An Improved Method for Restoring the Shape of 3D Point Cloud Surfaces

Introduction

Nowadays, the development of 3D data acquisition techniques can help us obtain the shape of 3D object that is very close to its original. They are used in every fields such as extractive exploration, construction of digital map or digital museum, restoration of cultural heritage, images processing and entertainment (e.g. movies, game technology, simulation, virtual reality, etc.). The high-tech devices like laser or LiDAR scans, exploration geophysics or seismic reflection are more and more developing. They can collect data very fast and become much easier to get the 3D representation of a real object. After pre-processing the data, they are 3D points and exported into a 3D grid for the next modeling step.

With the support of computer software, the 3D data points can be reconstructed to obtain their original shapes. However, depends on materials of the objects, the used techniques, the environment, distance from measured devices to the objects, etc., the obtained results may be different. They are normally generating the problems of irregular 3D point sets or lack of information in some areas on the surface. Besides, the missing data points may also come from occlusion, reflectance, angle of capturing and scanning, etc. That are all problems leading to the holes on the surface.

Therefore, the studied methods for holes filling on the surfaces are important to the final expectation of the reconstructing step. The existing methods for filling the hole on the surface of 3D objects have been studied and published in recent years (Nguyen, 2015; Pérez, 2016; Chunhong, 2017). These methods are mostly processed on a triangular mesh (or called mesh repairing), on both open and closed surfaces. At first, the holes on a triangular mesh are determined based on boundary triangles of the holes. The holes filling step is then implemented by computing inserted triangles starting from the boundary triangles to the inside of the hole. At the end, the holes are repaired to adapt the local curvature of the surface. In practice, processing directly on the 3D point clouds is still a challenge to the researchers.

The researched work in this article is a new proposed method for restoring the shape of the surface of 3D point clouds. They are surfaces of oil reservoir, very large, extracted from seismic data, organized in the 3D volume and defined by a method of Philippe (2009). We process directly these surfaces without triangulation step. For each surface, after extracting its exterior boundary (Nguyen, 2012), we determine the hole boundary inside. In order to fill the holes, we compute Bezier curves that create surface patches of the holes. After that, we refine the holes based on computation of a tangent plane for each inserted point on the surface patch. This process is repeated on each ring of the surface patch, from the first to the next one toward the inside of the hole. Each inserted point is therefore adjusted its coordinate to get along with local curvature of the surface. Comparing to the existing methods, our contribution in this method is filling the holes directly on a surface of 3D point clouds. This is also the novelty of the proposed method to obtain a reconstructed surface that is watertight and similar to its original shape.

The rest of paper is organized as follows: in the section of literature review, we study the methods for reconstructing the surface of 3D objects and triangular meshes by filling the holes. The proposed method is detailed in the next section. After that, we present our implementation and obtained results. We discuss, compare and evaluate our method to the existing methods before the last section of our conclusion.