Geometric Correspondences involve establishing relationships between corresponding geometric elements in two or more images. These geometric elements can include points, lines, curves, or more complex structures. The goal is to identify how these geometric elements transform or relate to each other across images. Geometric correspondences play a vital role in various computer vision applications, enabling the understanding of spatial relationships between objects or scenes captured in different images. Techniques for establishing geometric correspondences contribute to tasks such as image stitching, object recognition, and 3D reconstruction.

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Hierarchical Metric Learning and Matching for 2D and 3D Geometric Correspondences

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Interest point descriptors have fueled progress on almost every problem in computer vision. Recent advances in deep neural networks have enabled task-specific learned descriptors that outperform hand-crafted descriptors on many problems. We demonstrate that commonly used metric learning approaches do not optimally leverage the feature hierarchies learned in a Convolutional Neural Network (CNN), especially when applied to the task of geometric feature matching. While a metric loss applied to the deepest layer of a CNN, is often expected to yield ideal features irrespective of the task, in fact the growing receptive field as well as striding effects cause shallower features to be better at high precision matching tasks. We leverage this insight together with explicit supervision at multiple levels of the feature hierarchy for better regularization, to learn more effective descriptors in the context of geometric matching tasks. Further, we propose to use activation maps at different layers of a CNN, as an effective and principled replacement for the multi-resolution image pyramids often used for matching tasks. We propose concrete CNN architectures employing these ideas and evaluate them on multiple datasets for 2D and 3D geometric matching as well as optical flow, demonstrating state-of-the-art results and generalization across datasets.

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