Mammogram analysis using two-dimensional autoregressive models: Sufficient or not?

Abstract

Two-dimensional (2 - D) autoregressive (AR) models have been used as one of the methods to characterise the textures of tumours in mammograms. Previously, the 2 - D AR model coefficients were estimated for the block containing the tumour and the blocks in its 3 × 3 neighbourhood. In this paper, the possibility of having the estimated set of AR model coefficients of the block containing the tumour as a unique set of AR model coefficients for the entire mammogram is looked into. Based on the information given from the MiniMammography database, the possible number of blocks of the same size of the block containing the tumour is obtained from the entire mammogram and for each block a set of AR model coefficients is estimated using a method that combines both the Yule-Walker system of equations and the Yule-Walker system of equations in the third-order statistical domain. These sets of AR model coefficients are then compared. The simulation results show that 98.6% of the time we can not find another set of AR model coefficients representing the blocks of pixels in the possible neighbourhood of the entire mammogram for the data (95 mammograms with 5 of them having two tumours) available in the MiniMammography database. © Springer-Verlag Berlin Heidelberg 2005.