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Abstract
AbstractQuantitative 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 and 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 article, 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 Geometric‐Arithmetic 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 nonlinear correlation measure that is invariant to nonlinear 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 nonlinear transformations and contrast it with the clustering performance of the linear correlation coefficient. © 2007 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 16, 130–145, 2006
Highlights
The accuracy of image matching algorithms critically depend on two factors: the selection of a highly discriminating image feature space and the choice of similarity measure to match these image features
As compared to previous work in which estimated Jensen differences were used for registration, these divergence measures have the advantage of invariance to re-parameterization of the feature space
Our numerical evaluations show that these divergence estimators outperform previous approaches to image registration
Summary
The accuracy of image matching algorithms critically depend on two factors: the selection of a highly discriminating image feature space and the choice of similarity measure to match these image features These factors are especially important when some of the intensity differences are due to the sensor itself, as arises in registration of speckle-limited images or when images of objects exhibit non-linear intensity relationship. To overcome limitations of linear correlation, Viola and Wells [1] and Maes et al [2] devised a similarity measure based on the Kullback-Liebler [3] information divergence between the joint feature density and the product of the marginal densities This is the mutual information (MI) measure and it quantifies the non-linear correlation between images as the amount of statistical dependency in the underlying joint probability distribution functions (pdf); where the pdf is estimated using pixel intensity histograms.
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