Hole filling of triangular mesh segments using systematic grey prediction

Abstract

Recent advances in reverse engineering technology have made it possible to acquire accurate point information about model surfaces using 3D laser scanners. However, data capture can be reduced by limitations in the scanner structure or characteristics of the scanned objects, resulting in holes in the triangular mesh model and reducing the model’s quality. The current study seeks to fill these holes using software-based calculations and systematic grey prediction, thus preserving the original exterior surface of the reconstructed model. A 3D digital dental model was acquired using a 3D laser scanner, followed by hole detection and surface mending. Due to the simplicity and minimal dataset used in grey theory, a grey prediction system was built to perform prediction-adjustment to preserve the original dental exterior surface.

Introduction

Reverse engineering applications basically involve the direct measurement and reconstruction of the surface information of a solid model using 3D instrumentation. 3D measurement methods can be divided into two categories: contact and non-contact. Contact measurement methods are highly precise but slow, and require contact with the surface of the object, thus limiting their usefulness. Non-contact measurement methods utilize many different sensing techniques to reconstruct the object’s 3D geometry, and are particularly suitable for measuring complex solid models which are difficult to draw. Non-contact methods also have an advantage in that they are faster. The successful adaptation of computer vision techniques in dentistry to supplement missing dental model information would have considerable potential for future medical applications.

Triangular mesh segments have been widely used to represent 3D digital models in computer animations, virtual reality, the reconstruction of human organs from CT images, and so on. All models are represented using triangular mesh segments. The mesh models are generated by scanning and measuring the object structure, which may result in a partial loss of scanned information due to many factors including poor reflection of surface colour, or a blind spot in the measurement due to the design limitations of the measuring instrumentation, potentially leaving holes in the triangular mesh model. This study attempts to fill the holes in the model using software-based calculations to obtain a solid model faithful to the geometry of the original subject, and to adjust the apex coordinates of the newly added mesh segments using systematic grey prediction, thus allowing the new mesh segments to be integrated into the surrounding mesh segments.

Dental models are characterized by complex surface irregularities. During 3D scanning, the laser may be unable to adequately penetrate into gaps between the teeth, thus leaving holes in the resulting mesh segments. In addition, the significant curvature change rate of the gingival line is not easily reflected by the laser beam, making it difficult to acquire point information. The complexity of various types of holes, combined with the advantages and disadvantages of various algorithms is the greatest challenge for hole filling. Most algorithms are composed of complex mathematical calculations.

This study targets holes generated during the process of scanning dental models, and focuses on developing a high-quality hole filling method by repairing and refining the object’s surface, followed by predicting and adjusting the coordinates of the newly added points using the grey prediction model taken from grey theory.