Knot calculation for spline fitting via sparse optimization |
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| Affiliation: | 1. State Key Laboratory of Oncology in South China, Collaborative Innovation Center for Cancer Medicine, Sun Yat-sen University Cancer Center, Guangzhou, China;2. Department of Cancer Prevention Center, Sun Yat-sen University Cancer Center, Guangzhou, China;3. Department of Nasopharyngeal Carcinoma, Sun Yat-sen University Cancer Center, Guangzhou, China;4. Department of Radiation Oncology, Cancer Center of Guangzhou Medical University, Guangzhou, China;5. Department of Radiation Oncology, Cancer Center of Shantou University Medical College, Shantou, China;6. Department of Radiation Oncology, Guangdong General Hospital, Guangzhou, China;7. Department of Clinical Trial Center, Sun Yat-sen University Cancer Center, Guangzhou, China;1. Mathematics Department, Zhejiang University, Hangzhou 310027, China;2. School of Computer Engineering, Nanyang Technological University, Singapore 639798, Singapore;3. School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798, Singapore;4. School of Mechanical Engineering and Automation, Beihang University, Beijing 100191, China;1. Dipartimento di Matematica e Informatica, Università di Cagliari, Via Ospedale, 72, 09124 Cagliari, Italy;2. Faculty of Informatics, Università della Svizzera italiana, Via Giuseppe Buffi 13, 6904 Lugano, Switzerland |
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| Abstract: | Curve fitting with splines is a fundamental problem in computer-aided design and engineering. However, how to choose the number of knots and how to place the knots in spline fitting remain a difficult issue. This paper presents a framework for computing knots (including the number and positions) in curve fitting based on a sparse optimization model. The framework consists of two steps: first, from a dense initial knot vector, a set of active knots is selected at which certain order derivative of the spline is discontinuous by solving a sparse optimization problem; second, we further remove redundant knots and adjust the positions of active knots to obtain the final knot vector. Our experiments show that the approximation spline curve obtained by our approach has less number of knots compared to existing methods. Particularly, when the data points are sampled dense enough from a spline, our algorithm can recover the ground truth knot vector and reproduce the spline. |
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| Keywords: | Spline fitting Knot calculation Sparse optimization |
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