Abstract
While the reconstruction of 3D objects is increasingly used today, the simplification of 3D point cloud, however, becomes a substantial phase in this process of reconstruction. This is due to the huge amounts of dense 3D point cloud produced by 3D scanning devices. In this paper, a new approach is proposed to simplify 3D point cloud based on k-nearest neighbor (k-NN) and clustering algorithm. Initially, 3D point cloud is divided into clusters using k-means algorithm. Then, an entropy estimation is performed for each cluster to remove the ones that have minimal entropy. In this paper, MATLAB is used to carry out the simulation, and the performance of our method is testified by test dataset. Numerous experiments demonstrate the effectiveness of the proposed simplification method of 3D point cloud.
Highlights
Introduction e simplification of a 3D point cloud, obtained from the digitization of a real object, is a primordial and important step in the field of 3D reconstruction. is step ensures the optimization of the number of points that constitute the 3D point cloud [1]. e scanning of a real object is facilitated by a device called 3D scanner [2]. is device may be broken down into three primary sorts: contact, active noncontact, and passive noncontact
Et al [3] proposed a method based on hierarchical decomposition of the sample of points, calculated by binary partition of space. e cutting planes are defined by the centre and the main direction of each region. e partitioning criterion depends both on a maximum number of points and on variations in local geometry in a region
Shannon’s entropy, which has been largely used in data processing, and k-means clustering algorithm, which has been extensively used in pattern recognition and machine learning literature, have been extended to reduce 3D point cloud. is simplification procedure is achieved through the removal of redundant and less attractive 3D groups of points that have a minimum entropy value
Summary
Simplified point cloud Figure 2: A diagram that shows how the new point cloud simplification method works. For each sample point q ∈ X, the geometric error d(q, X′) can be defined as the Hausdorff distance between the q on the original surface and its projection point q′ on the simplified surface X′. To measure the quality of the obtained meshes, Gueziec [37] proposes a formula to compute the quality of the triangles. It is called compactness formula and is defined as follows:. Note that this measure is equals to 1 for an equilateral triangle and 0 for a triangle whose vertices are collinear. ALGORITHM 1: Simplification of 3D point cloud based on the clustering algorithm and Shannon’s entropy
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