An inexact Newton-Krylov algorithm for constrained diffeomorphic image registration

We propose numerical algorithms for solving large deformation diffeomorphic image registration problems. We formulate the nonrigid image registration problem as a problem of optimal control. This leads to an infinite-dimensional partial differential equation (PDE) constrained optimization problem. The PDE constraint consists, in its simplest form, of a hyperbolic transport equation for the evolution of the image intensity. The control variable is the velocity field. Tikhonov regularization on the control ensures well-posedness. We consider standard smoothness regularization based on $H^1$- or $H^2$-seminorms. We augment this regularization scheme with a constraint on the divergence of the velocity field rendering the deformation incompressible and thus ensuring that the determinant of the deformation gradient is equal to one, up to the numerical error. We use a Fourier pseudospectral discretization in space and a Chebyshev pseudospectral discretization in time. We use a preconditioned, globalized, matrix-free, inexact Newton-Krylov method for numerical optimization. A parameter continuation is designed to estimate an optimal regularization parameter. Regularity is ensured by controlling the geometric properties of the deformation field. Overall, we arrive at a black-box solver. We study spectral properties of the Hessian, grid convergence, numerical accuracy, computational efficiency, and deformation regularity of our scheme. We compare the designed Newton-Krylov methods with a globalized preconditioned gradient descent. We study the influence of a varying number of unknowns in time. The reported results demonstrate excellent numerical accuracy, guaranteed local deformation regularity, and computational efficiency with an optional control on local mass conservation. The Newton-Krylov methods clearly outperform the Picard method if high accuracy of the inversion is required.Comment: 32 pages; 10 figures; 9 table

Affine Registration of label maps in Label Space

Two key aspects of coupled multi-object shape\ud analysis and atlas generation are the choice of representation\ud and subsequent registration methods used to align the sample\ud set. For example, a typical brain image can be labeled into\ud three structures: grey matter, white matter and cerebrospinal\ud fluid. Many manipulations such as interpolation, transformation,\ud smoothing, or registration need to be performed on these images\ud before they can be used in further analysis. Current techniques\ud for such analysis tend to trade off performance between the two\ud tasks, performing well for one task but developing problems when\ud used for the other.\ud This article proposes to use a representation that is both\ud flexible and well suited for both tasks. We propose to map object\ud labels to vertices of a regular simplex, e.g. the unit interval for\ud two labels, a triangle for three labels, a tetrahedron for four\ud labels, etc. This representation, which is routinely used in fuzzy\ud classification, is ideally suited for representing and registering\ud multiple shapes. On closer examination, this representation\ud reveals several desirable properties: algebraic operations may\ud be done directly, label uncertainty is expressed as a weighted\ud mixture of labels (probabilistic interpretation), interpolation is\ud unbiased toward any label or the background, and registration\ud may be performed directly.\ud We demonstrate these properties by using label space in a gradient\ud descent based registration scheme to obtain a probabilistic\ud atlas. While straightforward, this iterative method is very slow,\ud could get stuck in local minima, and depends heavily on the initial\ud conditions. To address these issues, two fast methods are proposed\ud which serve as coarse registration schemes following which the\ud iterative descent method can be used to refine the results. Further,\ud we derive an analytical formulation for direct computation of the\ud "group mean" from the parameters of pairwise registration of all\ud the images in the sample set. We show results on richly labeled\ud 2D and 3D data sets

Diffeomorphic density registration

In this book chapter we study the Riemannian Geometry of the density registration problem: Given two densities (not necessarily probability densities) defined on a smooth finite dimensional manifold find a diffeomorphism which transforms one to the other. This problem is motivated by the medical imaging application of tracking organ motion due to respiration in Thoracic CT imaging where the fundamental physical property of conservation of mass naturally leads to modeling CT attenuation as a density. We will study the intimate link between the Riemannian metrics on the space of diffeomorphisms and those on the space of densities. We finally develop novel computationally efficient algorithms and demonstrate there applicability for registering RCCT thoracic imaging.Comment: 23 pages, 6 Figures, Chapter for a Book on Medical Image Analysi

Registration and Fusion of Multi-Spectral Images Using a Novel Edge Descriptor

In this paper we introduce a fully end-to-end approach for multi-spectral image registration and fusion. Our method for fusion combines images from different spectral channels into a single fused image by different approaches for low and high frequency signals. A prerequisite of fusion is a stage of geometric alignment between the spectral bands, commonly referred to as registration. Unfortunately, common methods for image registration of a single spectral channel do not yield reasonable results on images from different modalities. For that end, we introduce a new algorithm for multi-spectral image registration, based on a novel edge descriptor of feature points. Our method achieves an accurate alignment of a level that allows us to further fuse the images. As our experiments show, we produce a high quality of multi-spectral image registration and fusion under many challenging scenarios

Retrieval and Registration of Long-Range Overlapping Frames for Scalable Mosaicking of In Vivo Fetoscopy

Purpose: The standard clinical treatment of Twin-to-Twin Transfusion Syndrome consists in the photo-coagulation of undesired anastomoses located on the placenta which are responsible to a blood transfer between the two twins. While being the standard of care procedure, fetoscopy suffers from a limited field-of-view of the placenta resulting in missed anastomoses. To facilitate the task of the clinician, building a global map of the placenta providing a larger overview of the vascular network is highly desired. Methods: To overcome the challenging visual conditions inherent to in vivo sequences (low contrast, obstructions or presence of artifacts, among others), we propose the following contributions: (i) robust pairwise registration is achieved by aligning the orientation of the image gradients, and (ii) difficulties regarding long-range consistency (e.g. due to the presence of outliers) is tackled via a bag-of-word strategy, which identifies overlapping frames of the sequence to be registered regardless of their respective location in time. Results: In addition to visual difficulties, in vivo sequences are characterised by the intrinsic absence of gold standard. We present mosaics motivating qualitatively our methodological choices and demonstrating their promising aspect. We also demonstrate semi-quantitatively, via visual inspection of registration results, the efficacy of our registration approach in comparison to two standard baselines. Conclusion: This paper proposes the first approach for the construction of mosaics of placenta in in vivo fetoscopy sequences. Robustness to visual challenges during registration and long-range temporal consistency are proposed, offering first positive results on in vivo data for which standard mosaicking techniques are not applicable.Comment: Accepted for publication in International Journal of Computer Assisted Radiology and Surgery (IJCARS