source_code/gliomasam3_moe/GliomaSAM3D-MoE_updated.tex

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\title{GliomaSAM3D-MoE: Concept-Prompted 3D Glioma Segmentation with Dual-Domain Enhancement and Sparse Mixture-of-Experts}
\author{Anonymous}
\date{}

\begin{document}
\maketitle

\begin{abstract}
Accurate delineation of glioma subregions in multi-parametric MRI is central to treatment planning and longitudinal assessment, and has been standardized by the Brain Tumor Segmentation (BraTS) benchmark~\cite{Menze2015BraTS,Baid2021BraTS,SynapseBraTS2023}.
While recent 3D CNN/Transformer segmenters achieve strong overlap metrics, they remain brittle to boundary ambiguity, class imbalance, and the frequent absence of enhancing tumor (\ET), where spurious \ET predictions can disproportionately degrade surface-distance criteria (e.g., HD95).
Inspired by the promptable design of the Segment Anything Model (SAM), we propose \textbf{GliomaSAM3D-MoE}, a fully automatic 3D glioma segmentation framework that replaces manual prompts with learned concept tokens.
Our method combines an \ET-existence gate with direction-aware dual-domain enhancement and a task-structured sparse mixture-of-experts decoder to reduce false positives and improve boundary fidelity.
\end{abstract}

\section{Introduction}\label{sec:intro}
Gliomas are among the most common primary brain tumors, and accurate segmentation of tumor subregions from multi-parametric MRI (mpMRI) is essential for diagnosis, treatment planning, radiotherapy targeting, and longitudinal response assessment.
To foster reproducible evaluation, the Brain Tumor Segmentation (BraTS) challenges provide multi-institutional mpMRI scans with expert annotations and standardized evaluation protocols~\cite{Menze2015BraTS,Baid2021BraTS,SynapseBraTS2023}.
In the conventional BraTS setting, methods segment three clinically-relevant regions---whole tumor (\WT), tumor core (\TC), and enhancing tumor (\ET)---derived from voxel-wise labels of edema, non-enhancing/necrotic core, and enhancing components~\cite{Menze2015BraTS,Baid2021BraTS}.

Despite steady progress, BraTS glioma segmentation remains challenging for three recurring reasons.
First, tumor boundaries can be ambiguous due to partial volume effects, intensity inhomogeneity, and infiltrative growth patterns, making boundary-sensitive metrics (e.g., HD95) particularly unforgiving.
Second, the region hierarchy (\ET $\subseteq$ \TC $\subseteq$ \WT) induces severe class imbalance, where small \ET volumes are easily overwhelmed by \WT/\TC during optimization.
Third, \ET is frequently absent in low-grade cases and in portions of the cohort; in such \ET-absent volumes, even a small number of false-positive \ET voxels can yield large surface-distance penalties and clinically misleading ``enhancing'' findings.
These properties suggest that effective models should (i) emphasize high-frequency boundary cues, (ii) respect the nested region structure, and (iii) explicitly model \emph{existence} (whether a region should appear) separately from \emph{localization} (where it appears).

Most state-of-the-art BraTS solutions build on volumetric encoder--decoder architectures, including 3D CNN families~\cite{Cicek2016,Milletari2016VNet,Kamnitsas2017DeepMedic,Isensee2021nnUNet,Roy2023MedNeXt} and transformer-based variants~\cite{Wang2021TransBTS,Hatamizadeh2022UNETR,Hatamizadeh2022SwinUNETR}.
While these models can achieve strong Dice scores, they typically treat each subregion as a dense per-voxel classification problem, without an explicit mechanism to prevent anatomically-implausible ``hallucinations'' of \ET in \ET-absent cases, and without a targeted strategy to align optimization with surface-distance behavior.

In parallel, promptable segmentation foundation models such as SAM~\cite{Kirillov2023SAM} introduce a compelling alternative abstraction: the user (or an upstream module) specifies \emph{what} to segment via prompts, and the model focuses on \emph{where} to segment.
Recent medical adaptations demonstrate that SAM-style pretraining can transfer to medical targets~\cite{Ma2024MedSAM}, and that SAM-inspired designs can be extended to volumetric data~\cite{Bui2023SAM3D,Wang2023SAMMed3D}.
However, most promptable approaches are interactive (requiring points/boxes), operate slice-wise, or do not explicitly address BraTS-specific challenges such as \ET absence, nested region constraints, and boundary-driven evaluation.

