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We present an approach to solving hard geometric optimization problems in the RANSAC framework. The hard minimal problems arise from relaxing the original geometric optimization problem into a minimal problem with many spurious solutions. Our approach avoids computing large numbers of spurious solutions. We design a learning strategy for selecting a starting problem-solution pair that can be numerically continued to the problem and the solution of interest. We demonstrate our approach by developing a RANSAC solver for the problem of computing the relative pose of three calibrated cameras, via a minimal relaxation using four points in each view. On average, we can solve a single problem in under 70 microseconds. We also benchmark and study our engineering choices on the very familiar problem of computing the relative pose of two calibrated cameras, via the minimal case of five points in two views.
Visual vibrometry is a highly useful tool for remote capture of audio, as well as the physical properties of materials, human heart rate, and more. While visually-observable vibrations can be captured directly with a high-speed camera, minute imperceptible object vibrations can be optically amplified by imaging the displacement of a speckle pattern, created by shining a laser beam on the vibrating surface. In this paper, we propose a novel method for sensing vibrations at high speeds (up to 63kHz), for multiple scene sources at once, using sensors rated for only 130Hz operation. Our method relies on simultaneously capturing the scene with two cameras equipped with rolling and global shutter sensors, respectively. The rolling shutter camera captures distorted speckle images that encode the highspeed object vibrations. The global shutter camera captures undistorted reference images of the speckle pattern, helping to decode the source vibrations. We demonstrate our method by capturing vibration caused by audio sources (e.g. speakers, human voice, and musical instruments) and analyzing the vibration modes of a tuning fork.
Locating 3D objects from a single RGB image via Perspective-n-Points (PnP) is a long-standing problem in computer vision. Driven by end-to-end deep learning, recent studies suggest interpreting PnP as a differentiable layer, so that 2D-3D point correspondences can be partly learned by backpropagating the gradient w.r.t. object pose. Yet, learning the entire set of unrestricted 2D-3D points from scratch fails to converge with existing approaches, since the deterministic pose is inherently non-differentiable. In this paper, we propose the EPro-PnP, a probabilistic PnP layer for general end-to-end pose estimation, which outputs a distribution of pose on the SE(3) manifold, essentially bringing categorical Softmax to the continuous domain. The 2D-3D coordinates and corresponding weights are treated as intermediate variables learned by minimizing the KL divergence between the predicted and target pose distribution. The underlying principle unifies the existing approaches and resembles the attention mechanism. EPro-PnP significantly outperforms competitive baselines, closing the gap between PnP-based method and the task-specific leaders on the LineMOD 6DoF pose estimation and nuScenes 3D object detection benchmarks.
Neural Radiance Fields (NeRF) is a popular view synthesis technique that represents a scene as a continuous volumetric function, parameterized by multilayer perceptrons that provide the volume density and view-dependent emitted radiance at each location. While NeRF-based techniques excel at representing fine geometric structures with smoothly varying view-dependent appearance, they often fail to accurately capture and reproduce the appearance of glossy surfaces. We address this limitation by introducing Ref-NeRF, which replaces NeRF's parameterization of view-dependent outgoing radiance with a representation of reflected radiance and structures this function using a collection of spatially-varying scene properties. We show that together with a regularizer on normal vectors, our model significantly improves the realism and accuracy of specular reflections. Furthermore, we show that our model's internal representation of outgoing radiance is interpretable and useful for scene editing.