Geometric Algebra Planes: Convex Implicit Neural Volumes

Authors: Irmak Sivgin, Sara Fridovich-Keil, Gordon Wetzstein, Mert Pilanci

ICML 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental We demonstrate that this matrix decomposition is expressive for natural images, outperforming the classic low-rank plus sparse approximation. In 3D, GA-Planes models exhibit competitive expressiveness, model size, and optimizability across tasks such as radiance field reconstruction, 3D segmentation, and video segmentation.
Researcher Affiliation Academia 1Department of Electrical Engineering, Stanford University, CA, USA 2School of Electrical & Computer Engineering, Georgia Institute of Technology, GA, USA. Correspondence to: Mert Pilanci <EMAIL>.
Pseudocode No The paper describes methods and formulations in regular paragraph text and mathematical equations (e.g., Section 3.1, 3.2, 3.3) but does not include any explicitly labeled or structured pseudocode or algorithm blocks.
Open Source Code Yes Code is available at https://github.com/sivginirmak/ Geometric-Algebra-Planes.
Open Datasets Yes Our experiments for the radiance field reconstruction task are built with Ne RFStudio (Tancik et al., 2023) and use all 8 scenes from Ne RF-Blender (Mildenhall et al., 2020). We lift these 2D segmentation masks to 3D. ... Our dataset preparation pipeline uses the skateboarding video and preprocessing steps described at Labelbox.com, which involves first extracting a bounding box with YOLOv8 (Jocher et al., 2023) and then segmenting the skateboarder with SAM (Kirillov et al., 2023). ... with a simple experiment, in which we approximate a grayscale image (the astronaut image from Sci Py).
Dataset Splits Yes Our video segmentation task is similar to volume segmentation with 3D supervision: here the dimensions are x, y, t rather than x, y, z, and the supervision is performed directly in 3D using segmentation masks for a subset of the video frames (every third frame is held out for testing).
Hardware Specification No The paper does not provide specific hardware details (e.g., GPU models, CPU types, or memory amounts) used for running the experiments. It generally discusses model size and memory requirements.
Software Dependencies No The paper mentions several tools used, such as Ne RFStudio (Tancik et al., 2023), YOLOv8 (Jocher et al., 2023), and SAM (Kirillov et al., 2023). However, it does not provide specific version numbers for software libraries or environments beyond the mentioned tools, which are more citations than specific dependency versions for reproducibility.
Experiment Setup Yes In Figure 6 we compare test intersection-over-union (Io U) curves for very small models for our video fitting task (hidden dimension 4 in the decoder MLP, and feature dimensions [d1, d2, d3] = [4, 4, 2] and resolutions [r1, r2, r3] = [32, 32, 16] for line, plane, and volume features, respectively). We repeat optimization with 10 different random seeds used to initialize the optimizable parameters... (Appendix A.6.2) GA-Planes model uses feature dimensions [d1, d2, d3] = [36, 24, 8] (with ) or [d1, d2, d3] = [25, 25, 8] (with ) and resolutions [r1, r2, r3] = [128, 32, 24]. (Appendix A.6.3) GA-Planes model uses feature dimensions [d1, d2, d3] = [32, 16, 8] and resolutions [r1, r2, r3] = [128, 128, 64].