To bridge these gaps, we propose \textbf{GliomaSAM3D-MoE}, a fully automatic SAM-style volumetric segmenter tailored to BraTS glioma subregions.
Our key idea is to replace manual prompts with \emph{learned concept tokens} predicted from the 3D volume, and to structure the decoder as a \emph{task-aware sparse mixture-of-experts} so that different experts specialize to \WT/\TC/\ET decoding.
Crucially, we introduce an explicit \ET-existence classifier whose probability gates the \ET mask to reduce false positives in \ET-absent volumes, and we design a direction-aware dual-domain enhancement module that injects high-frequency priors and spectral modulation to improve boundary fidelity and robustness.

Our main contributions are:
\begin{itemize}
    \item \textbf{Concept-prompted automatic segmentation.} We introduce a SAM-style framework that predicts discrete concept tokens from the input volume and uses them as prompts for region-specific mask decoding, enabling fully automatic volumetric glioma segmentation.
    \item \textbf{\ET-aware existence gating.} We decouple \emph{existence} from \emph{localization} by adding an \ET-presence predictor and an explicit gating mechanism to suppress spurious \ET predictions in \ET-absent cases, targeting improved boundary-sensitive evaluation.
    \item \textbf{Direction-aware dual-domain enhancement.} We combine high-frequency directional priors with calibrated multi-scale fusion and spectral modulation to sharpen boundaries and improve robustness to acquisition/style shifts.
    \item \textbf{Task-structured sparse MoE decoding.} We propose a region-aware sparse mixture-of-experts decoder for \WT/\TC/\ET that promotes expert specialization without incurring the full cost of dense multi-branch decoding.
\end{itemize}

\section{Related Work}\label{sec:related}
\subsection{Glioma segmentation on BraTS}
Early BraTS approaches combined hand-crafted features with classical classifiers, but modern solutions are dominated by deep volumetric segmentation networks.
3D encoder--decoders, such as 3D U-Net~\cite{Cicek2016} and V-Net~\cite{Milletari2016VNet}, established a strong baseline for dense volumetric prediction.
Multi-scale and context-aware designs (e.g., DeepMedic~\cite{Kamnitsas2017DeepMedic}) further improved robustness for heterogeneous lesions.
More recently, nnU-Net~\cite{Isensee2021nnUNet} popularized automated pipeline configuration and remains a widely used competitive baseline in medical challenges, including BraTS.
Transformer-based volumetric segmenters improve global context modeling, exemplified by TransBTS~\cite{Wang2021TransBTS}, UNETR~\cite{Hatamizadeh2022UNETR}, and Swin UNETR~\cite{Hatamizadeh2022SwinUNETR}.
Convolutional architectures inspired by transformer design principles (e.g., MedNeXt~\cite{Roy2023MedNeXt}) also show competitive performance with favorable efficiency.

Despite strong overlap metrics, BraTS segmentation is still hampered by (i) boundary ambiguity and (ii) rare/absent subregions (notably \ET), where naive voxel-wise decoding can yield false positives that severely affect surface-distance measures.
Our work focuses on explicitly modeling \ET existence and improving boundary fidelity within a SAM-style prompt-conditioned decoding paradigm.

\subsection{Promptable and foundation models for medical segmentation}
SAM~\cite{Kirillov2023SAM} introduced a promptable segmentation paradigm that generalizes across diverse natural-image targets via point/box/mask prompts.
MedSAM~\cite{Ma2024MedSAM} demonstrated that SAM can be adapted to medical images through large-scale fine-tuning, improving performance on typical medical targets.
Extending promptable segmentation to volumetric data is an active research direction: SAM3D~\cite{Bui2023SAM3D} adapts SAM-style features to 3D volumes, and SAM-Med3D~\cite{Wang2023SAMMed3D} constructs a fully learnable 3D promptable model trained on large-scale volumetric masks.
While these approaches advance general-purpose promptable segmentation, BraTS requires \emph{fully automatic} multi-region decoding (\WT/\TC/\ET), careful handling of \ET-absent cases, and improved boundary behavior.
We therefore replace manual prompts with learned concept tokens and add an \ET-existence gate that targets BraTS-specific failure modes.

