Orthogonal decomposition network for pixel-wise binary classification

The weight sharing scheme and spatial pooling operations in Convolutional Neural Networks (CNNs) introduce semantic correlation to neighboring pixels on feature maps and therefore deteriorate their pixel-wise classification performance. In this paper, we implement an Orthogonal Decomposition Unit (ODU) that transforms a convolutional feature map into orthogonal bases targeting at de-correlating neighboring pixels on convolutional features. In theory, complete orthogonal decomposition produces orthogonal bases which can perfectly reconstruct any binary mask (ground-truth). In practice, we further design incomplete orthogonal decomposition focusing on de-correlating local patches which balances the reconstruction performance and computational cost. Fully Convolutional Networks (FCNs) implemented with ODUs, referred to as Orthogonal Decomposition Networks (ODNs), learn de-correlated and complementary convolutional features and fuse such features in a pixel-wise selective manner. Over pixel-wise binary classification tasks for two-dimensional image processing, specifically skeleton detection, edge detection, and saliency detection, and one-dimensional keypoint detection, specifically S-wave arrival time detection for earthquake localization, ODNs consistently improves the state-of-the-arts with significant margins.