Perception-based Visualization of High-Dimensional Medical Images Using Distance Preserving Dimensionality Reduction

A method for visualizing high dimensional medical image data is proposed. The method operates on images in which each pixel contains a high dimensional vector, e.g. a time activity curve (TAC) in a dynamic positron emission tomography (dPET) image, or a tensor, as is the case in diffusion tensor magnetic resonance images (DTMRI). A nonlinear mapping reduces the dimensionality of the data to achieve two goals: Distance preservation and embedding into a perceptual color space. We use multidimensional scaling distance preserving mapping to render similar pixels (e.g. DT or TAC pixels) with perceptually similar colors. The 3D CIELAB perceptual color space is adopted as the range of the distance preserving mapping, with a final similarity transform mapping colors to a maximum gamut size. Similarity between pixels is determined analytically as geodesics on the manifold of pixels or approximated using manifold learning techniques. In particular, dissimilarity between DTMRI pixels is evaluated via a LogEuclidean Riemannian metric respecting the manifold of the rank 3, 2nd order positive semi-definite DTs. Dissimilarity between TACs is approximated via ISOMAP. We demonstrate our approach via artificial highdimensional data, as well as clinical DTMRI and dPET images. Our results demonstrate the effectiveness of our approach in capturing, in a perceptually meaningful way, important structures in the data.