Fast B-spline Curve Fitting by L-BFGS

We propose a novel method for fitting planar B-spline curves to unorganized data points. In traditional methods, optimization of control points and foot points are performed in two very time-consuming steps in each iteration: 1) control points are updated by setting up and solving a linear system of equations; and 2) foot points are computed by projecting each data point onto a B-spline curve. Our method uses the L-BFGS optimization method to optimize control points and foot points simultaneously and therefore it does not need to perform either matrix computation or foot point projection in every iteration. As a result, our method is much faster than existing methods

Studies on geometric shape reconstruction

This thesis, on geometric shape modeling problems, contains two major chapters. In the first chapter, we propose a fast method for fitting planar Bspline curves to unorganized data points. In traditional methods, optimization of control points and foot points are performed in two alternating timeconsuming steps in every iteration: 1) control points are updated by setting up and solving a linear system of equations; and 2) foot points are computed by projecting each data point onto a B-spline curve. Our method uses the LBFGS optimization method to optimize control points and foot points simultaneously and therefore it does not need to solve a linear system of equations or performing foot point projection in every iteration. As a result, the proposed method is much faster than existing methods. In the second chapter, we propose a new shape description method using a radial basis function built on the medial axis of the shape. By formulating our approach as a constrained L^1-minimization problem, our method produces sparse reconstruction result which uses much fewer basis functions than previous approaches. Besides the sparse representation capacity, our method also has advantages in two aspects: 1) Our method does not rely on normal information of input points. 2) Our method has stronger capacity in representing multi-scale shapes compared with existing methods. All these characteristics will be illustrated in the corresponding chapters and sections.published_or_final_versionComputer ScienceDoctoralDoctor of Philosoph

An exploration of clinical features and factors associated with pain frequency and pain intensity in children with growing pains: a cross-sectional study from Chongqing, China

Abstract. Instruction:. Growing pains are the most common cause of musculoskeletal pain in children, affecting both children's and caregivers' well-being. The lack of definitive diagnostic criteria complicates diagnosis and treatment. Objectives:. This study aims to outline the clinical features and identify factors associated with the frequency and intensity of growing pains in children in Chongqing, China. Methods:. A cross-sectional study was conducted in a children's hospital using its Internet hospital follow-up platform. Children initially diagnosed with growing pains between July and September 2022 were enrolled. Sociodemographics, pain locations, duration, frequency, intensity, and potentially related factors were collected. Results:. Eight hundred sixty-three children were enrolled (average age: 8.19 ± 3.24 years; 455 boys [52.72%]). Pain frequency was reported as quarterly (62.11%), monthly (24.80%), biweekly (1.74%), weekly (10.08%), and daily (1.27%). The prevalence of mild, moderate, and severe pain was 26.65%, 55.74%, and 17.61%, respectively. The knee was the most common pain location (63.85%), mostly encountered between 4 pm and 5 pm (20.51%). Multivariate analysis revealed that pain frequency negatively correlated with vitamin supplementation during pregnancy, positively correlated with underweight, bad temper, increased exercise, and cold lower extremities. Pain intensity positively correlated with irritability, increased exercise, and pain sensitivity but negatively correlated with age and vitamin supplementation during lactation. Conclusion:. Growing pains typically occur on a quarterly basis, predominantly affecting the knees during 4 pm to 5 pm. Factors in sociodemographics, maternal aspect, temperament, and exercise levels can influence pain frequency and intensity. Clinicians should consider these aspects when developing comprehensive strategies for pain management