\section{Introduction}
\label{sec:intro}




Histopathology evaluation of hematoxylin and eosin (H\&E)-stained tissue specimens through microscopic examination is pivotal in the diagnosis and prognosis of diseases. 
Through evaluation of tissue architecture, cell morphology, and biomarker expression, pathologists can accurately diagnose conditions, assess disease progression, and inform treatment decisions. 
However, traditional manual analysis of histopathological specimens by specially trained pathologists is labor-intensive, expensive, subjective, and prone to inter-rater variability~\cite{Karimi2020_TMAdata_6path}, which can impact diagnostic consistency and accuracy.
As the volume of digital pathology images continues to grow~\cite{Mukhopadhyay2018-ln}, there is a critical need for automated analysis. 
Machine learning (ML), and in particular deep learning based on computer vision techniques, have shown promising performance on histopathological analysis tasks such as classification~\cite{Bulten2022-wk,Silva-Rodriguez2020-xn,Kather2019-xy,Nir2018-kn,Han2017-hg}, segmentation~\cite{Wilm2022-gh,Nir2018-kn}, and analysis~\cite{Veta2019-pi,Aubreville2023-mb}.

Despite the promise of ML in digital pathology, several significant limitations remain~\cite{Madabhushi2016-md}. 
In particular, ML models can struggle with the inherent variability and complexity of histopathology images, which lack explicit meaningful orientation and exhibit diverse staining patterns, tissue structures, and cellular arrangements. 
Many models are also data-intensive, requiring extensively annotated training sets that are time-consuming and costly to produce. 
Thus, while supervised learning approaches have shown success, they are limited by the quality and quantity of labeled data available and might not generalize well to new, unseen datasets.

In this work, we address these limitations and make the following contributions:
\begin{inparaenum}[(1)]
    \item apply equivariant feature learning to learn robust histopathologic imaging biomarkers that are resilient to rotations; 
    \item develop an unsupervised learning pipeline to perform equivariant biomarker-based segmentation in the absence of manual ground-truth annotations; and
    \item validate our approach on a prostate tissue micro-array (TMA) dataset.
\end{inparaenum}

