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    Registration of Image Cubes Using Multivariate Mutual Information

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    Abslrad -A new method for simultaneously registering a collection of multispectral or hyperspectral images (spectral image cubes) using mutual inlormation is presented. In this paper, %\e derive a new algorithm based on mutual optimization between pairs of images and extend it to any finite number of images. We present results on the convergence and stability of the new algorithm, showing that the algorithm registers each image to a weighted average of its alignment with every other image. This method has application to other multi-image applications as well. INTRODUCTTON When registering image pairs, a common approach is to designate one image as the reference and apply a spatial shift, rotation, or warping function to the second image in order to bring it into alignment with the reference. Some measure of similarity between the images is used to determine when the optimal alignment has occurred. This measure might be based on point or boundary matching, the cross-correlation between the images, or some other statistical measure. A good survey of these image registration techniques can be found in [I]. Three related phenomena tend to impair the success of these similarity measures when registering multispectral or hyperspectral imagery. The fmt is a general lack of similarity between widely separated wavelengths. This is particularly pronounced when comparing images collected at wavelengths shorter than 4-5 pm to those at longer wavelengths. This is because image contrasts are primarily due to reflectance of solar energy in the shorter wavelengths (reflectance bands) and primarily due to thermal emissions in the long wave infrared (LWIR, also referred to as thermal bands). A second impairment to registration occurs because thermal emissions are often weak leading to very subtle contrast variations. We will address these phenomena later in the paper. The thud is a phenomenon, known as contrast reversal (or contrast inversion), is caused by differences in the reflectance of various materials as a function of wavelength. To illustrate this, refer to A great deal of literature exists that describes correlationbased registration methods. These methods are based on using the correlation coefficient between corresponding pixels in two images as measure of similarity C(u,l.)= where tii and vi represent the values for each pixel in two images U and V, and i is the index of each pixel in the image. The difficulty with correlation-based similarity measures is that they are degraded by contrast reversals. In extreme 0-7803-
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