Generative adversarial nets (GANs) and variational auto-encoders have significantly improved our distribution modeling capabilities, showing promise for dataset augmentation, image-to-image translation and feature learning. However, to model high-dimensional distributions, sequential training and stacked architectures are common, increasing the number of tunable hyper-parameters as well as the training time. Nonetheless, the sample complexity of the distance metrics remains one of the factors affecting GAN training. We first show that the recently proposed sliced Wasserstein distance has compelling sample complexity properties when compared to the Wasserstein distance. To further improve the sliced Wasserstein distance we then analyze its 'projection complexity' and develop the max-sliced Wasserstein distance which enjoys compelling sample complexity while reducing projection complexity, albeit necessitating a max estimation. We finally illustrate that the proposed distance trains GANs on high-dimensional images up to a resolution of 256x256 easily.

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With the aim to improve the performance of feature matching, we present an unsupervised approach for adaptive description selection in the space of homographies. Inspired by the observation that the homographies of correct feature correspondences vary smoothly along the spatial domain, our approach stands on the unsupervised nature of feature matching, and can choose a good descriptor locally for matching each feature point, instead of using one global descriptor. To this end, the homography space serves as the domain for selecting various heterogeneous descriptors. Correspondences obtained by any descriptors are considered as points in the space, and their geometric coherence and spatial continuity are measured via computing the geodesic distances. In this way, mutual verification across different descriptors is allowed, and correct correspondences will be highlighted with a high degree of consistency short geodesic distances here. It follows that one-class SVM can be applied to identifying these correct correspondences, and achieves adaptive descriptor selection. The proposed approach is comprehensively compared with the state-of-the-art approaches, and evaluated on five benchmarks of image matching. The promising results manifest its effectiveness.

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