\subsection{Boundary-aware learning and frequency-domain robustness}
Region-overlap losses (e.g., Dice) may under-penalize boundary errors, motivating boundary-aware objectives such as boundary loss~\cite{Kervadec2019BoundaryLoss} and losses that explicitly target Hausdorff distance behavior~\cite{Karimi2019HDLoss}.
In parallel, domain shift across scanners, protocols, and institutions has motivated frequency-domain adaptation and augmentation.
FDA~\cite{Yang2020FDA} reduces style discrepancy by swapping low-frequency amplitude components, and AmpMix~\cite{Xu2023AmpMix} perturbs amplitude while preserving phase semantics to improve domain generalization.
Our method integrates boundary-centric high-frequency priors and spectral modulation as complementary mechanisms for robust BraTS segmentation across dataset editions.

\subsection{Mixture-of-experts for dense prediction}
Mixture-of-experts (MoE) enables conditional computation by routing each input to a sparse subset of specialized experts, improving capacity without proportional cost~\cite{Shazeer2017MoE,Fedus2022Switch}.
In computer vision, MoE has been explored for multi-task learning and dense prediction with adaptive routing~\cite{Chen2023AdaMVMoE}.
Motivated by the heterogeneity of BraTS subregions and the nested (\ET $\subseteq$ \TC $\subseteq$ \WT) structure, we design a task-structured sparse MoE decoder that encourages expert specialization across regions while remaining efficient for 3D inference.

\section{Method}\label{sec:method}

\subsection{Problem formulation and notation}
Given a multi-modal MRI volume
$\mathbf{X}\in\R^{C\times H\times W\times D}$ with $C=4$ modalities,
our goal is to predict a voxel-wise label map
$\widehat{\mathbf{Y}}\in\{0,1,2,3\}^{H\times W\times D}$.
Equivalently, we predict three standard BraTS region masks
$\widehat{\mathbf{m}}_{r}\in[0,1]^{H\times W\times D}$ for $r\in\{\WT,\TC,\ET\}$ (using the canonical definitions \ET$\subseteq$\TC$\subseteq$\WT).
The method is \emph{fully automatic}: no user interactions at inference time.

\subsection{Overview}
GliomaSAM3D-MoE consists of five key components:
\begin{enumerate}[leftmargin=*]
    \item a parameter-free high-frequency direction injection module (HFDI-3D) to provide directional boundary priors,
    \item a SAM-style 2D image encoder $E_{\mathrm{img}}(\cdot)$ applied to each slice,
    \item a lightweight slice-as-sequence 3D adaptation module $T_{\mathrm{seq}}(\cdot)$ for inter-slice context,
    \item a concept-prompt module with (i) a fixed discrete token vocabulary and (ii) an attribute predictor $h_{\mathrm{attr}}(\cdot)$ to infer tokens at test time,
    \item a direction-aware dual-domain enhancement branch (MSDA-3D + FA + FCF + spectral modulation) and a task-structured sparse MoE decoder to output region logits.
\end{enumerate}

\subsection{High-frequency direction injection (HFDI-3D)}
To strengthen boundary cues and tiny-fragment sensitivity, we inject a \emph{directional} high-frequency prior using parameter-free operators.
We first compute a modality-averaged volume:
\begin{equation}
\bar{\mathbf{X}}=\frac{1}{C}\sum_{c=1}^{C}\mathbf{X}^{(c)}\in\R^{H\times W\times D}.
\end{equation}
Using fixed finite-difference (or 3D Sobel) operators $\nabla_x,\nabla_y,\nabla_z$, we extract directional high-frequency maps:
\begin{equation}
\mathbf{G}_x=\nabla_x \bar{\mathbf{X}},\qquad \mathbf{G}_y=\nabla_y \bar{\mathbf{X}},\qquad \mathbf{G}_z=\nabla_z \bar{\mathbf{X}}.
\end{equation}
We form a normalized direction stack
\begin{equation}
\mathbf{H}=\mathrm{Norm}\!\Big(\Concat\big(|\mathbf{G}_x|,|\mathbf{G}_y|,|\mathbf{G}_z|\big)\Big)\in\R^{3\times H\times W\times D},
\end{equation}
and concatenate it with the original modalities:
\begin{equation}
\mathbf{X}^{+}=\Concat(\mathbf{X},\mathbf{H})\in\R^{(C+3)\times H\times W\times D}.
\end{equation}
This augmentation is deterministic and parameter-free, serving as an explicit directional prior that is especially helpful for fragmented \ET boundaries.

