3D Gaussian Point Encoders

In this work, we introduce the 3D Gaussian Point Encoder, an explicit per-point embedding built on mixtures of learned 3D Gaussians. This explicit geometric representation for 3D recognition tasks is a departure from widely used implicit representations such as PointNet. However, it is difficult to learn 3D Gaussian encoders in end-to-end fashion with standard optimizers. We develop optimization techniques based on natural gradients and distillation from PointNets to find a Gaussian Basis that can reconstruct PointNet activations. The resulting 3D Gaussian Point Encoders are faster and more parameter efficient than traditional PointNets. As in the 3D reconstruction literature where there has been considerable interest in the move from implicit (e.g., NeRF) to explicit (e.g., Gaussian Splatting) representations, we can take advantage of computational geometry heuristics to accelerate 3D Gaussian Point Encoders further. We extend filtering techniques from 3D Gaussian Splatting to construct encoders that run 2.7 times faster as a comparable accuracy PointNet while using 46% less memory and 88% fewer FLOPs. Furthermore, we demonstrate the effectiveness of 3D Gaussian Point Encoders as a component in Mamba3D, running 1.27 times faster and achieving a reduction in memory and FLOPs by 42% and 54% respectively. 3D Gaussian Point Encoders are lightweight enough to achieve high framerates on CPU-only devices.

3D Convolutional Neural Networks for Dendrite Segmentation Using Fine-Tuning and Hyperparameter Optimization

Dendritic microstructures are ubiquitous in nature and are the primary solidification morphologies in metallic materials. Techniques such as x-ray computed tomography (XCT) have provided new insights into dendritic phase transformation phenomena. However, manual identification of dendritic morphologies in microscopy data can be both labor intensive and potentially ambiguous. The analysis of 3D datasets is particularly challenging due to their large sizes (terabytes) and the presence of artifacts scattered within the imaged volumes. In this study, we trained 3D convolutional neural networks (CNNs) to segment 3D datasets. Three CNN architectures were investigated, including a new 3D version of FCDense. We show that using hyperparameter optimization (HPO) and fine-tuning techniques, both 2D and 3D CNN architectures can be trained to outperform the previous state of the art. The 3D U-Net architecture trained in this study produced the best segmentations according to quantitative metrics (pixel-wise accuracy of 99.84% and a boundary displacement error of 0.58 pixels), while 3D FCDense produced the smoothest boundaries and best segmentations according to visual inspection. The trained 3D CNNs are able to segment entire 852 x 852 x 250 voxel 3D volumes in only ~60 seconds, thus hastening the progress towards a deeper understanding of phase transformation phenomena such as dendritic solidification.