Essay About Yuz4 Andrew Id And Fundamental Matrix

3d Reconstruction
Math Fundamentals for Robotics Project Report
Yu Zhang Haoqi Fan
Andrew ID: yuz4 Andrew ID: haoqif
Robotics Institute, School of Computer Science
Carnegie Mellon University
Pittsburgh, PA 15213
fyuz4, [email protected]
Abstract
In this project, we explored and implemented a structure from motion algorithm
to reconstruct 3D structure from a pair of 2D images. The input stereo image
contains almost same scene but taken from a slightly different perspective. After
obtaining sufficient number of corresponding points of the two input images,
we computed fundamental matrix using seven point algorithm and eight point
algorithm. To enhance the robustness of the algorithm, we also use RANSAC
algorithm to remove the noise of corresponding points. After obtaining the fundamental
matrix as well as intrinsic and extrinsic matrix, we use dense sampling
strategy to get new sample points. Here, epipolar constraints are used to find corresponding
points of the corresponding image. Then, we use least square method
during the triangulation process and extract global 3D points from two camera 2D
points. Finally, we visualize the cloud points. The result shows that stereo vision
provides enough information to reconstruct 3D structure.
1 Introduction
Nowadays, there are a lot of ideas and techniques for obtaining information about the geometry
of 3D scenes from 2D images, which is called Structure from motion (SfM). SfM is defined as the
process of estimating three-dimensional structures from two-dimensional image. It is able to recover
3D structure from the projected 2D motion field of a moving object or scene.
Figure 1: Structure from motion standard setting
Several simplifying assumptions are made to the general problem of 3D models from 2D imagery
to formulate the Structure from Motion task. In a standard SfM setup as shown in Fig. 1 where a
camera is viewing a scene. One key