(The talk will be given in English)

Speaker:     Dr. Yoni Kasten

                        NVIDIA Research, Tel Aviv

Monday, January 20^th, 2025

12:00 - 13:00

Algebraic Approaches and Deep Neural Models for 3D Scene Reconstruction and Camera Pose Estimation in Static and Dynamic Environments

Abstract

This talk will explore advances in 3D scene reconstruction, focusing on approaches to estimate camera poses and scene structures in challenging multiview and dynamic content scenarios. First, I will outline foundational aspects of my earlier work, where we characterized the algebraic structure of fundamental and essential matrices in multiview settings and developed deep learning methods for joint recovery of camera parameters and sparse 3D scene structures. The main part of the talk introduces TracksTo4D (NeurIPS 2024), a novel, efficient method for reconstructing dynamic 3D structures and camera motion from casual videos. TracksTo4D leverages a dedicated encoder, trained in an unsupervised way on a dataset of casual videos, that uses 2D point tracks as input to infer dynamic 3D structures and camera motion. Our architecture takes into account symmetries in the problem, enforces the reconstruction to be of low rank, and models both static and dynamic scene components. Our model demonstrates strong generalization to unseen videos from new categories, achieving accurate 3D reconstruction and camera localization through a single feed-forward pass while drastically reducing running times.

Short Bio

Yoni Kasten is a Senior Research Scientist at NVIDIA Research in Tel Aviv, in Prof. Gal Chechik’s team. His research in 3D computer vision focuses on algebraic characterizations of multi-camera systems and deep neural models for surface reconstruction, dynamic scene modeling, and 4D scene reconstruction. Yoni earned his PhD from the Weizmann Institute, where his work on structure from motion estimation using algebraic characterizations, supervised by Prof. Ronen Basri, received the John F. Kennedy Prize for Outstanding Doctoral Research. He also completed his M.Sc. in Computer Science at the Hebrew University of Jerusalem, under the supervision of Prof. Shmuel Peleg and Prof. Michael Werman.

השתתפות בסמינר תיתן קרדיט שמיעה לתלמידי תואר שני ושלישי = עפ"י רישום שם מלא + מספר ת.ז. בטופס הנוכחות שיועבר באולם במהלך הסמינר

Lecture by Tzach Zemer

12:20

 Recruiting team and ice cream yogurt will be waiting for you

11:00-14:00

(The talk will be given in English)

Speaker:     Dr. Elad Romanov

                    Department of Statistics, Stanford

Sunday, January 19^th, 2025

15:00 - 14:00

On Principal Component Regression in High Dimension 

Abstract

Principal component regression (PCR) is a classical two-step approach to linear regression, where one first reduces the data dimension by projecting onto its leading principal components, and then performs ordinary least squares regression. We study PCR in an asymptotic high-dimensional regression setting, where the number of data points is proportional to the dimension. Our main deliverables are asymptotically exact limiting formulas for the estimation and prediction risks, which depend in a nuanced way on the eigenvalues of the population covariance, the alignment between the population principal components and the true signal, and the number of selected components.

A key challenge in the high-dimensional regime is that the sample covariance matrix is an inconsistent estimate of its population counterpart, and thus sample principal components may fail to capture potential latent low-dimensional structure in the data. We demonstrate this point through several case studies, including that of a spiked covariance matrix.

The analysis of (random design) linear regression in high dimension typically builds on powerful results from random matrix theory, such as the Marchenko–Pastur law and deterministic equivalents for the resolvent of a sample covariance matrix. However, these standard tools alone are not sufficient for analyzing the prediction risk of PCR. To that end, we leverage and develop somewhat less standard techniques, which, to our knowledge, have not seen wide use in the statistics literature to date: multi-resolvent traces and their associated eigenvector overlap measures.

Based on joint work with Alden Green (Stanford).

https://arxiv.org/abs/2405.11676

Short Bio

Elad Romanov is a postdoctoral researcher in the Department of Statistics, Stanford, where he is hosted by Prof. David Donoho. Prior to that, he completed his PhD in the School of Computer Science, the Hebrew University of Jerusalem, where he was advised by Profs. Or Ordentlich and Matan Gavish. His research interests broadly span high-dimensional statistics, information theory and signal processing, and the mathematics of data science.

השתתפות בסמינר תיתן קרדיט שמיעה לתלמידי תואר שני ושלישי = עפ"י רישום שם מלא + מספר ת.ז. בטופס הנוכחות שיועבר באולם במהלך הסמינר

ٍاخ

  -סמינר זה יחשב כסמינר שמיעה לתלמידי תואר שני ושלישי-  This Seminar Is Considered A Hearing Seminar For Msc/Phd Students