Elliptically symmetric distributions for directional data of arbitrary dimension

We formulate a class of angular Gaussian distributions that allows different degrees of isotropy for directional random variables of arbitrary dimension. Through a series of novel reparameterization, this distribution family is indexed by parameters with meaningful statistical interpretations that can range over the entire real space of an adequate dimension. The new parameterization greatly simplifies maximum likelihood estimation of all model parameters, which in turn leads to theoretically sound and numerically stable inference procedures to infer key features of the distribution. Byproducts from the likelihood-based inference are used to develop graphical and numerical diagnostic tools for assessing goodness of fit of this distribution in a data application. Simulation study and application to data from a hydrogeology study are used to demonstrate implementation and performance of the inference procedures and diagnostics methods.Comment: 22 pages, 15 figure

PlaneDepth: Plane-Based Self-Supervised Monocular Depth Estimation

Self-supervised monocular depth estimation refers to training a monocular depth estimation (MDE) network using only RGB images to overcome the difficulty of collecting dense ground truth depth. Many previous works addressed this problem using depth classification or depth regression. However, depth classification tends to fall into local minima due to the bilinear interpolation search on the target view. Depth classification overcomes this problem using pre-divided depth bins, but those depth candidates lead to discontinuities in the final depth result, and using the same probability for weighted summation of color and depth is ambiguous. To overcome these limitations, we use some predefined planes that are parallel to the ground, allowing us to automatically segment the ground and predict continuous depth for it. We further model depth as a mixture Laplace distribution, which provides a more certain objective for optimization. Previous works have shown that MDE networks only use the vertical image position of objects to estimate the depth and ignore relative sizes. We address this problem for the first time in both stereo and monocular training using resize cropping data augmentation. Based on our analysis of resize cropping, we combine it with our plane definition and improve our training strategy so that the network could learn the relationship between depth and both the vertical image position and relative size of objects. We further combine the self-distillation stage with post-processing to provide more accurate supervision and save extra time in post-processing. We conduct extensive experiments to demonstrate the effectiveness of our analysis and improvements.Comment: 12 pages, 7 figure

Mip-Splatting: Alias-free 3D Gaussian Splatting

Recently, 3D Gaussian Splatting has demonstrated impressive novel view synthesis results, reaching high fidelity and efficiency. However, strong artifacts can be observed when changing the sampling rate, \eg, by changing focal length or camera distance. We find that the source for this phenomenon can be attributed to the lack of 3D frequency constraints and the usage of a 2D dilation filter. To address this problem, we introduce a 3D smoothing filter which constrains the size of the 3D Gaussian primitives based on the maximal sampling frequency induced by the input views, eliminating high-frequency artifacts when zooming in. Moreover, replacing 2D dilation with a 2D Mip filter, which simulates a 2D box filter, effectively mitigates aliasing and dilation issues. Our evaluation, including scenarios such a training on single-scale images and testing on multiple scales, validates the effectiveness of our approach.Comment: Project page: https://niujinshuchong.github.io/mip-splatting