3-D Reconstruction of Three Views Based on Manifold Study - Advances in Image and Graphics Technologies - page 181

3-D Reconstruction of Three Views Based on Manifold
Study

Li Cong 1 , Zhao Hongrui 1 , Fu Gang 1 , and Peng Xingang 2

1 Institute of Geomatics, Department of Civil engineering, Tsinghua University, Beijing, China
2 College of Geoscience and Surveying Engineering, China University of Mining & Technology,
Beijing, China

Abstract. Obtaining 3-D reconstruction directly and expediently for the real
world has became a hot topic in many fields. A 3-D reconstruction method of
three views based on manifold study is proposed. Firstly, the fundamental matrix
is estimated by adjacent view and optimized under three views constraint. Then
3-D point cloud is reconstructed after getting the projection matrixes of views.
Further more, benefitting from minimum spanning tree, outliers are almost
excluded. To increase point cloud's density, the optimized 3-D point cloud is
interpolated based on Radial Basis Function. Afterwards, the dense point cloud is
mapped to two dimensional plane using manifold study algorithm, and then
divided into plane Delaunay triangle nets. Completing that, the topological
relations of points are mapped back to 3-D space and 3-D reconstruction is
realized. Many experiments show the method proposed in paper can achieve 3-D
reconstruction for three views with quite good results.

Keywords: Manifold study, three views, 3-D reconstruction, fundamental
matrix, minimum spanning tree.

1 Introduction

3-D reconstruction is a fundamental issue in the fields of computer vision and
photogrammetry. Approaches based on image sequences can directly and quickly
reconstruct for the real world just rely on epipolar geometry of adjacent view. Due to its
low cost and immediately color acquisition power, image-based 3-D reconstruction has
broad application prospects and becomes a hot topic in many fields.
The fundamental matrix is the algebraic representation of epipolar geometry, and it's
the only geometry information obtaining from un-calibrated image sequences. So
accurate computation of fundamental matrix is an necessary and important step to
realize 3-D reconstruction. Fundamental matrix is commonly calculated by matching
points between views, and its methods are mainly divided into 3 categories: linear
algorithms, non-linear algorithms and robust algorithms[1]. Because of the ability of
distinguishing mismatches, robust algorithms could calculate correct fundamental
matrix by selecting inliers set. Consequently, a vast amount of research effort has been
dedicated to robust methods. However, not only the traditional robust methods[2] but
also the advanced methods[3,4,5,6,7,]based on them just are adopted with the constrain