From a few Accurate 2D Correspondences to 3D Point Clouds

TL;DR

This paper introduces a novel method for 3D reconstruction that uses geodesic features to generate comprehensive point clouds covering entire object surfaces, improving the accuracy and completeness of 3D models.

Contribution

It proposes a new geodesic feature and algorithms for estimating world points and projection matrices, enabling complete surface coverage in 3D reconstruction.

Findings

Closed-form and iterative solutions for world points and projection matrices.

Global optimality when fewer than seven world points and at least five images.

Effective algorithms for point cloud creation from correspondences.

Abstract

Key points, correspondences, projection matrices, point clouds and dense clouds are the skeletons in image-based 3D reconstruction, of which point clouds have the important role in generating a realistic and natural model for a 3D reconstructed object. To achieve a good 3D reconstruction, the point clouds must be almost everywhere in the surface of the object. In this article, with a main purpose to build the point clouds covering the entire surface of the object, we propose a new feature named a geodesic feature or geo-feature. Based on the new geo-feature, if there are several (given) initial world points on the object's surface along with all accurately estimated projection matrices, some new world points on the geodesics connecting any two of these given world points will be reconstructed. Then the regions on the surface bordering by these initial world points will be covered by the point clouds. Thus, if the initial world points are around the surface, the point clouds will cover the entire surface. This article proposes a new method to estimate the world points and projection matrices from their correspondences. This method derives the closed-form and iterative solutions for the world points and projection matrices and proves that when the number of world points is less than seven and the number of images is at least five, the proposed solutions are global optimal. We propose an algorithm named World points from their Correspondences (WPfC) to estimate the world points and projection matrices from their correspondences, and another algorithm named Creating Point Clouds (CrPC) to create the point clouds from the world points and projection matrices given by the first algorithm.