662 research outputs found
Rigid and Articulated Point Registration with Expectation Conditional Maximization
This paper addresses the issue of matching rigid and articulated shapes through probabilistic point registration. The problem is recast into a missing data framework where unknown correspondences are handled via mixture models. Adopting a maximum likelihood principle, we introduce an innovative EM-like algorithm, namely the Expectation Conditional Maximization for Point Registration (ECMPR) algorithm. The algorithm allows the use of general covariance matrices for the mixture model components and improves over the isotropic covariance case. We analyse in detail the associated consequences in terms of estimation of the registration parameters, and we propose an optimal method for estimating the rotational and translational parameters based on semi-definite positive relaxation. We extend rigid registration to articulated registration. Robustness is ensured by detecting and rejecting outliers through the addition of a uniform component to the Gaussian mixture model at hand. We provide an in-depth analysis of our method and we compare it both theoretically and experimentally with other robust methods for point registration
Rigid and Articulated Point Registration with Expectation Conditional Maximization
International audienceThis paper addresses the issue of matching rigid and articulated shapes through probabilistic point registration. The problem is recast into a missing data framework where unknown correspondences are handled via mixture models. Adopting a maximum likelihood principle, we introduce an innovative EM-like algorithm, namely the Expectation Conditional Maximization for Point Registration (ECMPR) algorithm. The algorithm allows the use of general covariance matrices for the mixture model components and improves over the isotropic covariance case. We analyse in detail the associated consequences in terms of estimation of the registration parameters, and we propose an optimal method for estimating the rotational and translational parameters based on semi-definite positive relaxation. We extend rigid registration to articulated registration. Robustness is ensured by detecting and rejecting outliers through the addition of a uniform component to the Gaussian mixture model at hand. We provide an in-depth analysis of our method and we compare it both theoretically and experimentally with other robust methods for point registration
DNSS: Dual-Normal-Space Sampling for 3-D ICP Registration
Rigid registration is a fundamental process in many applications that require alignment of different datasets. Iterative closest point (ICP) is a widely used algorithm that iteratively finds point correspondences and updates the rigid transformation. One of the key variants of ICP to its success is the selection of points, which is directly related to the convergence and robustness of the ICP algorithm. Besides uniform sampling, there are a number of normal-based and feature-based approaches that consider normal, curvature, and/or other signals in the point selection. Among them, normal-space sampling (NSS) is one of the most popular techniques due to its simplicity and low computational cost. The rationale of NSS is to sample enough constraints to determine all the components of transformation, but this paper finds that NSS actually can constrain the translational normal space only. This paper extends the fundamental idea of NSS and proposes Dual NSS (DNSS) to sample points in both translational and rotational normal spaces. Compared with NSS, this approach has similar simplicity and efficiency without any need of additional information, but has a much better effectiveness. Experimental results show that DNSS can outperform the normal-based and feature-based methods in terms of convergence and robustness. For example, DNSS can achieve convergence from an orthogonal initial position while no other methods can achieve. Note to Practitioners-ICP is commonly used to align different data to a same coordination system. While NSS is often used to speed up the alignment process by down-sampling the data uniformly in the normal space. The implementation of NSS only has three steps: 1) construct a set of buckets in the normal-space; 2) put all points of the data into buckets based on their normal direction; and 3) uniformly pick points from all the buckets until the desired number of points is selected. The algorithm is simple and fast, so that it is still the common practice. However, the weakness of NSS comes from the reason that it cannot handle rotational uncertainties. In this paper, a new algorithm called DNSS is developed to constrain both translation and rotation at the same time by introducing a dual-normal space. With a new definition of the normal space, the algorithm complexity of DNSS is the same as that of NSS, and it can be readily implemented in all types of application that are currently using ICP. The experimental results show that DNSS has better efficiency, quality, and reliability than both normal-based and feature-based methods have
Robust Point Cloud Registration Framework Based on Deep Graph Matching(TPAMI Version)
3D point cloud registration is a fundamental problem in computer vision and
robotics. Recently, learning-based point cloud registration methods have made
great progress. However, these methods are sensitive to outliers, which lead to
more incorrect correspondences. In this paper, we propose a novel deep graph
matching-based framework for point cloud registration. Specifically, we first
transform point clouds into graphs and extract deep features for each point.
