Localization by image retrieval is inexpensive and scalable due to simple mapping and matching techniques. Such localization, however, depends upon the quality of image features often obtained using Contrastive learning frameworks. Most contrastive learning strategies opt for features to distinguish different classes. In the context of localization, however, there is no natural definition of classes. Therefore, images are usually artificially separated into positive and negative classes, with respect to the chosen anchor images, based on some geometric proximity measure. In this paper, we show why such divisions are problematic for learning localization features. We argue that any artificial division based on some proximity measure is undesirable, due to the inherently ambiguous supervision for images near proximity threshold. To this end, we propose a novel technique that uses soft positive/negative assignments of images for contrastive learning, avoiding the aforementioned problem. Our soft assignment makes a gradual distinction between close and far images in both geometric and feature spaces. Experiments on four large-scale benchmark datasets demonstrate the superiority of the proposed soft contrastive learning over the state-of-the-art method for retrieval-based visual localization.

Building on progress in feature representations for image retrieval, image-based localization has seen a surge of research interest. Image-based localization has the advantage of being inexpensive and efficient, often avoiding the use of 3D metric maps altogether. That said, the need to maintain a large amount of reference images as an effective support of localization in a scene, nonetheless calls for them to be organized in a map structure of some kind. The problem of localization often arises as part of a navigation process. We are, therefore, interested in summarizing the reference images as a set of landmarks, which meet the requirements for image-based navigation. A contribution of this paper is to formulate such a set of requirements for the two sub-tasks involved: compact map construction and accurate self localization. These requirements are then exploited for compact map representation and accurate self-localization, using the framework of a network flow problem. During this process, we formulate the map construction and self-localization problems as convex quadratic and second-order cone programs, respectively. We evaluate our methods on publicly available indoor and outdoor datasets, where they outperform existing methods significantly.

In generative modeling, the Wasserstein distance (WD) has emerged as a useful metric to measure the discrepancy between generated and real data distributions. Unfortunately, it is challenging to approximate the WD of high-dimensional distributions. In contrast, the sliced Wasserstein distance (SWD) factorizes high-dimensional distributions into their multiple one-dimensional marginal distributions and is thus easier to approximate. In this paper, we introduce novel approximations of the primal and dual SWD. Instead of using a large number of random projections, as it is done by conventional SWD approximation methods, we propose to approximate SWDs with a small number of parameterized orthogonal projections in an end-to-end deep learning fashion. As concrete applications of our SWD approximations, we design two types of differentiable SWD blocks to equip modern generative frameworks---Auto-Encoders (AE) and Generative Adversarial Networks (GAN). In the experiments, we not only show the superiority of the proposed generative models on standard image synthesis benchmarks, but also demonstrate the state-of-the-art performance on challenging high resolution image and video generation in an unsupervised manner.