Ultrarobust support vector registration
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Ultrarobust support vector registration Lei Yin1 · Chong Yu2 · Yuyi Wang3,4 · Bin Zou1
· Yuan Yan Tang5
Accepted: 21 September 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract An iterativeframework based on finding point correspondences and estimating the transformation function is widely adopted for nonrigid point set registration. However, correspondences established based on feature descriptors are likely to be inaccurate. In this paper, we propose a novel transformation model that can learn from such correspondences. The model is built by means of weighted support vector (SV) regression with a quadratic ε-insensitive loss and manifold regularization. The loss is insensitive to noise, and the regularization forces the transformation function to preserve the intrinsic geometry of the input data. To assess the confidences of correspondences, we introduce a probabilistic model that is solved using the expectation maximization (EM) algorithm. Then, we input the confidences into the transformation model as instance weights to guide model training. We use the coordinate descent method to solve the transformation model in a reproducing kernel Hilbert space and accelerate its speed by means of sparse approximation. Extensive experiments show that our approach is efficient and outperforms other state-of-the-art methods. Keywords Point set registration · Weighted SV regression · Manifold regularization · EM algorithm · Coordinate descent method
1 Introduction Matching two point sets is a fundamental problem in the fields of computer vision, pattern recognition and Bin Zou
[email protected] Lei Yin [email protected] Chong Yu [email protected] Yuyi Wang [email protected] Yuan Yan Tang [email protected] 1
Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan 430062, China
2
Mornengchen Intelligent Technology Co. Ltd., Shanghai 200090, China
3
Department Electrical Engineering, ETH Zurich, Zurich 358092, Switzerland
4
Theory Lab, Huawei 2012 Lab, Shanghai 201206, China
5
Faculty of Science and Technology, University of Macau, Macau 999078, China
remote sensing. In particular, point set registration is widely used in specific tasks in these fields, such as motion tracking, facial recognition and coastline detection, since points are obvious features that are easy to extract [16, 32, 39]. The points that are typically of interest are image features, such as corner points, boundary points and scale-invariant feature transform (SIFT) points [18]. According to the characteristics of the applications and data of interest, point set registration can usually be classified as either rigid or nonrigid registration. Rigid registration is relatively simple, as a rigid transformation is defined by only a few parameters, and has been actively studied [5, 7, 12, 14, 27]. Nonrigid registration is more challenging since the underlying nonrigid transformation is often unknown and difficult to model. However, nonrigid registration is import
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