Then, we develop a module based on deep graph matching to calculate a soft
correspondence matrix. By using graph matching, not only the local geometry of
each point but also its structure and topology in a larger range are considered
in establishing correspondences, so that more correct correspondences are
found. We train the network with a loss directly defined on the
correspondences, and in the test stage the soft correspondences are transformed
into hard one-to-one correspondences so that registration can be performed by a
correspondence-based solver. Furthermore, we introduce a transformer-based
method to generate edges for graph construction, which further improves the
quality of the correspondences. Extensive experiments on object-level and
scene-level benchmark datasets show that the proposed method achieves
state-of-the-art performance. The code is available at:
\href{https://github.com/fukexue/RGM}{https://github.com/fukexue/RGM}.Comment: accepted by TPAMI 2022. arXiv admin note: substantial text overlap
with arXiv:2103.0425
Automatic registration of 3D models to laparoscopic video images for guidance during liver surgery
Laparoscopic liver interventions offer significant advantages over open surgery, such as less pain and trauma, and shorter recovery time for the patient. However, they also bring challenges for the surgeons such as the lack of tactile feedback, limited field of view and occluded anatomy. Augmented reality (AR) can potentially help during laparoscopic liver interventions by displaying sub-surface structures (such as tumours or vasculature). The initial registration between the 3D model extracted from the CT scan and the laparoscopic video feed is essential for an AR system which should be efficient, robust, intuitive to use and with minimal disruption to the surgical procedure. Several challenges of registration methods in laparoscopic interventions include the deformation of the liver due to gas insufflation in the abdomen, partial visibility of the organ and lack of prominent geometrical or texture-wise landmarks. These challenges are discussed in detail and an overview of the state of the art is provided. This research project aims to provide the tools to move towards a completely automatic registration. Firstly, the importance of pre-operative planning is discussed along with the characteristics of the liver that can be used in order to constrain a registration method. Secondly, maximising the amount of information obtained before the surgery, a semi-automatic surface based method is proposed to recover the initial rigid registration irrespective of the position of the shapes. Finally, a fully automatic 3D-2D rigid global registration is proposed which estimates a global alignment of the pre-operative 3D model using a single intra-operative image. Moving towards incorporating the different liver contours can help constrain the registration, especially for partial surfaces. Having a robust, efficient AR system which requires no manual interaction from the surgeon will aid in the translation of such approaches to the clinics
Robust and Optimal Methods for Geometric Sensor Data Alignment
Geometric sensor data alignment - the problem of finding the
rigid transformation that correctly aligns two sets of sensor
data without prior knowledge of how the data correspond - is a
fundamental task in computer vision and robotics. It is
inconvenient then that outliers and non-convexity are inherent to
the problem and present significant challenges for alignment
algorithms. Outliers are highly prevalent in sets of sensor data,
particularly when the sets overlap incompletely. Despite this,
many alignment objective functions are not robust to outliers,
leading to erroneous alignments. In addition, alignment problems
are highly non-convex, a property arising from the objective
function and the transformation. While finding a local optimum
may not be difficult, finding the global optimum is a hard
optimisation problem. These key challenges have not been fully
and jointly resolved in the existing literature, and so there is
a need for robust and optimal solutions to alignment problems.
Hence the objective of this thesis is to develop tractable
algorithms for geometric sensor data alignment that are robust to
outliers and not susceptible to spurious local optima.
This thesis makes several significant contributions to the
geometric alignment literature, founded on new insights into
robust alignment and the geometry of transformations. Firstly, a
novel discriminative sensor data representation is proposed that
has better viewpoint invariance than generative models and is
time and memory efficient without sacrificing model fidelity.
Secondly, a novel local optimisation algorithm is developed for
nD-nD geometric alignment under a robust distance measure. It
manifests a wider region of convergence and a greater robustness
to outliers and sampling artefacts than other local optimisation
algorithms. Thirdly, the first optimal solution for 3D-3D
geometric alignment with an inherently robust objective function
is proposed. It outperforms other geometric alignment algorithms
on challenging datasets due to its guaranteed optimality and
outlier robustness, and has an efficient parallel implementation.
Fourthly, the first optimal solution for 2D-3D geometric
alignment with an inherently robust objective function is
proposed. It outperforms existing approaches on challenging
datasets, reliably finding the global optimum, and has an
efficient parallel implementation. Finally, another optimal
solution is developed for 2D-3D geometric alignment, using a
robust surface alignment measure.
Ultimately, robust and optimal methods, such as those in this
thesis, are necessary to reliably find accurate solutions to
geometric sensor data alignment problems
Efficient Deformable Shape Correspondence via Kernel Matching
We present a method to match three dimensional shapes under non-isometric
deformations, topology changes and partiality. We formulate the problem as
matching between a set of pair-wise and point-wise descriptors, imposing a
continuity prior on the mapping, and propose a projected descent optimization
procedure inspired by difference of convex functions (DC) programming.
Surprisingly, in spite of the highly non-convex nature of the resulting
quadratic assignment problem, our method converges to a semantically meaningful
and continuous mapping in most of our experiments, and scales well. We provide
preliminary theoretical analysis and several interpretations of the method.Comment: Accepted for oral presentation at 3DV 2017, including supplementary
materia
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