Paper Summary

The point set registration problem can be described as: for two finite size point sets ${M, S}$, where $M$ represents the moving “model” set and $S$ represents the fixed “scene” set, and both $M$ and $S$ are assumed to be subsets of a finite dimensional real vector space $\mathbb{R}^d$, and they can be of different sizes. The registration task involves estimating a mapping from $\mathbb{R}^d$ to $\mathbb{R}^d$ which yields the best alignment between the two sets $M$ and $S$. An important consideration here is that apart from the set of points being treated as a collection of isolated unstructured points, there is no assumption of additional information about the points (such as mesh structure, labels, features, etc.). ...

The authors propose using an implicit shape representation for the source and the target shapes. The Euclidean signed distance transform is used to model the shape of interest as the zero level set of a distance function. Let $\Phi: \Omega \to R^+$ denote the distance transform of a shape $S$. The shape defines a partition of the image domain $\Omega$ - the region enclosed by $S$ is denoted by $[R_S]$ and the background region is denoted by $[\Omega - R_S]$. Using signed Euclidean distance transform, we have ...

Mutual Information Given two discrete random variables $A$ and $B$ with pardinal probability distributions $p_A(a)$ and $p_B(b)$ and joint probability distribution $p_{AB}(a,b)$, the two variables are said to be statistically independent is $p_{AB}(a,b) = p_A(a).p_B(b)$, and are said to be maximally dependent if they are related by a one-to-one mapping $T$ such that $p_A(a) = p_B(T(a)) = p_{AB}(a, T(a))$. The mutual information $I(A,B)$ represents the degree of dependence of A and B ...

Introduction This paper presents an algorithm for non-rigid registration formulated as a discrete labeling problem. The authors note that the two major contemporary works for image registration had inherent flaws - Free-Form Deformation (FFD) based model was crippled by the choice of the set of control points to represent the deformation, while Demons Based Method did not penalize large displacements of pixels and was highly sensitive to local artifacts. The authors demonstrate the proposed algorithm’s superior performance for 2D and 3D registration compared to the two aforementioned algorithms. ...

Introduction This paper presents an algorithm for non-rigid registration of contrast-enhanced breast MR image sequences. The authors propose a model incorporating both global transformations (represented by affine transformation) as well as local transformation (free-form deformation represented using B-splines). Normalized mutual information was used as the similarity measure across images. The authors demonstrate the algorithm’s superior performance compared to the rigid and affine registration techniques. ...