly utilized; 2) huge amount of training data can be leveraged. However, in the task of extensive facial landmark localization, a large number of facial landmarks (more than 50 points) are required to be located in a unified system, which poses great difficulty in the structure design and training process of traditional convolutional networks. In this paper, we design a four-level convolutional network cascade, which tackles the problem in a coarse-to-fine manner. In our system, each network level is trained to locally refine a subset of facial landmarks generated by previous network levels. In addition, each level predicts explicit geometric constraints (the position and rotation angles of a specific facial component) to rectify the inputs of the current network level. The combination of coarse-to-fine cascade and geometric refinement enables our system to locate extensive facial landmarks (68 points) accurately in the 300-W facial landmark localization challenge.

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This letter proposes a few-shot physics-guided spatial temporal graph convolutional network (FPG-STGCN) to fast solve unit commitment (UC). Firstly, STGCN is tailored to parameterize UC. Then, few-shot physics-guided learning scheme is proposed. It exploits few typical UC solutions yielded via commercial optimizer to escape from local minimum, and leverages the augmented Lagrangian method for constraint satisfaction. To further enable both feasibility and continuous relaxation for integers in learning process, straight-through estimator for Tanh-Sign composition is proposed to fully differentiate the mixed integer solution space. Case study on the IEEE benchmark justifies that, our method bests mainstream learning ways on UC feasibility, and surpasses traditional solver on efficiency.