How many sample points are sufficient for 3D model surface representation and accurate mesh simplification?
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How many sample points are sufficient for 3D model surface representation and accurate mesh simplification? Lida Asgharian 1 & Hossein Ebrahimnezhad 1 Received: 11 September 2019 / Revised: 11 July 2020 / Accepted: 21 July 2020 # Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract
Growing of 3D model products and its applications in mobile devices and multimedia tools increases demands to establish an effective approach for representing and compressing of these models. In this paper, we propose an algorithm to simplify a complex 3D mesh and reduce the number of vertices by re-sampling the mesh based on the Nyquist theorem in order to find the sufficient number of samples that is necessary to save the quality of the reconstructed mesh, precisely. To achieve the optimum number of samples in the simplified mesh, both maximum curvature (Cmax) and minimum curvature (Cmin) in the original mesh are employed for adaptive sampling in different directions. Since the samples are adaptively taken regarding the curvature variations in both directions of maximum and minimum curvatures, the least number of vertices is obtained to represent the model. Hence, the method not only simplifies the complex mesh, but also preserves fine scale features in the mesh. The proposed method is applied to different complex mesh surfaces. The experimental results demonstrate that our proposed framework can represent a mesh surface with the least number of samples besides preserving important features in the surface. Keywords Mesh simplification . 3D model approximation . Re-meshing . Detail preservation . Nyquist theorem . Adaptive sampling . Surface representation
* Hossein Ebrahimnezhad [email protected] Lida Asgharian [email protected]
1
Computer Vision Research Lab, Electrical Engineering Faculty, Sahand University of Technology, Tabriz, Iran
Multimedia Tools and Applications
1 Introduction In recent decade, usage of social networks has been extensively developed for transmitting the information. These networks are used to transmit different types of data such as image, document, video, advertisement and animation. If the operating system be able to express the proposed data with low bitrates, the speed of data transmission will be increased, consequently. During the last decade, many approaches have been presented to compress various types of signals including audio, video and 3D models. An optimal rate of compression is defined as the least number of samples that are required to represent the signal besides preserving its quality. High speed data transmission is an important subject in communication systems. Nowadays, animation industry has been widely extended which requires a huge space of memory for processing of 3D models. This processing consists of reading, editing, deforming and writing of a large amount of vertices. Since providing high speed systems is expensive for all consumers, presenting an efficient simplification algorithm is necessary to deal with this problem. In the simplification
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