Prostate Cancer Diagnosis: A Geometric Approach Based on the Beer Index

Abstract

[eng] Convexity is a well-known property of sets, but it is still not clear how to measure the degree of convexity of a set. In this paper, we seek to measure the degree of convexity of a set making use of the Beer index, which is based on the visibility of its points. The aforesaid index involves the so-called visibility function, a continuous function that allows to compute the area of the region that sees every point. An application of this method for measuring the convexity degree to prostate cancer diagnosis is presented. Here, pathologists aim to determine whether a patient has a potential risk of cancer.Here, pathologists aim to determine whether a patient has a potential risk of cancer. In our case, the Beer index is used to determine the state of individual glands present in biopsy samples by determining the degree of convexity of the lumens. This is done to help pathologists to assess whether these glands are healthy or exhibit a cancerous state. Thus, the main objective in this work is to show that the Beer index captures and reflects a morphological feature which is inherent in prostatic glands and, therefore it allows the distinction between healthy and pathological glands.