A statistical methodology for mammographic density detection

Abstract

A statistical methodology is presented based on a chi-square probability analysis that allows the automated discrimination of radiolucent tissue (fat) from radiographic densities (fibroglandular tissue) in digitized mammograms. The method is based on earlier work developed at this facility that shows mammograms may be considered as evolving from a linear filtering operation where a random input field is passed through a 1/f filtering process. The filtering process is reversible which allows the solution of the input field with knowledge obtained from the raw image (the output). The input field solution is analogous to a prewhitening technique or deconvolution. This field contains all the information of the raw image in a much simplified format that can be approximated and analyzed with parametric methods. In the work presented here evidence indicates that there are two random events occurring in the input field with differing variances: (1) one relating to fat tissue with the smaller variance, and (2) the second relating to all other tissue with the larger variance. A statistical comparison of the variances is made by scanning the image with a small search window. A relaxation method allows for making a reliable estimate of the smaller variance which is considered as the global reference. If a local variance deviates significantly from the reference variance, based on chi-square analysis, it is labeled as nonfat; otherwise it is labeled as fat. This statistical test procedure results in a region by region continuous labeling of fat and nonfat tissue across the image. In the work presented here, the emphasis is on the methodology development with supporting preliminary results that are very encouraging. It is widely accepted that mammographic density is a breast cancer risk factor. An important application of this work is to incorporate density-based risk analysis into the ongoing statistical-based detection work developed at this facility. Additional applications include risk analysis dependent on either percentages or total amounts of fat or dense tissue. This work may be considered as the initial step in introducing many of the known breast cancer risk factors into the actual image data analysis.