Learning Deep Similarity Metric for 3D MR-TRUS Registration

Purpose: The fusion of transrectal ultrasound (TRUS) and magnetic resonance (MR) images for guiding targeted prostate biopsy has significantly improved the biopsy yield of aggressive cancers. A key component of MR-TRUS fusion is image registration. However, it is very challenging to obtain a robust automatic MR-TRUS registration due to the large appearance difference between the two imaging modalities. The work presented in this paper aims to tackle this problem by addressing two challenges: (i) the definition of a suitable similarity metric and (ii) the determination of a suitable optimization strategy. Methods: This work proposes the use of a deep convolutional neural network to learn a similarity metric for MR-TRUS registration. We also use a composite optimization strategy that explores the solution space in order to search for a suitable initialization for the second-order optimization of the learned metric. Further, a multi-pass approach is used in order to smooth the metric for optimization. Results: The learned similarity metric outperforms the classical mutual information and also the state-of-the-art MIND feature based methods. The results indicate that the overall registration framework has a large capture range. The proposed deep similarity metric based approach obtained a mean TRE of 3.86mm (with an initial TRE of 16mm) for this challenging problem. Conclusion: A similarity metric that is learned using a deep neural network can be used to assess the quality of any given image registration and can be used in conjunction with the aforementioned optimization framework to perform automatic registration that is robust to poor initialization.Comment: To appear on IJCAR

Piecewise rigid curve deformation via a Finsler steepest descent

This paper introduces a novel steepest descent flow in Banach spaces. This extends previous works on generalized gradient descent, notably the work of Charpiat et al., to the setting of Finsler metrics. Such a generalized gradient allows one to take into account a prior on deformations (e.g., piecewise rigid) in order to favor some specific evolutions. We define a Finsler gradient descent method to minimize a functional defined on a Banach space and we prove a convergence theorem for such a method. In particular, we show that the use of non-Hilbertian norms on Banach spaces is useful to study non-convex optimization problems where the geometry of the space might play a crucial role to avoid poor local minima. We show some applications to the curve matching problem. In particular, we characterize piecewise rigid deformations on the space of curves and we study several models to perform piecewise rigid evolution of curves

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