Generalizing the Prediction Sum of Squares Statistic and Formula, Application to Linear Fractional Image Warp and Surface Fitting

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• 作者：Adrien Bartoli
• 关键词：PRESS ; Cross ; validation ; Image registration ; Warp estimation ; Surface reconstruction
• 刊名：International Journal of Computer Vision
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：122
• 期：1
• 页码：61-83
• 全文大小：
• 刊物类别：Computer Science
• 刊物主题：Computer Imaging, Vision, Pattern Recognition and Graphics; Artificial Intelligence (incl. Robotics); Image Processing and Computer Vision; Pattern Recognition;
• 出版者：Springer US
• ISSN：1573-1405
• 卷排序：122

文摘

The prediction sum of squares statistic uses the principle of leave-one-out cross-validation in linear least squares regression. It is computationally attractive, as it can be computed non-iteratively. However, it has limitations: it does not handle coupled measurements, which should be held out simultaneously, and is specific to the principle of leave-one-out, which is known to overfit when used for selecting a model’s complexity. We propose multiple-exclusion PRESS (MEXPRESS), which generalizes PRESS to coupled measurements and other types of cross-validation, while retaining computational efficiency with the non-iterative MEXPRESS formula. Using MEXPRESS, various strategies to resolve overfitting can be efficiently implemented. The core principle is to exclude training data too ‘close’ or too ‘similar’ to the validation data. We show that this allows one to select the number of control points automatically in three cases: (i) the estimation of linear fractional warps for dense image registration from point correspondences, (ii) surface reconstruction from a dense depth-map obtained by a depth sensor and (iii) surface reconstruction from a sparse point cloud obtained by shape-from-template.