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Research Paper#Mathematics (Harmonic Analysis)🔬 ResearchAnalyzed: Jan 3, 2026 06:35

Proof of Fourier Extension Conjecture for Paraboloid

Published:Dec 31, 2025 17:36
1 min read
ArXiv

Analysis

This paper provides a proof of the Fourier extension conjecture for the paraboloid in dimensions greater than 2. The authors leverage a decomposition technique and trilinear equivalences to tackle the problem. The core of the proof involves converting a complex exponential sum into an oscillatory integral, enabling localization on the Fourier side. The paper extends the argument to higher dimensions using bilinear analogues.
Reference

“The trilinear equivalence only requires an averaging over grids, which converts a difficult exponential sum into an oscillatory integral with periodic amplitude.”

PermalinkArXiv
Research#Computer Vision📝 BlogAnalyzed: Dec 29, 2025 08:29

Semantic Segmentation of 3D Point Clouds with Lyne Tchapmi - TWiML Talk #123

Published:Mar 29, 2018 16:11
1 min read
Practical AI

Analysis

This article summarizes a podcast episode discussing semantic segmentation of 3D point clouds. The guest, Lyne Tchapmi, a PhD student, presents her research on SEGCloud, a framework for 3D point-level segmentation. The conversation covers the fundamentals of semantic segmentation, including sensor data, 2D vs. 3D data representations, and automated class identification. The discussion also delves into the specifics of obtaining fine-grained point labeling and the conversion from point clouds to voxels. The article provides a high-level overview of the research and its key aspects, making it accessible to a broad audience interested in AI and computer vision.
Reference

“SEGCloud is an end-to-end framework that performs 3D point-level segmentation combining the advantages of neural networks, trilinear interpolation and fully connected conditional random fields.”

PermalinkPractical AI