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Use of Approximate Set Differences to Infer the Movement of Objects in Point Clouds
AuthorClifford, James A.
AdvisorOlson, Eric J.
Mathematics and Statistics
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To support the mathematical eld of change detection, we present a novel detec- tion algorithm based on approximate set di erences. Our goal is to determine how e ective the algorithm is for detecting the movement of objects and what factors a ect its performance. A theoretical foundation for this algorithm is built by prov- ing mathematical theorems relating to its e ectiveness. To optimize calculations, we developed a method of recursively boxing a point cloud into a tree structure. We then tested computational e ciency by applying the algorithm to synthetic data. Further optimization was performed by parallelizing the calculation of the approxi- mate set di erence. Finally, the e ectiveness of the algorithm for detecting changes was determined by testing data from a 3D scanner. The results indicate that the approximate set di erence is an e cient algorithm that can e ectively detect changes in three-dimensional data in O(n log2 n) time.