Entropic Graphs for Registration

Abstract

In many applications, fusion of images acquired via two or more sensors requires image alignment to an identical pose, a process called image registration. Image registration methods select a sequence of transformations to maximize an image similarity measure. Recently a new class of entropic-graph similarity measures was introduced for image registration, feature clustering and classification. This chapter provides an overview of entropic graphs in image registration and demonstrates their performance advantages relative to conventional similarity measures. In this chapter we introduce : techniques to extend image registration to higher dimension feature spaces using Rényi's generalized «-entropy. The «-entropy is estimated directly through continuous quasi additive power weighted graphs such as the minimal spanning tree (MST) and k-Nearest Neighbor graph (kNN). Entropic graph methods are further used to approximate similarity measures like the « mutual information, «-Jensen divergence, Henze-Penrose affinity and Geometric-Arithmetic mean affinity. These similarity measures offer robust registration benefits in a multisensor environment. Higher dimensional features used for this work include basis functions like multidimensional wavelets and independent component analysis (ICA). Registration is performed on a database of multisensor satellite images. Lastly, we demonstrate the sensitivity of our approach by matching local image regions in a multimodal medical imaging example.

Self-similarity Weighted Mutual Information: A New Nonrigid Image Registration Metric

“…Minimal spanning tree (MST) [12] and k-nearest neighbor (kNN) [11,15] are among different methods for estimating α-MI from multi-feature samples. With N samples, the complexities of constructing MST and kNN graphs are O(N 2 log N ) and O(N log N ) respectively [14]. Therefore, we choose kNN.…”

“…α-mutual information (α-MI) similarity metric [11,12,13,14,15] is also graph based and has been recently shown to outperform MI in nonrigid registration applications. Therefore, we choose to incorporate self-similarity into this powerful registration framework.…”

Quasi-supervised learning for biomedical data analysis

“…Note that in such a minimum spanning tree, the mixed dataset samples that share edges only with other mixed dataset samples would be the ones that reduce a graph-theoretic estimate of the Henze-Penrose affinity between the datasets [12,16,13]. Note also that this strategy produces only a single false alarm rate and a single detection rate as the detection rule cannot be varied by changing a threshold as in the previous two cases, though a receiver operating characteristics curve can be constructed by joining the paired false alarm and detection rates with the origin on one side, and paired unit false alarm and detection rates on the other.…”

“…The significance of a as the specificity threshold is in ensuring that no more than a fraction a of samples in either specific group is included in that group erroneously. A second measure of class overlap can be defined in inspiration from the Henze-Penrose affinity [12,13] that computes the integral Z x 2p 1 ðxÞp 2 ðxÞ p 1 ðxÞþp 2 ðxÞ dx for any given probability distributions p 1 (x) and p 2 (x), and goes to 1 when p 1 (x) ¼p 2 (x) for all x. We define the measure M HP-like (x) for a sample x as a variant of the integrand above by…”

Multi-feature Statistical Nonrigid Registration Using High-Dimensional Generalized Information Measures

“…Whereas mutual information and its variations arise as a first choice [8], generalized information measures, such as f -informations [11,12] and Jensen f -divergences [9], have been shown to be relevant alternatives in specific clinical contexts.…”