Registration of Images With Varying Topology Using Embedded Maps

Abstract

In medical images, intensity changes caused by certain pathology can change the topology of image level-sets and are thus commonly referred to as topological changes. Topological changes cause false deformation in existing deformable registration algorithms, which in turn leads to unreliable observations in the clinical study that relies on the deformation fields, such as deformation based morphometry (DBM). In this work, we develop a new deformable registration algorithm for images with topological changes. In our proposed algorithm, 3D images are embedded as 4D surfaces in a Riemannian space. The registration is therefore conducted as a surface evolution, which is modeled by a diffusion process. Our algorithm differs from existing methods in the sense that it takes an a-priori estimation of areas with topological change as an additional input and generates dense deformation vector fields which are free of false deformation. In particular, the output of our algorithm is composed of a diffeomorphic deformation field and an intensity displacement which corrects intensity difference caused by topological changes. By conducting multiple sets of experiments, we demonstrate that our proposed algorithm is capable of accurately registering images with considerable topological changes. More importantly, the resulting deformation field is not impacted by topological changes, i.e., there is no false deformation.

The Alzheimer's Disease Neuroimaging Initiative: A review of papers published since its inception

“…This multiatlas propagation with enhanced registration approach was found to create accurate atlas-based segmentations and was more robust in the presence of pathology than previous approaches. Li et al [229] presented another approach to account for ventricular expansion and other variations in tissue composition that occur in older subjects, such as WM hyper- and hypo-intensities, and changes in subcortical shape and cortical thickness. They employed a deformable registration algorithm that embeds 3D images in surfaces in a 4D Reimannian space to topological changes caused by false deformation.…”

Abnormality Detection via Iterative Deformable Registration and Basis-Pursuit Decomposition

“…Further, it is not clear how to balance the geometric deformation and intensity change in the Riemannian metric. In [17], images are embedded as surfaces in ${\mathrm{ℝ}}^4$ Riemannian space, and registration is performed as a surface revolution that matches one embedded image to another, again accounting for both shape and intensity changes necessary to match them. As in CFM, an a priori estimate of the pathological regions is required in order to attain a robust deformation field.…”

Diffeomorphic Registration With Intensity Transformation and Missing Data: Application to 3D Digital Pathology of Alzheimer's Disease

“…However, throughout the majority of images, transformations are diffeomorphic, and we have chosen to work in the computational anatomy random orbit model to preserve properties that are useful for morphometry in addition to registration, such as the embedding of human anatomy into a metric space. Metamorphosis-based models (Miller et al, 2002;Li et al, 2011;Nithiananthan et al, 2012) allow image intensity to vary in certain regions to match anomalies, while maskbased models (Periaswamy and Farid, 2006;Sdika and Pelletier, 2009;Vidal et al, 2009;Chitphakdithai and Duncan, 2010b) or 9 manually or automatically ignore these anomalies. Our method leverages the strengths of these last two, modeling both nonmonotonic image intensity variation and masking in a generative statistical framework.…”