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Register a new userGlobally optimal point set registration by joint symmetry plane fitting
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Added by
Lan Hu
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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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.
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We propose a self-supervised method for partial point set registration. While recent proposed learning-based methods have achieved impressive registration performance on the full shape observations, these methods mostly suffer from performance degradation when dealing with partial shapes. To bridge the performance gaps between partial point set registration with full point set registration, we proposed to incorporate a shape completion network to benefit the registration process. To achieve this, we design a latent code for each pair of shapes, which can be regarded as a geometric encoding of the target shape. By doing so, our model does need an explicit feature embedding network to learn the feature encodings. More importantly, both our shape completion network and the point set registration network take the shared latent codes as input, which are optimized along with the parameters of two decoder networks in the training process. Therefore, the point set registration process can thus benefit from the joint optimization process of latent codes, which are enforced to represent the information of full shape instead of partial ones. In the inference stage, we fix the network parameter and optimize the latent codes to get the optimal shape completion and registration results. Our proposed method is pure unsupervised and does not need any ground truth supervision. Experiments on the ModelNet40 dataset demonstrate the effectiveness of our model for partial point set registration.
The rigid registration of two 3D point sets is a fundamental problem in computer vision. The current trend is to solve this problem globally using the BnB optimization framework. However, the existing global methods are slow for two main reasons: the computational complexity of BnB is exponential to the problem dimensionality (which is six for 3D rigid registration), and the bound evaluation used in BnB is inefficient. In this paper, we propose two techniques to address these problems. First, we introduce the idea of translation invariant vectors, which allows us to decompose the search of a 6D rigid transformation into a search of 3D rotation followed by a search of 3D translation, each of which is solved by a separate BnB algorithm. This transformation decomposition reduces the problem dimensionality of BnB algorithms and substantially improves its efficiency. Then, we propose a new data structure, named 3D Integral Volume, to accelerate the bound evaluation in both BnB algorithms. By combining these two techniques, we implement an efficient algorithm for rigid registration of 3D point sets. Extensive experiments on both synthetic and real data show that the proposed algorithm is three orders of magnitude faster than the existing state-of-the-art global methods.
We present Free Point Transformer (FPT) - a deep neural network architecture for non-rigid point-set registration. Consisting of two modules, a global feature extraction module and a point transformation module, FPT does not assume explicit constraints based on point vicinity, thereby overcoming a common requirement of previous learning-based point-set registration methods. FPT is designed to accept unordered and unstructured point-sets with a variable number of points and uses a model-free approach without heuristic constraints. Training FPT is flexible and involves minimizing an intuitive unsupervised loss function, but supervised, semi-supervised, and partially- or weakly-supervised training are also supported. This flexibility makes FPT amenable to multimodal image registration problems where the ground-truth deformations are difficult or impossible to measure. In this paper, we demonstrate the application of FPT to non-rigid registration of prostate magnetic resonance (MR) imaging and sparsely-sampled transrectal ultrasound (TRUS) images. The registration errors were 4.71 mm and 4.81 mm for complete TRUS imaging and sparsely-sampled TRUS imaging, respectively. The results indicate superior accuracy to the alternative rigid and non-rigid registration algorithms tested and substantially lower computation time. The rapid inference possible with FPT makes it particularly suitable for applications where real-time registration is beneficial.
We give a polynomial-time constant-factor approximation algorithm for maximum independent set for (axis-aligned) rectangles in the plane. Using a polynomial-time algorithm, the best approximation factor previously known is $O(loglog n)$. The results are based on a new form of recursive partitioning in the plane, in which faces that are constant-complexity and orthogonally convex are recursively partitioned into a constant number of such faces.
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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