Matching a reference image to a secondary image extracted from a database of transformed exemplars constitutes an important image retrieval task. Two related problems are: specification of a general class of discriminatory image features and an appropriate similarity measure to rank the closeness of the query to the database. In this paper we present a general method based on matching high dimensional image features, using entropic similarity measures that can be empirically estimated using entropic graphs such as the minimal spanning tree (MST). The entropic measures we consider are generalizations of the well known Kullback-Liebler (KL) distance, the mutual information (MI) measure, and the Jensen difference. Our entropic graph approach has the advantage of being implementable for high dimensional feature spaces for which other entropy-based pattern matching methods are computationally difficult. We compare our technique to previous entropy matching methods for a variety of continuous and discrete features sets including: single pixel gray levels; tag subimage features; and independent component analysis (ICA) features. We illustrate the methodology for multimodal face retrieval and ultrasound (US) breast image registration.

Quantitative evaluation of similarity between feature densities of images is an important step in several computer vision and data-mining applications such as registration of two or more images, retrieval and clustering of images. Previously we had introduced a new class of similarity measures based on entropic graphs to estimate Rènyi's α-entropy, α-Jensen difference divergence, α-mutual information and other divergence measures for image registration. Entropic graphs such as the minimum spanning tree (MST) and k-Nearest neighbor (kNN) graph allow the estimation of such similarity measures in higher dimensional feature spaces. A major drawback of histogram-based estimates of such measures is that they cannot be reliably constructed in higher dimensional feature spaces.In this paper, we shall briefly extrapolate upon the use of entropic graph based divergence measures mentioned above. Additionally, we shall present estimates of other divergence viz the GeometricArithmetic mean divergence and Henze-Penrose affinity. We shall present the application of these measures for pairwise image registration using features derived from independent component analysis of the images. An extension of pairwise image registration is to simultaneously register multiple images, a challenging problem that arises while constructing atlases of organs in medical imaging. Using entropic graph methods we show the feasibility of such simultaneous registration using graph based higher dimensional estimates of entropy measures. Finally we present a new non-linear correlation measure that is invariant to non-linear transformations of the underlying feature space and can be reliably constructed in higher dimensions. We present an image clustering experiment to demonstrate the robustness of this measure to non-linear transformations and contrast it with the clustering performance of the linear correlation coefficient.

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.

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Abstract-Registration of an image, the query or reference, to a database of rotated and translated exemplars constitutes an important image retrieval and indexing application which arises in biomedical imaging, digital libraries, georegistration, and other areas. Two important issues are the specification of a class of discriminatory and generalizable image features and determination of an appropriate image-dissimilarity measure to rank the closenes of the query image with respect to images in the database. The theoretically best set of features and dissimilarity measure are those which can be implemented with the lowest misregistration error rate-In this paper we study a method based on feature discrimination using feature coincidence tree and mutnal a-information measures of feature correlation. Feature coincidence trees represent the commonality between pairs of images using joint histograms of many simple features, or tags, which are organized in a data s t~c t n~ similar to that Amit and Geman's randomized trees for shape recognition. The mutual alpha-information meamre is a ranking discriminant applied to the joint histograms which is motivated by a large deviations framework for detection error rates. We illustrate the methodology in the context of registering ultrasound scans of homan breast images.

Image registration requires the specification of a class of discriminatory image features and an appropriate imagedissimilarity measure. Entropic spanning graphs produce a consistent estimator of feature entropy and divergence. We compare direct estimators with non-parametric "plugin" density estimators, on single pixels and independent image component feature vectors. We have also investigated a technique for minimum spanning tree construction with significantly lower memory and time complexity. On the basis of misregistration errors with decreasing SNR, the minimal graph entropy estimator can have better performance than indirect estimators. In general, misregistration errors are lower with higher dimensional ICA feature vectors as compared to single pixels.

Image registration is a difficult task especially when spurrious image intensity differences and spatial variations between the two images are present. To robustify image registration algorithms to such spurrious variations it can be useful to employ an image registration matching criteria on higher dimensional feature spaces. This paper will present an overview of our recent work on image registration using high dimensional image features and entropic graph matching criteria. New entropic graph estimates of information divergence measures will be presented. We will demonstrate the advantage of our approach for ultrasound breast image registration.

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