\section{Result}
\label{sec:results}

We conducted a comparative analysis of our proposed Universal Proposition Learning approach against various baseline models. These models include multi-class segmentation architectures such as (1) U-Nets~\cite{gonzalez2018multi}, (2) DeepLabV3~\cite{lutnick2019integrated}, (3) Residual-U-Net~\cite{salvi2021automated}, (4) a CNN-based multi-class kidney pathology model~\cite{bouteldja2021deep}, (5) Omni-Seg~\cite{deng2023omni}, (6) Segmenter-ViT/16~\cite{strudel2021segmenter}, (7) SegFormer~\cite{xie2021segformer}, (8) Unetr~\cite{hatamizadeh2022unetr}, and (9) Swin-Unetr~\cite{hatamizadeh2021swin}.

\subsection{Panoramic Segmentation Performance}
\label{subsec:segmentationresult}

Table \textcolor{red}{2} and \Cref{Fig.Qualitative} showcase the results from an 8-class segmentation evaluation. Table \textcolor{red}{2} demonstrates that our proposed method, PrPSeg, surpasses baseline models in most evaluated metrics. \Cref{Fig.Qualitative} further highlights the qualitative superiority of our approach, evidenced by reduced instances of false positives, false negatives, and morphological errors. The Dice similarity coefficient (Dice: \%, the higher, the better) was employed as the primary metric for quantitative performance assessment. The results indicate that, while multi-head designs struggle with managing spatial relationships between objects (e.g., subset/superset relationships between the capsule and tuft), the dynamic-head paradigm exhibits superior performance compared to other methods.


\subsection{Ablation Study}
\label{subsec:ablationstudy}
\Cref{tab:differentdesigns} showcases the enhancements brought about by our proposed token-based design and learning strategy across two different backbone architectures. The results indicate that the token-based dynamic head design boosts the model's performance in segmenting all levels of objects. With the integration of the token-based dynamic head architecture and universal proposition learning, the proposed method exhibited superior performance across all considered metrics.

We also provide an ablation study for two data extension scenarios in the Appendix (\textcolor{red}{A.1}). The proposed PrPSeg method is flexible to extend to new classes by merely updating tokens and the adaptable proposition matrix, without changing the backbone network, while demonstrating superior performance compared to baseline methods across all seven new classes.

\begin{table}
\caption{Ablation study of different design. Dice similarity coefficient scores (\%) are reported.}
%\centering
\begin{center}
\begin{adjustbox}{width=0.45\textwidth}
\begin{tabular}{lcccccc}
\hline
Backbone & TDH & UPL & Regions & Units & Cells & Average\\
\hline
Swin-Unetr~\cite{hatamizadeh2021swin} & & & 41.37 & 75.47 & 57.19 & 62.38 \\
Swin-Unetr~\cite{hatamizadeh2021swin} & \checkmark & & 68.55 & 82.70 & 49.90 & 70.97 \\
\hline
Omni-Seg~\cite{deng2023omni} & & & 72.40 & 83.98 & 66.29 & 76.66 \\
Omni-Seg~\cite{deng2023omni} & \checkmark & & 72.43   & 86.39 & 66.49 & 77.89 \\
PrPSeg (Ours) & \checkmark & \checkmark & \textbf{72.51} & \textbf{86.58} & \textbf{68.97} & \textbf{78.66}\\
\hline
\end{tabular}
\end{adjustbox}
\end{center}
\text{*TDH is Token-based Dynamic Head}\\
\text{*UPL is Universal Proposition Learning}\\
\vspace{-7mm}
\label{tab:differentdesigns} 
\end{table}

