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Received Nov 22, 2017; Accepted Jan 1, 2018
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1. Introduction
In this paper, we propose an efficient and robust algorithm for volume reconstruction from a point cloud. Reconstructing the three-dimensional model from a point cloud is important in medical applications. Surface reconstruction from a point cloud is a process of finding a surface model that approximates an unknown surface for a given set of sample points lying on or near the unknown surface [1].
Hoppe et al. developed an algorithm to reconstruct a surface in the three-dimensional space from unorganized points scattered on or near the unknown surface. The algorithm is based on the idea of determining the zero level set of a signed distance function [2]. Kazhdan proposed a surface reconstruction method which takes an oriented point set and returns a solid model. The method uses Stokes’ theorem to calculate the characteristic function (one inside the model and zero outside of it) of the solid model [3]. To reconstruct implicit surfaces from scattered unorganized data set, Li et al. presented a novel numerical method for surface embedding narrow volume reconstruction from unorganized points [4, 5]. Yang et al. proposed a 3D reconstruction technique from nonuniform point clouds via local hierarchical clustering [6]. Zhao et al. developed a fast sweeping level set and tagging methods [7]. Yezzi Jr. et al. proposed a new medical image segmentation based on feature-based metrics on a given image [8].
Beneš et al. used the Allen-Cahn equation with a forcing term to achieve image segmentation [9]. Caselles et al. proposed a model for active contours which could extract smooth shapes and could be adapted to find several contours simultaneously [10]. Methods using geometric active contour were introduced in [11–14]. Zhang et al. developed a weighted sparse penalty and a weighted grouping effect penalty in modeling the subspace structure [15]. Chen used an ICKFCM method (ICA analysis and KFCM algorithm) in medical image segmentation and made a good result in extracting the complicated images [16]. Zhang et al. proposed a novel fuzzy level set method based on finding the minimum of...