Numerical Computation of Weil-Peterson Geodesics in the Universal Teichm\"uller Space

We propose an optimization algorithm for computing geodesics on the universal Teichm\"uller space T(1) in the Weil-Petersson ($W P$) metric. Another realization for T(1) is the space of planar shapes, modulo translation and scale, and thus our algorithm addresses a fundamental problem in computer vision: compute the distance between two given shapes. The identification of smooth shapes with elements on T(1) allows us to represent a shape as a diffeomorphism on $S^1$. Then given two diffeomorphisms on $S^1$ (i.e., two shapes we want connect with a flow), we formulate a discretized $W P$ energy and the resulting problem is a boundary-value minimization problem. We numerically solve this problem, providing several examples of geodesic flow on the space of shapes, and verifying mathematical properties of T(1). Our algorithm is more general than the application here in the sense that it can be used to compute geodesics on any other Riemannian manifold.Comment: 21 pages, 11 figure

SiLK -- Simple Learned Keypoints

Keypoint detection & descriptors are foundational tech-nologies for computer vision tasks like image matching, 3D reconstruction and visual odometry. Hand-engineered methods like Harris corners, SIFT, and HOG descriptors have been used for decades; more recently, there has been a trend to introduce learning in an attempt to improve keypoint detectors. On inspection however, the results are difficult to interpret; recent learning-based methods employ a vast diversity of experimental setups and design choices: empirical results are often reported using different backbones, protocols, datasets, types of supervisions or tasks. Since these differences are often coupled together, it raises a natural question on what makes a good learned keypoint detector. In this work, we revisit the design of existing keypoint detectors by deconstructing their methodologies and identifying the key components. We re-design each component from first-principle and propose Simple Learned Keypoints (SiLK) that is fully-differentiable, lightweight, and flexible. Despite its simplicity, SiLK advances new state-of-the-art on Detection Repeatability and Homography Estimation tasks on HPatches and 3D Point-Cloud Registration task on ScanNet, and achieves competitive performance to state-of-the-art on camera pose estimation in 2022 Image Matching Challenge and ScanNet

NOVIS: A Case for End-to-End Near-Online Video Instance Segmentation

Until recently, the Video Instance Segmentation (VIS) community operated under the common belief that offline methods are generally superior to a frame by frame online processing. However, the recent success of online methods questions this belief, in particular, for challenging and long video sequences. We understand this work as a rebuttal of those recent observations and an appeal to the community to focus on dedicated near-online VIS approaches. To support our argument, we present a detailed analysis on different processing paradigms and the new end-to-end trainable NOVIS (Near-Online Video Instance Segmentation) method. Our transformer-based model directly predicts spatio-temporal mask volumes for clips of frames and performs instance tracking between clips via overlap embeddings. NOVIS represents the first near-online VIS approach which avoids any handcrafted tracking heuristics. We outperform all existing VIS methods by large margins and provide new state-of-the-art results on both YouTube-VIS (2019/2021) and the OVIS benchmarks