Cancer Cell Profiling Using Image Moments and Neural Networks with Model Agnostic Explainability: A Case Study of Breast Cancer Histopathological (BreakHis) Database

With the evolution of modern digital pathology, examining cancer cell tissues has paved the way to quantify subtle symptoms, for example, by means of image staining procedures using Eosin and Hematoxylin. Cancer tissues in the case of breast and lung cancer are quite challenging to examine by manual expert analysis of patients suffering from cancer. Merely relying on the observable characteristics by histopathologists for cell profiling may under-constrain the scale and diagnostic quality due to tedious repetition with constant concentration. Thus, automatic analysis of cancer cells has been proposed with algorithmic and soft-computing techniques to leverage speed and reliability. The paper’s novelty lies in the utility of Zernike image moments to extract complex features from cancer cell images and using simple neural networks for classification, followed by explainability on the test results using the Local Interpretable Model-Agnostic Explanations (LIME) technique and Explainable Artificial Intelligence (XAI). The general workflow of the proposed high throughput strategy involves acquiring the BreakHis public dataset, which consists of microscopic images, followed by the application of image processing and machine learning techniques. The recommended technique has been mathematically substantiated and compared with the state-of-the-art to justify the empirical basis in the pursuit of our algorithmic discovery. The proposed system is able to classify malignant and benign cancer cell images of 40× resolution with 100% recognition rate. XAI interprets and reasons the test results obtained from the machine learning model, making it reliable and transparent for analysis and parameter tuning.

Stable recovery of planar regions with algebraic boundaries in Bernstein form

We present a new method for the stable reconstruction of a class of binary images from a small number of measurements. The images we consider are characteristic functions of algebraic domains, that is, domains defined as zero loci of bivariate polynomials, and we assume to know only a finite set of uniform samples for each image. The solution to such a problem can be set up in terms of linear equations associated to a set of image moments. However, the sensitivity of the moments to noise makes the numerical solution highly unstable. To derive a robust image recovery algorithm, we represent algebraic polynomials and the corresponding image moments in terms of bivariate Bernstein polynomials and apply polynomial-generating, refinable sampling kernels. This approach is robust to noise, computationally fast and simple to implement. We illustrate the performance of our reconstruction algorithm from noisy samples through extensive numerical experiments. Our code is released open source and freely available.