Grading of invasive breast carcinoma through Grassmannian VLAD encoding

In this paper we address the problem of automated grading of invasive breast carcinoma through the encoding of histological images as VLAD (Vector of Locally Aggregated Descriptors) representations on the Grassmann manifold. The proposed method considers each image as a set of multidimensional spatially-evolving signals that can be efficiently modeled through a higher-order linear dynamical systems analysis. Subsequently, each H&E (Hematoxylin and Eosin) stained breast cancer histological image is represented as a cloud of points on the Grassmann manifold, while a vector representation approach is applied aiming to aggregate the Grassmannian points based on a locality criterion on the manifold. To evaluate the efficiency of the proposed methodology, two datasets with different characteristics were used. More specifically, we created a new medium-sized dataset consisting of 300 annotated images (collected from 21 patients) of grades 1, 2 and 3, while we also provide experimental results using a large dataset, namely BreaKHis, containing 7,909 breast cancer histological images, collected from 82 patients, of both benign and malignant cases. Experimental results have shown that the proposed method outperforms a number of state of the art approaches providing average classification rates of 95.8% and 91.38% with our dataset and the BreaKHis dataset, respectively.