\subsection{Slice-as-sequence 3D adaptation}
We interpret the axial dimension as a sequence of ``frames'': $\{\mathbf{x}_t\}_{t=1}^{D}$,
where $\mathbf{x}_t\in\R^{C\times H\times W}$ denotes the $t$-th slice.
After HFDI-3D, the image encoder ingests the augmented slice $\mathbf{x}^{+}_t\in\R^{(C+3)\times H\times W}$.
The 2D image encoder produces per-slice token embeddings:
\begin{equation}
\mathbf{F}_t = E_{\mathrm{img}}(\mathbf{x}^{+}_t)\in\R^{N\times d},
\end{equation}
where $N$ is the number of tokens and $d$ is the token dimension.

To inject 3D context, we aggregate neighboring slice information within a short window
$\mathcal{W}_t=\{t-K,\ldots,t-1\}$ using memory-style cross-attention:
\begin{equation}
\widetilde{\mathbf{F}}_t =
\Attn\!\left(
\mathbf{Q}=\mathbf{F}_t,\,
\mathbf{K}=\Concat(\mathbf{F}_{t-K},\ldots,\mathbf{F}_{t-1}),\,
\mathbf{V}=\Concat(\mathbf{F}_{t-K},\ldots,\mathbf{F}_{t-1})
\right).
\end{equation}
In practice, $K$ is small (e.g., 4--8) for efficiency.
During training we randomize traversal direction (forward/backward) to encourage bidirectional consistency without doubling inference cost.

\subsection{Discrete concept tokens and prompt injection}
\paragraph{Fixed concept vocabulary.}
Instead of free-form natural language (which can be non-deterministic at inference), we define a fixed vocabulary $\mathcal{V}$ of discrete concept tokens:
\begin{equation}
\mathcal{V}=\{\texttt{WT},\texttt{TC},\texttt{ET},\texttt{ET\_PRESENT},\texttt{ET\_ABSENT},\texttt{FRAG\_BIN}_i,\texttt{SCALE\_BIN}_j,\ldots\}.
\end{equation}
During training, token supervision is derived from the ground truth masks (e.g., \ET presence, fragmentation bins, scale bins).
At inference, tokens are predicted by a lightweight attribute predictor, avoiding train/test mismatch.

\paragraph{Attribute predictor and prompt embeddings.}
We compute a global volume descriptor by pooling over tokens and slices:
\begin{equation}
\mathbf{z} = \Pool(\{\widetilde{\mathbf{F}}_t\}_{t=1}^{D}).
\end{equation}
An attribute head $h_{\mathrm{attr}}(\cdot)$ outputs predicted concept labels $\widehat{\mathbf{c}}$ and an \ET presence probability $\pi_{\ET}\in[0,1]$:
\begin{equation}
(\widehat{\mathbf{c}},\, \pi_{\ET}) = h_{\mathrm{attr}}(\mathbf{z}).
\end{equation}
The selected tokens are embedded and injected via a prompt encoder $E_{\mathrm{prm}}(\cdot)$:
\begin{equation}
\mathbf{p} = E_{\mathrm{prm}}(\mathrm{Embed}(\widehat{\mathbf{c}})).
\end{equation}

\paragraph{\ET presence gating.}
Let $\mathbf{l}_{\ET}\in\R^{H\times W\times D}$ denote the \ET logits from the decoder.
We convert logits to probabilities and gate with $\pi_{\ET}$ to suppress false positives in \ET-absent volumes:
\begin{equation}
\widehat{\mathbf{m}}_{\ET} = \sigma(\mathbf{l}_{\ET})\cdot \pi_{\ET}.
\end{equation}
This explicitly decouples existence and localization for \ET and stabilizes HD95 under small spurious detections.

