\section{Relative Work}
\label{sec:relativework}

\subsection{Renal Pathology Segmentation}
\label{subsec:segmentation}
Recent advancements in deep learning have positioned Convolutional Neural Networks (CNNs) and Transformer-based networks as leading methods for image segmentation, particularly in renal pathology~\cite{feng2022artificial,hara2022evaluating}. Innovations in this field have ranged from CNN cascades for sparse tissue segmentation~\cite{gadermayr1708cnn} to the deployment of AlexNet for pixel-wise classification and detection~\cite{gallego2018glomerulus}. Notably, multi-class learning approaches using SegNet-VGG16 and DeepLab v2 have been implemented for detecting various glomerular structures and renal pathologies~\cite{bueno2020glomerulosclerosis,lutnick2019integrated}. In addition, instance segmentation and Vision Transformers (ViTs) have begun to find applications in this domain~\cite{johnson2019automatic,nguyen2021evaluating, gao2021instance,yan2023self}.

However, most existing methods focus on segmenting single tissue types or multiple structures at similar levels, such as glomeruli and tubules~\cite{gupta2018iterative,kannan2019segmentation, marechal2022automatic}. Comprehensive approaches capable of spanning from tissue region level to cell level remain unexplored. Moreover, some methods prioritize disease-positive region segmentation over a holistic understanding of kidney morphology~\cite{jing2022segmentation,lin2022adversarial}.

Recent methods utilize hierarchical information for semantic segmentation~\cite{Li_2022_CVPR,ke2022hsg} or classification and prediction~\cite{chen2022scaling}. However, these methods primarily focus on class-based relationships between objects. While all objects have a uniform resolution in natural images, this approach neglects the emphasis on pixel-wise anatomical and spatial relationships at multiple resolutions in kidney datasets.

Building upon these insights, our work introduces a token-based approach, leveraging class-specific and scale-specific tokens. This method is designed to capture heterogeneous features and employs semi-supervised learning to understand pixel-wise spatial relationships across multiple scales, achieving panoramic segmentation in renal pathology.

\subsection{Dynamic Single Network}
\label{subsec:dynamicnetwork}

\begin{figure*}[t]
\centering 
\includegraphics[width=1\linewidth]{{fig/Anatomy.pdf}}
\caption{
\textbf{Universal proposition matrix with anatomy loss -- }
This figure shows the key innovation of the proposed method. (a) Multi-scale (region-level, unit-level, and cell-level) hierarchical semantic taxonomy is presented. (b) The proposed PrPSeg mathematically models the semantic taxonomy as a universal proposition matrix, which delineates robust constraints and relationships between anatomical entities. (c) We further encode the universal proposition matrix as a novel anatomy loss function, designed to operationalize the affirmative and negatory relationships inherent in kidney anatomy.}
\label{fig.anatomy} 
\end{figure*}


While multi-head single network designs have been proposed for multi-class renal pathology segmentation~\cite{gonzalez2018multi,fang2020multi,bouteldja2021deep,chen2019med3d}, they often require dense multi-class annotations. Given the labor-intensive nature of such annotations, pathology data is frequently partially labeled. Additionally, forming spatial correlations, such as subset/superset relationships, remains a challenge in multi-class uplsegmentation frameworks.

Recent developments in dynamic neural networks have paved the way for more comprehensive segmentation using single multi-label networks, even with partially labeled data~\cite{zhang2021dodnet,deng2023omni}. These networks dynamically generate neural network parameters, adapting to various imaging contexts. However, they predominantly rely on binary segmentation approaches and do not fully integrate spatial correlations in their training processes.


Our work extends these concepts by translating spatial correlations from anatomy into a programming model, represented as a matrix coupled with an anatomy-based loss for semi-supervised learning. This strategy effectively harnesses the affirmative and negatory relationships in kidney anatomy, enabling detailed and comprehensive segmentation. It enhances the model’s ability to distinguish and classify the complex structures within kidney, representing a significant advancement in the field.
