Hyperspectral imaging for tumor detectionHyperspectral images of high spatial and spectral resolutions are employed to perform the challenging task of brain tissue characterization and subsequent segmentation for visualization of invivo images. Each pixel is a highdimensional spectrum. Working on the hypothesis of purepixels on account of high spectral resolution, we perform unsupervised clustering by hierarchical nonnegative matrix factorization to identify the pure pixel spectral signatures of blood, brain tissues, tumor and other materials. This subspace clustering was further used to train a random forest for subsequent classification of test set images constituent of invivo and exvivo images. Unsupervised hierarchical clustering helps visualize tissue structure in invivo test images and provides a interoperative tool for surgeons. The study also provides a preliminary study of the classification and sources of errors, eg specularity. Global overview
Hierarchical segmentation by H2NMF for joint unmixing & segmentationThe H2NMF algorithms aims at using the purepixel assumption for nonnegative matrix factorization. The algorithms performs clustering as well as spectralunmixing iteratively. Once a flat cluster is obtained the H2NMF uses the Nonnegative Least Squares (NNLS) to solve for the abundances/coefficients. The goal is to evaluate a rank2 approximation of the input pixelset (vectors) and find a division that is tradeoff between low approximation error and a balanced 2cluster. The cluster to be split next shall maximize : \[ \text{next}k = \arg\min_\mathcal{K} \sigma_1^2(X[:,\mathcal{K}^1]) + \sigma_1^2(X[:,\mathcal{K}^2])  \sigma_1^2(X[:,\mathcal{K}]) \] so as to produce the steepest decrease in the approximation error. This step is repeated recursively \(r1\) times, thus leading to \(r\)clusters. The subsets/clusters created are now further divided until a good rank1 matrix approximation are achieved at the leaves. Thus the H2NMF algorithm is trying to segment the hyperspectral image to achieve the best rank1 approximation of each segment w.r.t to its first principal component. MSRARepresentative purepixels are ones with minimal Mean removed spectral angle(MRSA) w.r.t \(u_k\) \[ phi(\mathbf{x},\mathbf{y}) = \frac{1}{\pi} \arccos \bigg( \frac{(x  \bar{x})^T(y  \bar{y})}{\ x  \bar{x}\^2 \ y  \bar{y} \^2}\bigg) \in [0,1] \] Abundances are evaluated by Nonnegative least squares (NNLS). Preprocessing tools for hyperspectral images
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