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In this paper, we propose a novel convolutional neural architecture for facial action unit intensity estimation. While Convolutional Neural Networks (CNNs) have shown great promise in a wide range of computer vision tasks, these achievements have not translated as well to facial expression analysis, with hand crafted features (e.g. the Histogram of Orientated Gradient) still being very competitive. We introduce a novel Edge Convolutional Network (ECN) that is able to capture subtle changes in facial appearance. Our model is able to learn edge-like detectors that can capture subtle wrinkles and facial muscle contours at multiple orientations and frequencies. The core novelty of our ECN model is in its first layer which integrates three main components: an edge filter generator, a receptive gate and a filter rotator. All the components are differentiable and our ECN model is end-to-end trainable and learns the important edge detectors for facial expression analysis. Experiments on two facial action unit datasets show that the proposed ECN outperforms state-of-the-art methods for both AU intensity estimation tasks.