Feature-based registration of medical images: Estimation and validation of the pose accuracy

Abstract

Abstract. We provide in this article a generic framework for pose estimation from geometric features. We propose more particularly two algorithms: a gradient descent on the Riemannian least squares distance and on the Mahalanobis distance. For each method, we provide a way to compute the uncertainty of the resulting transformation. The analysis and comparison of the algorithms show their advantages and drawbacks and point out the very good prediction on the transformation accuracy. An application in medical image analysis validates the uncertainty estimation on real data and demonstrates that, using adapted and rigorous tools, we can detect very small modifications in medical images. We believe that these algorithms could be easily embedded in many applications and provide a thorough basis for computing many image statistics.

Intrinsic Statistics on Riemannian Manifolds: Basic Tools for Geometric Measurements

“…The interested reader will find practical applications in computer vision to compute the mean rotation [32,33] or for the generalization of matching algorithms to arbitrary geometric features [65]. In medical image analysis, selected applications cover the validation of the rigid registration accuracy [4,66,67], shape statistics [7] and more recently tensor computing, either for processing and analyzing diffusion tensor images [10,8,9,11], or to model the brain variability [12]. One can even find applications in rock mechanics with the analysis of fracture geometry [68].…”

“…Examples of manifolds we routinely use in medical imaging applications are 3D rotations, 3D rigid transformations, frames (a 3D point and an orthonormal trihedron), semi-or non-oriented frames (where 2 (resp. 3) of the trihedron unit vectors are given up to their sign) [3,4], oriented or directed points [5,6], positive definite symmetric matrices coming from diffusion tensor imaging [7,8,9,10,11] or from variability measurements [12]. We have already shown in [13,2] that this is not an easy problem and that some paradoxes can arise.…”

“…Since then, several authors in the area of stochastic differential geometry and stochastic calculus on manifolds proposed results related to mean values [25,26,27,28,29,30]. On the applied mathematics and computer science side, people get interested in computing and optimizing in specific manifolds, like rotations and rigid body transformations [4,31,32,33,34], Stiefel and Grassmann manifolds [35], etc.…”

Performance Evaluation of Grid-Enabled Registration Algorithms Using Bronze-Standards

“…Here, d is a distance function between transformations chosen as a robust variant of the left invariant distance on rigid transformation developed in [6]:…”

“…Then, the variability of the transformation can be propagated to some target points using standard first order linearizations to obtain the covariance on the transformed test points, or its trace, the variance (see e.g. [6]). …”