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Register a new userLinearly Converging Quasi Branch and Bound Algorithms for Global Rigid Registration
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Added by
Nadav Dym
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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In recent years, several branch-and-bound (BnB) algorithms have been proposed to globally optimize rigid registration problems. In this paper, we suggest a general framework to improve upon the BnB approach, which we name Quasi BnB. Quasi BnB replaces the linear lower bounds used in BnB algorithms with quadratic quasi-lower bounds which are based on the quadratic behavior of the energy in the vicinity of the global minimum. While quasi-lower bounds are not truly lower bounds, the Quasi-BnB algorithm is globally optimal. In fact we prove that it exhibits linear convergence -- it achieves $epsilon$-accuracy in $~O(log(1/epsilon)) $ time while the time complexity of other rigid registration BnB algorithms is polynomial in $1/epsilon $. Our experiments verify that Quasi-BnB is significantly more efficient than state-of-the-art BnB algorithms, especially for problems where high accuracy is desired.
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Quasi branch and bound is a recently introduced generalization of branch and bound, where lower bounds are replaced by a relaxed notion of quasi-lower bounds, required to be lower bounds only for sub-cubes containing a minimizer. This paper is devoted to studying the possible benefits of this approach, for the problem of minimizing a smooth function over a cube. This is accomplished by suggesting two quasi branch and bound algorithms, qBnB(2) and qBnB(3), that compare favorably with alternative branch and bound algorithms. The first algorithm we propose, qBnB(2), achieves second order convergence based only on a bound on second derivatives, without requiring calculation of derivatives. As such, this algorithm is suitable for derivative free optimization, for which typical algorithms such as Lipschitz optimization only have first order convergence and so suffer from limited accuracy due to the clustering problem. Additionally, qBnB(2) is provably more efficient than the second order Lipschitz gradient algorithm which does require exact calculation of gradients. The second algorithm we propose, qBnB(3), has third order convergence and finite termination. In contrast with BnB algorithms with similar guarantees who typically compute lower bounds via solving relatively time consuming convex optimization problems, calculation of qBnB(3) bounds only requires solving a small number of Newton iterations. Our experiments verify the potential of both these methods in comparison with state of the art branch and bound algorithms.
Imperfect data (noise, outliers and partial overlap) and high degrees of freedom make non-rigid registration a classical challenging problem in computer vision. Existing methods typically adopt the $ell_{p}$ type robust estimator to regularize the fitting and smoothness, and the proximal operator is used to solve the resulting non-smooth problem. However, the slow convergence of these algorithms limits its wide applications. In this paper, we propose a formulation for robust non-rigid registration based on a globally smooth robust estimator for data fitting and regularization, which can handle outliers and partial overlaps. We apply the majorization-minimization algorithm to the problem, which reduces each iteration to solving a simple least-squares problem with L-BFGS. Extensive experiments demonstrate the effectiveness of our method for non-rigid alignment between two shapes with outliers and partial overlap, with quantitative evaluation showing that it outperforms state-of-the-art methods in terms of registration accuracy and computational speed. The source code is available at https://github.com/Juyong/Fast_RNRR.
Since the mapping relationship between definitized intra-interventional 2D X-ray and undefined pre-interventional 3D Computed Tomography(CT) is uncertain, auxiliary positioning devices or body markers, such as medical implants, are commonly used to determine this relationship. However, such approaches can not be widely used in clinical due to the complex realities. To determine the mapping relationship, and achieve a initializtion post estimation of human body without auxiliary equipment or markers, proposed method applies image segmentation and deep feature matching to directly match the 2D X-ray and 3D CT images. As a result, the well-trained network can directly predict the spatial correspondence between arbitrary 2D X-ray and 3D CT. The experimental results show that when combining our approach with the conventional approach, the achieved accuracy and speed can meet the basic clinical intervention needs, and it provides a new direction for intra-interventional registration.
The present work proposes a solution to the challenging problem of registering two partial point sets of the same object with very limited overlap. We leverage the fact that most objects found in man-made environments contain a plane of symmetry. By reflecting the points of each set with respect to the plane of symmetry, we can largely increase the overlap between the sets and therefore boost the registration process. However, prior knowledge about the plane of symmetry is generally unavailable or at least very hard to find, especially with limited partial views, and finding this plane could strongly benefit from a prior alignment of the partial point sets. We solve this chicken-and-egg problem by jointly optimizing the relative pose and symmetry plane parameters, and notably do so under global optimality by employing the branch-and-bound (BnB) paradigm. Our results demonstrate a great improvement over the current state-of-the-art in globally optimal point set registration for common objects. We furthermore show an interesting application of our method to dense 3D reconstruction of scenes with repetitive objects.
In the unsupervised open set domain adaptation (UOSDA), the target domain contains unknown classes that are not observed in the source domain. Researchers in this area aim to train a classifier to accurately: 1) recognize unknown target data (data with unknown classes) and, 2) classify other target data. To achieve this aim, a previous study has proven an upper bound of the target-domain risk, and the open set difference, as an important term in the upper bound, is used to measure the risk on unknown target data. By minimizing the upper bound, a shallow classifier can be trained to achieve the aim. However, if the classifier is very flexible (e.g., deep neural networks (DNNs)), the open set difference will converge to a negative value when minimizing the upper bound, which causes an issue where most target data are recognized as unknown data. To address this issue, we propose a new upper bound of target-domain risk for UOSDA, which includes four terms: source-domain risk, $epsilon$-open set difference ($Delta_epsilon$), a distributional discrepancy between domains, and a constant. Compared to the open set difference, $Delta_epsilon$ is more robust against the issue when it is being minimized, and thus we are able to use very flexible classifiers (i.e., DNNs). Then, we propose a new principle-guided deep UOSDA method that trains DNNs via minimizing the new upper bound. Specifically, source-domain risk and $Delta_epsilon$ are minimized by gradient descent, and the distributional discrepancy is minimized via a novel open-set conditional adversarial training strategy. Finally, compared to existing shallow and deep UOSDA methods, our method shows the state-of-the-art performance on several benchmark datasets, including digit recognition (MNIST, SVHN, USPS), object recognition (Office-31, Office-Home), and face recognition (PIE).
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