Optimal Geometric Fitting under the Truncated L2-Norm

Ask, Erik; Enqvist, Olof; Kahl, Fredrik

doi:10.1109/cvpr.2013.225

Cited by 24 publications

(20 citation statements)

References 18 publications

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“…For example, in 2D cases, branch-and-bound (BnB) has been used for image pattern matching [7,26,29]. A truncated L 2 optimization for optimal geometric fitting is recently addressed in [2]. However, most of these methods are focused on the much simpler 2D case.…”

Section: Related Workmentioning

confidence: 99%

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Go-ICP: Solving 3D Registration Efficiently and Globally Optimally

Yang

Jia

2013

2013 IEEE International Conference on Computer Vision

399

282

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Registration is a fundamental task in computer vision. The Iterative Closest Point (ICP) algorithm is one of the widely-used methods for solving the registration problem. Based on local iteration, ICP is however well-known to suffer from local minima. Its performance critically relies on the quality of initialization, and only local optimality is guaranteed. This paper provides the very first globally optimal solution to Euclidean registration of two 3D pointsets or two 3D surfaces under the L 2 error. Our method is built upon ICP, but combines it with a branch-and-bound (BnB) scheme which searches the 3D motion space SE(3) efficiently. By exploiting the special structure of the underlying geometry, we derive novel upper and lower bounds for the ICP error function. The integration of local ICP and global BnB enables the new method to run efficiently in practice, and its optimality is exactly guaranteed. We also discuss extensions, addressing the issue of outlier robustness.

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Section: Related Workmentioning

confidence: 99%

“…(1), and finding the closest-point matches by Eq. (2). Due to such iterative nature, ICP can only guarantee the convergence to a local minimum.…”

Section: The 3d Registration Problemmentioning

confidence: 99%

Go-ICP: Solving 3D Registration Efficiently and Globally Optimally

Yang

Jia

2013

2013 IEEE International Conference on Computer Vision

399

282

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“…However, as they are based on branch-and-bound, the computational complexity of the algorithm is exponential. The most closely related work to ours is [10,1], where a truncated L 2 -norm algorithm is derived with complexity O(n 4 ). However, the runtime tends to be prohibitive (see experimental section), making it a less tractable alternative.…”

Section: Related Workmentioning

confidence: 99%

“…To increase the speed even more we propose a fast outlier rejection step as preprocessing, inspired by the work in [1]. For this we need a variant of Algorithm 1 that works with the zero-one loss (denoted by L 0 ), that is, counting the number of outliers rather than truncated L 1 -norm.…”

Section: Fast Outlier Rejectionmentioning

confidence: 99%

“…The proposed algorithms were compared to the algorithm for truncated L 2 -norm from [1] as well as standard L 2 -minimization and RANSAC followed by L 2 -minimization on the inlier set. For each problem instance, 10 correspondences were manually picked by an expert and used to compute an optimal transformation under the L 2 -loss.…”

Section: Registering Histology Sectionsmentioning

confidence: 99%

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Tractable and Reliable Registration of 2D Point Sets

Ask

Enqvist

Svärm

et al. 2014

Computer Vision – ECCV 2014

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Abstract. This paper introduces two new methods of registering 2D point sets over rigid transformations when the registration error is based on a robust loss function. In contrast to previous work, our methods are guaranteed to compute the optimal transformation, and at the same time, the worst-case running times are bounded by a low-degree polynomial in the number of correspondences. In practical terms, this means that there is no need to resort to ad-hoc procedures such as random sampling or local descent methods that cannot guarantee the quality of their solutions. We have tested the methods in several different settings, in particular, a thorough evaluation on two benchmarks of microscopic images used for histologic analysis of prostate cancer has been performed. Compared to the state-of-the-art, our results show that the methods are both tractable and reliable despite the presence of a significant amount of outliers.

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