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, haoqifg@andrew.cmu.edu

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