Image staining and differential diagnosis of ultrasound scans based on the Mahalanobis distance

Abstract

The covariance matrices associated with each state of health or disease from a previous study are used as the basis of an image staining display technique for aid in quantitative differential diagnosis. A state of health or disease is chosen by the clinician: this selects the covariance matrix from the data base. A region of interest (ROI) is then scrolled through an abdominal B-scan. For each position of the ROI a point in the four-dimensional feature space is calculated. A natural measure of the distance of this point from the center of mass (multivariate mean) of the disease class is calculated in terms of the covariance matrix of this class; this measure is the Mahalanobis distance. The confidence level for acceptance or rejection of the hypothesized disease class is obtained from the probability distribution of this distance, the T(2) probability law. This confidence level is color coded and used as a color stain that overlays the original scan at that position. The variability of the calculated features is studied as a function of ROI size, or the spatial resolution of the color coded image, and it is found that for an ROI in the neighborhood of 4 cm(2) most of the variability due to the finite number of independent samples (speckles) is averaged out, leaving the "noise floor" associated with inter- and intra-patient variability. ROIs on the order of 1 cm(2) may result with technical advances in B-scan resolution. A small number of points on organ boundaries are entered by the user, to fit with arcs of ellipses to be used to switch between organ (liver and kidney) data bases as the ROI encounters the boundary. By selecting in turn various state-of-health or state-of-disease databases, such images of confidence levels may be used for quantitative differential diagnosis. The method is not limited to ultrasound, being applicable in principle to features obtained from any modality or multimodality combination.