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27 April 1995 Visualization of multiattribute medical images
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In this paper we present two new algorithms for visualization of multi attribute medical images. The aim of the algorithms is to provide as much information as possible from the multi attribute image in one gray scale or color image without making any rigid classification into different tissue categories. Gray scale images are of special interest as the human eye is considerably more sensitive to spatial variations in intensity than chromatic variations. A nonlinear mapping is made from the original N-dimensional feature space to a M-dimensional output space where M < N and M (epsilon) {1..3}. Two different nonlinear projection methods are investigated for this purpose. We first present a method based on Sammon's nonlinear projection algorithm. Sammon's algorithm is a gradient descent strategy which aims at preservation of inter pattern distances by minimizing a cost function which measures the so-called Sammon stress. To reduce computational complexity, we first find a set of X reference vectors in feature space by using a standard clustering technique such as the c- means algorithm. Each feature vector in N-space is associated with its nearest reference vector which we then map to a lower dimensional M-space by using Sammon's algorithm. Finally, we introduce a new algorithm which can be used to create gray scale images when the number of reference vectors is sufficiently small. The original multi attribute data is then projected onto a curve in feature-space defined by an ordered set of reference vectors, and a gray scale is mapped along this curve. The optimal ordering of the reference vectors is found as a minimal cost permutation, where the cost function is a weighted sum of inter pattern distances in N space. Our algorithms are compared to principal component analysis (PCA) and a recently published algorithm based on Kohonens self organizing maps. The usefulness of the new algorithms are demonstrated for visualization of both reproducible synthetic images and real MR images.
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Erik N. Steen, Bjoern Olstad, and Gaute Myklebust "Visualization of multiattribute medical images", Proc. SPIE 2431, Medical Imaging 1995: Image Display, (27 April 1995);

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