A study of moment-based registration method

• Main Authors: Hsiao, Yung Hsun, 蕭詠勳
• Other Authors: 黃子銘
• Format: Others
• Language: zh-TW
• Online Access: http://ndltd.ncl.edu.tw/handle/49925853847873453152

碩士 === 國立政治大學 === 統計研究所 === 101 === In functional data analysis, it is common that the data curves exhibit roughly the same structure with some variation in time. In order to estimate the common structure, it is necessary to align the curves. Early alignment approaches include landmark registration and continuous monotone registration. In landmark registration, curves are aligned by matching certain curve characters. In continuous monotone registration, curves are aligned by matching their shapes. James (2007) proposed an alignment method called curve alignment by moments (CAM). In the CAM approach, curves are aligned by matching both their shapes and moments, where curve moments may be chosen to reflect certain curve characters. The CAM approach is flexible, but the computation is time consuming. In this thesis, two modified versions of CAM are proposed based on a model assuming the curves are of the same shape. An algorithm is proposed to find the warping functions and the shape function iteratively. In the two modified versions, the number of parameters involved in the computation is largely reduced. Another modification considered in this thesis is to use moments based on pieces of curves instead of the whole curves. The advantage of using the modified moments is so that repeated characters in each curve may be identified. Simulation results indicate that such modification can lead to substantial improvement in certain cases.