Computer vision systems in real-world applications need to be robust to partial occlusion while also being explainable. In this work, we show that black-box deep convolutional neural networks (DCNNs) have only limited robustness to partial occlusion. We overcome these limitations by unifying DCNNs with part-based models into Compositional Convolutional Neural Networks (CompositionalNets) - an interpretable deep architecture with innate robustness to partial occlusion. Specifically, we propose to replace the fully connected classification head of DCNNs with a differentiable compositional model that can be trained end-to-end. The structure of the compositional model enables CompositionalNets to decompose images into objects and context, as well as to further decompose object representations in terms of individual parts and the objects' pose. The generative nature of our compositional model enables it to localize occluders and to recognize objects based on their non-occluded parts. We conduct extensive experiments in terms of image classification and object detection on images of artificially occluded objects from the PASCAL3D+ and ImageNet dataset, and real images of partially occluded vehicles from the MS-COCO dataset. Our experiments show that CompositionalNets made from several popular DCNN backbones (VGG-16, ResNet50, ResNext) improve by a large margin over their non-compositional counterparts at classifying and detecting partially occluded objects. Furthermore, they can localize occluders accurately despite being trained with class-level supervision only. Finally, we demonstrate that CompositionalNets provide human interpretable predictions as their individual components can be understood as detecting parts and estimating an objects' viewpoint.
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