Statistical fractal border features for MRI breast mass images

MRI has been proposed as an alternative method to mammography for detecting and staging breast cancer. Recent studies have shown that architectural features of breast masses may be useful in improving specificity. Since fractal dimension (fd) has been correlated with roughness, and border roughness is an indicator of malignancy, the fd of the mass border is a promising architectural feature for achieving improved specificity. Previous methods of estimating the fd of the mass border have been unreliable because of limited data or overly restrictive assumptions of the fractal model. We present preliminary results of a statistical approach in which a sample space of fd estimates is generated from a family of self-affine fractal models. The fd of the mass border is then estimated from the statistics of the sample space. The fd is estimated using fractal interpolation function models (FIFM), a method which has been previously applied to the analysis of bones and blood cells. The method uses a combinatoric approach of testing a large number of boundary segments and identifying those segments which are approximately self-affine. Self-affine fractal models with known fd values are constructed for each of the approximately self-affine boundary segments. The means of the fd values for the models are used as features for distinguishing the benign from malignant masses. Performance of the fd feature is evaluated by comparing the classification effectiveness of five architectural features generated by expert observers (expert features) with the effectiveness of the expert features in combination with fd. Performance measures include the area of the ROC curve between sensitivities 90% and 100% (the portion of the ROC area which is considered clinically significant) and improvement to specificity at the 95% sensitivity level. Classification effectiveness is computed using a 3-layer back-propagation artificial neural network with a minimal number of nodes. Test images are biopsy-proven MRI images of focal breast masses. We present experiment results demonstrating that the performance of a combination of fd and expert features is superior to the performance of the expert features alone. We also present evidence that the sample-space approach provides stability of the estimate with respect to changes in algorithm parameter settings; such robustness has not been demonstrated by other fractal algorithms for data-limited applications. The FIFM features may be useful in improving the performance of computer-aided-diagnosis (CAD) systems that use neural networks or other classifiers to combine several features into numeric measures of pathology.