A structure from motion inequality

We state an elementary inequality for the structure from motion problem for m cameras and n points. This structure from motion inequality relates space dimension, camera parameter dimension, the number of cameras and number points and global symmetry properties and provides a rigorous criterion for which reconstruction is not possible with probability 1. Mathematically the inequality is based on Frobenius theorem which is a geometric incarnation of the fundamental theorem of linear algebra. The paper also provides a general mathematical formalism for the structure from motion problem. It includes the situation the points can move while the camera takes the pictures.Comment: 15 pages, 22 figure

Non-Rigid Structure from Motion for Complex Motion

Recovering deformable 3D motion from temporal 2D point tracks in a monocular video is an open problem with many everyday applications throughout science and industry, or the new augmented reality. Recently, several techniques have been proposed to deal the problem called Non-Rigid Structure from Motion (NRSfM), however, they can exhibit poor reconstruction performance on complex motion. In this project, we will analyze these situations for primitive human actions such as walk, run, sit, jump, etc. on different scenarios, reviewing first the current techniques to finally present our novel method. This approach is able to model complex motion into a union of subspaces, rather than the summation occurring in standard low-rank shape methods, allowing better reconstruction accuracy. Experiments in a wide range of sequences and types of motion illustrate the benefits of this new approac

Learning 3D Human Pose from Structure and Motion

3D human pose estimation from a single image is a challenging problem, especially for in-the-wild settings due to the lack of 3D annotated data. We propose two anatomically inspired loss functions and use them with a weakly-supervised learning framework to jointly learn from large-scale in-the-wild 2D and indoor/synthetic 3D data. We also present a simple temporal network that exploits temporal and structural cues present in predicted pose sequences to temporally harmonize the pose estimations. We carefully analyze the proposed contributions through loss surface visualizations and sensitivity analysis to facilitate deeper understanding of their working mechanism. Our complete pipeline improves the state-of-the-art by 11.8% and 12% on Human3.6M and MPI-INF-3DHP, respectively, and runs at 30 FPS on a commodity graphics card.Comment: ECCV 2018. Project page: https://www.cse.iitb.ac.in/~rdabral/3DPose

Seeing Tree Structure from Vibration

Humans recognize object structure from both their appearance and motion; often, motion helps to resolve ambiguities in object structure that arise when we observe object appearance only. There are particular scenarios, however, where neither appearance nor spatial-temporal motion signals are informative: occluding twigs may look connected and have almost identical movements, though they belong to different, possibly disconnected branches. We propose to tackle this problem through spectrum analysis of motion signals, because vibrations of disconnected branches, though visually similar, often have distinctive natural frequencies. We propose a novel formulation of tree structure based on a physics-based link model, and validate its effectiveness by theoretical analysis, numerical simulation, and empirical experiments. With this formulation, we use nonparametric Bayesian inference to reconstruct tree structure from both spectral vibration signals and appearance cues. Our model performs well in recognizing hierarchical tree structure from real-world videos of trees and vessels.Comment: ECCV 2018. The first two authors contributed equally to this work. Project page: http://tree.csail.mit.edu