14 DAILY CVPR Wednesday Highlight Presentation directly sample articulated rotations in the articulated SO(3) space, which we call a product manifold of Riemannian quaternions.” Additionally, this work introduces RDFGrad, an innovative technique that streamlines the gradient descent process during inference. For Pose-NDF, after a normal gradient descent, you have to reproject the resulting pose onto the quaternion space because the quaternion should also be uniform, which slows down the projection process. In contrast, NRDF extends the original gradient descent procedure onto the Riemannian manifold during inference time projection. “Given a noisy pose, we obtain the gradient direction returned by the network propagation, which is the Euclidean gradient, and we iteratively project it onto the tangent space of a given pose and directly work along the geodesic” he explains. “This is crucial and makes the process faster.” Yannan tells us the breakthrough came with the realization that optimizing the training data distribution is crucial for distance fields. Finding this, out of all possible explanations for Pose-NDF limitations, was one of the biggest challenges and took several months of intense investigation. For NRDF, no network architecture was modified compared with PoseNDF.
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