Fractal bubble algorithm for simplification of 3D point cloud data

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Abstract
We present a novel technique for 3D point cloud simplification — the so-called fractal bubble algorithm — to minimize the computational time and overall storage space. The proposed fractal bubble algorithm generates 2D elastic bubbles and copies of themselves through 2D data sets representing planar geometric contours. Each of the bubbles, as it grows, is made to select a single point of its first contact, and all the selected points become the simplified set of points. The fractal bubble algorithm is repeatedly applied to the simplification of planar slices of general 3D point clouds corresponding to 3D geometric objects, leading to the global simplification of 3D point clouds. The benefits of the algorithm are: first the algorithm is computationally light and memory efficient, second it is simple to implement and inherently allows the organized selection of the points of contact and finally it enables us to simplify the point cloud data through a multi-scale fashion by varying a set of user-controlled algorithm parameters. Numerical results verify the effectiveness of the proposed algorithm.

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