Two-point correlation as a feature for histology images: Feature space structure and correlation updating

The segmentation of tissues in whole-slide histology images is a necessary step for the morphological analyses of tissues and cellular structures. Previous works have demonstrated the potential of two-point correlation functions (TPCF) as features for tissue segmentation, however the feature space is not yet well understood and computational methods are lacking. This paper illustrates several fundamental aspects of TPCF feature space and contributes a fast algorithm for deterministic feature computation. Despite the high-dimensionality of TPCF feature space, the features corresponding to different tissues are shown to be characterized by low-dimensional manifolds. The relationship between TPCF and the familiar co-occurrence matrix is highlighted, and it is shown that costly cross correlations are not necessary to achieve an accurate segmentation. For computation, the method of correlation updating, based on the linearity of the correlation operator, is proposed and shown to achieve up to a 67X speedup over frequency domain computation methods. Segmentation results are demonstrated on multiple tissues and natural texture images.