\subsection{Direction-aware dual-domain enhancement (MSDA-3D + FA + FCF)}
\paragraph{Learnable spectral modulation.}
For a training crop (or a full volume) $\mathbf{X}$, we compute a 3D Fourier transform per modality channel:
\begin{equation}
\FFT(\mathbf{X}) = \mathbf{A}\odot e^{\ii\mathbf{\Phi}},
\end{equation}
where $\mathbf{A}$ and $\mathbf{\Phi}$ denote amplitude and phase, respectively.
We apply a learnable radial frequency gate $w_{\theta}(r)$ (parameterized by $\theta$ and indexed by radial frequency magnitude $r$):
\begin{equation}
\mathbf{A}' = \mathbf{A}\odot w_{\theta}(r),\qquad
\mathbf{X}_{\mathrm{spec}} = \IFFT\!\left(\mathbf{A}'\odot e^{\ii\mathbf{\Phi}}\right).
\end{equation}
We summarize directional frequency statistics (used later for routing and fusion) by partitioning the frequency domain into $Q$ directional sectors $\{\mathbf{B}_q\}_{q=1}^{Q}$ and computing
\begin{equation}
s_q=\frac{\langle \mathbf{A},\mathbf{B}_q\rangle}{\langle \mathbf{A},\mathbf{1}\rangle},\qquad \mathbf{s}=[s_1,\ldots,s_Q].
\end{equation}
The spectral-enhanced volume $\mathbf{X}_{\mathrm{spec}}$ is fused with spatial features before decoding.

\paragraph{Multi-scale direction-aware module (MSDA-3D).}
We further enhance directional perception across scales.
Let $\mathbf{U}$ denote a 3D feature tensor (obtained by reshaping token embeddings to a grid and aggregating slices).
For each scale $k\in\mathcal{K}$ and direction $d\in\{x,y,z\}$, we apply a directional depthwise convolution:
\begin{equation}
\mathbf{U}_{k,d}=\mathrm{DWConv}_{k}^{(d)}(\mathbf{U}),
\end{equation}
and combine them with learned attention weights $a_{k,d}$:
\begin{equation}
a_{k,d}=\mathrm{Softmax}_{k,d}\big(\mathrm{MLP}(\Pool(\mathbf{U}))\big),\qquad
\mathbf{U}_{\mathrm{msda}}=\sum_{k\in\mathcal{K}}\sum_{d\in\{x,y,z\}} a_{k,d}\odot \mathbf{U}_{k,d}.
\end{equation}
This module promotes multi-scale local relation modeling while retaining explicit direction selectivity.

\paragraph{Feature aggregation (FA) and feature calibration fusion (FCF).}
To prevent tiny \ET targets from vanishing in high-level representations, we aggregate multi-level features into a lesion-preserving representation $\mathbf{U}_{\mathrm{fa}}=\mathrm{Agg}(\{\mathbf{U}^{(\ell)}\}_{\ell=1}^{L})$.
We then calibrate cross-source fusion (spatial vs.\ spectral, and multi-level vs.\ MSDA-enhanced) using a lightweight gate:
\begin{equation}
\boldsymbol{\eta}=\sigma\!\Big(\mathrm{MLP}\big(\Pool(\Concat(\mathbf{U}_{\mathrm{fa}},\mathbf{U}_{\mathrm{msda}}))\big)\Big),\qquad
\mathbf{U}_{\mathrm{fuse}}=\boldsymbol{\eta}\odot \mathbf{U}_{\mathrm{fa}}+(1-\boldsymbol{\eta})\odot \mathbf{U}_{\mathrm{msda}}.
\end{equation}
Finally, $\mathbf{U}_{\mathrm{fuse}}$ is fused with spectral features derived from $\mathbf{X}_{\mathrm{spec}}$ (e.g., via concatenation or cross-attention) and fed to the MoE decoder.

\paragraph{Fourier amplitude mixing augmentation.}
To improve robustness to acquisition/style variation, we randomly mix Fourier amplitudes across samples while preserving phase:
\begin{equation}
\mathbf{A}_{\mathrm{mix}} = \alpha \mathbf{A}^{(a)} + (1-\alpha)\mathbf{A}^{(b)},\qquad
\mathbf{X}_{\mathrm{mix}} = \IFFT\!\left(\mathbf{A}_{\mathrm{mix}}\odot e^{\ii\mathbf{\Phi}^{(a)}}\right),
\end{equation}
where $\alpha\sim\mathrm{Beta}(\beta,\beta)$ and $(a,b)$ denote two randomly paired training samples.

