Abstract
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.
Highlights
Breast cancer is the second most common cancer in the world and by far the most frequent cancer among women [1, 2]
We propose a novel approach for the grading of invasive breast carcinoma, which considers each histological image as a set of multidimensional spatially-evolving signals that can be efficiently represented as a cloud of points in a non-Euclidean space, such as a Grassmann manifold
The contributions of this paper are summarized as follows: i) We introduce a new methodology for the modelling of static breast cancer histological images through higher-order linear dynamical systems analysis. ii) We demonstrate that each histological image can be Grading of invasive breast carcinoma through Grassmannian VLAD encoding represented as a cloud of points on the Grassmann manifold and we propose the VLAD encoding of each image on the non-Euclidean space. iii) To evaluate the efficiency of the proposed methodology, we created a new dataset of 300 annotated images of grades 1–3 [11], while we provide experimental results using the well-known BreaKHis dataset [12, 13] containing 7,909 breast histological images of both benign and malignant cases
Summary
Breast cancer is the second most common cancer in the world and by far the most frequent cancer among women [1, 2]. According to the American Cancer Society, it is estimated that, only in 2017, there will be approximately 255,180 new cases of invasive breast cancer and around 41,070 deaths from breast cancer (for both women and men) in the U.S [3]. During the visual examination of the biopsy specimen of the tissue, pathologists look for certain features that can help them predict disease prognosis, i.e., how likely the cancer is to grow and spread. These features include the spatial arrangement of the cells, morphological characteristics of the nuclei (nuclear pleomorphism), whether they form tubules (tubule formation) and how many.
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