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Coordinate-based neural networks parameterizing implicit surfaces have emerged as efficient representations of geometry. They effectively act as parametric level sets with the zero-level set defining the surface of interest. We present a framework that allows applying deformation operations defined for triangle meshes onto such implicit surfaces. Several of these operations can be viewed as energy-minimization problems that induce an instantaneous flow field on the explicit surface. Our method uses the flow field to deform parametric implicit surfaces by extending the classical theory of level sets. We also derive a consolidated view for existing methods on differentiable surface extraction and rendering, by formalizing connections to the level-set theory. We show that these methods drift from the theory and that our approach exhibits improvements for applications like surface smoothing, mean-curvature flow, inverse rendering and user-defined editing on implicit geometry.
We present Pose-NDF, a continuous model for plausible human poses based on neural distance fields (NDFs). Pose or motion priors are important for generating realistic new poses and for reconstructing accurate poses from noisy or partial observations. Pose-NDF learns a manifold of plausible poses as the zero level set of a neural implicit function, extending the idea of modelling implicit surfaces in 3D to the high dimensional domain SO(3)K, where a human pose is defined by a single data point, represented by K quaternions. The resulting high dimensional implicit function can be differentiated with respect to the input poses and thus can be used to project arbitrary poses onto the manifold by using gradient descent on the set of 3-dimensional hyperspheres. In contrast to previous VAE-based human pose priors, which transform the pose space into a Gaussian distribution, we model the actual pose manifold, preserving the distances between poses. We demonstrate that this approach and thus, Pose-NDF, outperforms existing state-of-the-art methods as a prior in various downstream tasks, ranging from denoising real world human mocap data, pose recovery from occluded data to 3D pose reconstruction from images. Furthermore, we show that it can be used to generate more diverse poses by random sampling and projection than VAE based methods. We will release our code and pre-trained model for further research.
Comparing the functional behavior of neural network models, whether it is a single network over time or two (or more networks) during or post-training, is an essential step in understanding what they are learning (and what they are not), and for identifying strategies for regularization or efficiency improvements. Despite recent progress, e.g., comparing vision transformers to CNNs, systematic comparison of function, especially across different networks, remains difficult and is often carried out layer by layer. Approaches such as canonical correlation analysis (CCA) are applicable in principle, but have been sparingly used so far. In this paper, we revisit a (less widely known) from statistics, called distance correlation (and its partial variant), designed to evaluate correlation between feature spaces of different dimensions. We describe the steps necessary to carry out its deployment for large scale models -- this opens the door to a surprising array of applications ranging from conditioning one deep model w.r.t. another, learning disentangled representations as well as optimizing diverse models that would directly be more robust to adversarial attacks. Our experiments suggest a versatile regularizer (or constraint) with many advantages, which avoids some of the common difficulties one faces in such analyses.