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\begin{document}
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% \title{PrPSeg: Universal Proposition Learning for Panoramic Renal Pathology Segmentation} 
% \maketitle

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\appendix
\section{Appendix}
%%%%%%%%% BODY TEXT - ENTER YOUR RESPONSE BELOW


\subsection{Evaluation with Classes Extension}
\label{newclass}
We provide an ablation study for two data extension scenarios: (1) adding 3 new sub-types; (2) introducing 4 new objects to our dataset. The proposed PrPSeg method is flexible to extend new classes by merely updating tokens and the adaptable proposition matrix, without changing the backbone network (\Cref{fig.pipeline}). All models are trained for 30 epochs on the 15-class dataset using the same codebase and experimental settings as those described in the main manuscript. In \Cref{tab:dataextension}, PrPSeg demonstrated superior performance compared to baseline methods across all seven new classes, maintaining the trend observed in Table.\textcolor{red}{3} of the manuscript.

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\begin{table}[bth]
% \begin{tabular}{llllllll}
\caption{
Ablation study with 7 extended classes. Dice similarity coefficient scores (\%) are reported.}
\begin{adjustbox}{width=0.45\textwidth}
\begin{tabular}{lcc|cccccccc}
\toprule
\multirow{1}{0.8in}{Method} & \multirow{1}{0.2in}{TDH}  & \multirow{1}{0.2in}{UPL} & \multicolumn{3}{c}{Regions} & \multicolumn{3}{c}{Functional units}  & \multirow{1}{0.2in}{Cells} & \multirow{1}{0.2in}{Mean} \\
\cmidrule(lr){4-6}
\cmidrule(lr){7-9}
 & & & Inn. Cor.& Mid. Cor. & Out. Cor. & Art. & PTC & MV & Smooth. & \\
\midrule
Swin-Unetr & &  & 34.54 & 31.26 & 34.20 & 53.92 &57.46  &55.03  & 60.18 & 49.66\\
Swin-Unetr  & \checkmark & & 45.25 & 41.89 & 70.22 & 52.27 & 60.95 & 52.17 & 62.45  & 56.67 \\
\midrule
Omni-Seg  & & &39.84 & 43.98 & 70.96 & 47.33 & 63.23  & 48.67 & 56.91 & 53.86 \\
Omni-Seg  & \checkmark &  & 51.16 & 46.46 & 70.53 & 57.89 & 62.63 & 61.93  & 64.41 & 60.43\\
PrPSeg (Ours)  & \checkmark & \checkmark & \textbf{52.69} & \textbf{49.86} & \textbf{71.13} & \textbf{59.51} & \textbf{64.74} & \textbf{63.09} &  \textbf{64.91} & \textbf{61.74} \\
\bottomrule
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\text{*TDH is Token-based Dynamic Head}
\text{*UPL is Universal Proposition Learning}
% \text{*TDH is Token-based Dynamic Head; Pre. is Pre-trained Weights; UPL is Universal Proposition Learning.}\\
% \text{*Inn. is inner; Mid. is middle; out. is Outer; Cor. is cortex;}\\
% \text{*Art. is arteries; PTC is peritublar capillaries; } \\
% \text{*MV is micro-vasculature; Smooth. is smooth muscle.} \\
\label{tab:dataextension}
\end{table}


\subsection{Novelty Clarification}
The contributions of this paper are threefold: (1) A comprehensive universal proposition matrix is proposed to provide a simple and adaptable method to model the predominantly overlooked intricate spatial interrelations and class relationships among objects from clinical knowledge. This proposition matrix allows us to flexibly add unseen new classes via minimal changes (only modify tokens and this matrix); (2) The development of a token-based dynamic head in a single network architecture, improving partial label image segmentation. The backbone of the proposed PrPSeg network remains unchanged when new class tokens are introduced for new datasets, enabling the reuse of model weights on incomplete datasets. (3) The formulation of an anatomical loss function that quantifies the inter-object relationships across the kidney. %Since the universal proposition matrix in (1) and the anatomical loss function in (3) contribute in different directions, we demonstrate them separately.

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\captionof{figure}{
\textbf{The innovation of the pipeline when data is extended} -- The proposed PrPSeg method is flexible to extend new classes by merely updating tokens and the adaptable proposition matrix, without changing the backbone network.} 

\label{fig.pipeline} 
\end{figure}

\subsection{Comparison to Related Work and Contributions Beyond Medical Imaging}
Several recent methods that utilize hierarchical information for semantic segmentation~\cite{Li_2022_CVPR,ke2022hsg} or classificationand prediction~\cite{chen2022scaling}. Our method's innovations, beyond previous work, include: (1) Emphasizing pixel-wise anatomical and spatial relationships between objects, rather than solely taxonomy-based relationships (e.g., a glomerulus is located inside the cortex, not merely as a subset or sharing the cortex's morphology); (2) Introducing a hierarchical relationship with class tokens and scale tokens across multiple resolutions (regions at 5$\times$, cells at 20$\times$) to provide greater flexibility between classes and scales, as opposed to a uniform resolution in natural images; (3) Enhancing the extensibility and reusability in model design for data expansion. The proposed method aims to provide a pipeline that is scale-aware, adaptive, and anatomically aware, transitioning from the clinical domain to potential applications in incremental learning and multi-view, multi-scale learning beyond the medical field. 

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\end{document}

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