Robust point correspondence applied to two and three-dimensional image registration

Accurate and robust correspondence calculations are very important in many medical and biological applications. Often, the correspondence calculation forms part of a rigid registration algorithm, but accurate correspondences are especially important for elastic registration algorithms and for quantifying changes over time. In this paper, a new correspondence calculation algorithm, CSM (correspondence by sensitivity to movement), is described. A robust corresponding point is calculated by determining the sensitivity of a correspondence to movement of the point being matched. If the correspondence is reliable, a perturbation in the position of this point should not result in a large movement of the correspondence. A measure of reliability is also calculated. This correspondence calculation method is independent of the registration transformation and has been incorporated into both a 2D elastic registration algorithm for warping serial sections and a 3D rigid registration algorithm for registering pre and postoperative facial range scans. These applications use different methods for calculating the registration transformation and accurate rigid and elastic alignment of images has been achieved with the CSM method. It is expected that this method will be applicable to many different applications and that good results would be achieved if it were to be inserted into other methods for calculating a registration transformation from correspondence

SHREC'16: partial matching of deformable shapes

Matching deformable 3D shapes under partiality transformations is a challenging problem that has received limited focus in the computer vision and graphics communities. With this benchmark, we explore and thoroughly investigate the robustness of existing matching methods in this challenging task. Participants are asked to provide a point-to-point correspondence (either sparse or dense) between deformable shapes undergoing different kinds of partiality transformations, resulting in a total of 400 matching problems to be solved for each method - making this benchmark the biggest and most challenging of its kind. Five matching algorithms were evaluated in the contest; this paper presents the details of the dataset, the adopted evaluation measures, and shows thorough comparisons among all competing methods

Atlas-Based Prostate Segmentation Using an Hybrid Registration

Purpose: This paper presents the preliminary results of a semi-automatic method for prostate segmentation of Magnetic Resonance Images (MRI) which aims to be incorporated in a navigation system for prostate brachytherapy. Methods: The method is based on the registration of an anatomical atlas computed from a population of 18 MRI exams onto a patient image. An hybrid registration framework which couples an intensity-based registration with a robust point-matching algorithm is used for both atlas building and atlas registration. Results: The method has been validated on the same dataset that the one used to construct the atlas using the "leave-one-out method". Results gives a mean error of 3.39 mm and a standard deviation of 1.95 mm with respect to expert segmentations. Conclusions: We think that this segmentation tool may be a very valuable help to the clinician for routine quantitative image exploitation.Comment: International Journal of Computer Assisted Radiology and Surgery (2008) 000-99

A relaxed approach for curve matching with elastic metrics

In this paper we study a class of Riemannian metrics on the space of unparametrized curves and develop a method to compute geodesics with given boundary conditions. It extends previous works on this topic in several important ways. The model and resulting matching algorithm integrate within one common setting both the family of $H^2$-metrics with constant coefficients and scale-invariant $H^2$-metrics on both open and closed immersed curves. These families include as particular cases the class of first-order elastic metrics. An essential difference with prior approaches is the way that boundary constraints are dealt with. By leveraging varifold-based similarity metrics we propose a relaxed variational formulation for the matching problem that avoids the necessity of optimizing over the reparametrization group. Furthermore, we show that we can also quotient out finite-dimensional similarity groups such as translation, rotation and scaling groups. The different properties and advantages are illustrated through numerical examples in which we also provide a comparison with related diffeomorphic methods used in shape registration.Comment: 27 page

Gauge Invariant Framework for Shape Analysis of Surfaces

This paper describes a novel framework for computing geodesic paths in shape spaces of spherical surfaces under an elastic Riemannian metric. The novelty lies in defining this Riemannian metric directly on the quotient (shape) space, rather than inheriting it from pre-shape space, and using it to formulate a path energy that measures only the normal components of velocities along the path. In other words, this paper defines and solves for geodesics directly on the shape space and avoids complications resulting from the quotient operation. This comprehensive framework is invariant to arbitrary parameterizations of surfaces along paths, a phenomenon termed as gauge invariance. Additionally, this paper makes a link between different elastic metrics used in the computer science literature on one hand, and the mathematical literature on the other hand, and provides a geometrical interpretation of the terms involved. Examples using real and simulated 3D objects are provided to help illustrate the main ideas.Comment: 15 pages, 11 Figures, to appear in IEEE Transactions on Pattern Analysis and Machine Intelligence in a better resolutio

Finite Element Based Tracking of Deforming Surfaces

We present an approach to robustly track the geometry of an object that deforms over time from a set of input point clouds captured from a single viewpoint. The deformations we consider are caused by applying forces to known locations on the object's surface. Our method combines the use of prior information on the geometry of the object modeled by a smooth template and the use of a linear finite element method to predict the deformation. This allows the accurate reconstruction of both the observed and the unobserved sides of the object. We present tracking results for noisy low-quality point clouds acquired by either a stereo camera or a depth camera, and simulations with point clouds corrupted by different error terms. We show that our method is also applicable to large non-linear deformations.Comment: additional experiment