![]() ![]() ![]() In this paper, we exploit tools from random matrix theory to make a *precise* characterization of the Hessian eigenspectra for a broad family of nonlinear models that extends the classical generalized linear models, without relying on strong simplifying assumptions used previously. This leads to the question of how relevant the conclusions of such analyses are for realistic nonlinear models. When nonlinear models and non-convex problems are considered, strong simplifying assumptions are often made to make Hessian spectral analysis more tractable. Given an optimization problem, the Hessian matrix and its eigenspectrum can be used in many ways, ranging from designing more efficient second-order algorithms to performing model analysis and regression diagnostics. Furthermore, switching shape and appearance between scenes is possible due to the disentanglement of the two. ![]() Accurate sampling is important to provide a precise coupling of geometry and radiance and (iii) it allows efficient unsupervised disentanglement of shape and appearance in volume rendering.Īpplying this new density representation to challenging scene multiview datasets produced high quality geometry reconstructions, outperforming relevant baselines. This simple density representation has three benefits: (i) it provides a useful inductive bias to the geometry learned in the neural volume rendering process (ii) it facilitates a bound on the opacity approximation error, leading to an accurate sampling of the viewing ray. In more detail, we define the volume density function as Laplace's cumulative distribution function (CDF) applied to a signed distance function (SDF) representation. This is in contrast to previous work modeling the geometry as a function of the volume density. We achieve that by modeling the volume density as a function of the geometry. ![]() The goal of this paper is to improve geometry representation and reconstruction in neural volume rendering. Furthermore, the geometry itself was extracted using an arbitrary level set of the density function leading to a noisy, often low fidelity reconstruction. So far, the geometry learned by neural volume rendering techniques was modeled using a generic density function. Neural volume rendering became increasingly popular recently due to its success in synthesizing novel views of a scene from a sparse set of input images. ![]()
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December 2022
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