\subsection{Task-structured sparse MoE decoder}
We design $M$ expert decoders $\{D_m\}_{m=1}^{M}$ specialized for different targets:
\texttt{\WT/edema}, \texttt{\TC/core}, \texttt{\ET/fine}, \texttt{boundary}, and \texttt{FP-suppress}.
A gating network $G(\cdot)$ produces routing weights conditioned on global visual context and prompt embeddings:
\begin{equation}
\boldsymbol{\gamma} = G\!\left(\mathbf{z},\,\mathbf{p},\,\mathbf{s}\right),\qquad
\sum_{m=1}^{M}\gamma_m = 1,
\end{equation}
where $\mathbf{s}$ denotes optional spectral statistics (e.g., band-energy ratios).
Each expert outputs a 3-channel logit tensor $\mathbf{L}^{(m)}\in\R^{3\times H\times W\times D}$ for $\{\WT,\TC,\ET\}$.
We apply sparse top-$k$ routing (e.g., $k=2$) to combine expert logits:
\begin{equation}
\mathbf{L} =
\sum_{m\in \TopK(\boldsymbol{\gamma})}
\gamma_m \cdot D_m(\{\widetilde{\mathbf{F}}_t\}_{t=1}^{D}, \mathbf{p}) \;=\; \sum_{m\in \TopK(\boldsymbol{\gamma})}\gamma_m \mathbf{L}^{(m)}.
\end{equation}
We denote the region-specific logits by $\{\mathbf{l}_{\WT},\mathbf{l}_{\TC},\mathbf{l}_{\ET}\}$ as the three channels of $\mathbf{L}$.
A load-balancing regularizer encourages diverse expert utilization.

\subsection{Training objectives}
The overall loss is:
\begin{equation}
\mathcal{L} =
\mathcal{L}_{\mathrm{seg}}
 + \lambda_{\mathrm{pres}}\mathcal{L}_{\mathrm{pres}}
 + \lambda_{\mathrm{attr}}\mathcal{L}_{\mathrm{attr}}
 + \lambda_{\mathrm{moe}}\mathcal{L}_{\mathrm{moe}}
 + \lambda_{\mathrm{hier}}\mathcal{L}_{\mathrm{hier}}.
\end{equation}

\paragraph{Segmentation loss.}
We combine Dice and cross-entropy, with \ET-aware reweighting and focal emphasis:
\begin{equation}
\mathcal{L}_{\mathrm{seg}} =
\sum_{r\in\{\WT,\TC,\ET\}}
\lambda_r \cdot \mathcal{L}_{\mathrm{Dice}}^{(r)}
 + \lambda_{\mathrm{CE}}\cdot \mathcal{L}_{\mathrm{CE}}
 + \lambda_{\mathrm{Focal}}\cdot \mathcal{L}_{\mathrm{Focal}}^{(\ET)}.
\end{equation}

\paragraph{Presence and attribute supervision.}
\ET presence uses binary cross-entropy:
\begin{equation}
\mathcal{L}_{\mathrm{pres}} = \BCE(\pi_{\ET}, y_{\ET}^{\mathrm{pres}}),
\end{equation}
where $y_{\ET}^{\mathrm{pres}}\in\{0,1\}$ is the ground-truth \ET presence indicator.
Other concept attributes (fragmentation/scale bins) use multi-class cross-entropy:
\begin{equation}
\mathcal{L}_{\mathrm{attr}} = \sum_{u\in\mathcal{U}} \CE(\widehat{c}_u, c_u).
\end{equation}
Here, $\mathcal{U}$ denotes the set of non-presence concept attributes (e.g., fragmentation bin, scale bin), with ground-truth label $c_u$ and prediction $\widehat{c}_u$ for each attribute $u$.

\paragraph{Hierarchy consistency.}
We softly enforce logical constraints (e.g., \ET $\subseteq$ \TC $\subseteq$ \WT) by penalizing violations:
\begin{equation}
\mathcal{L}_{\mathrm{hier}} =
\left\|\max(\widehat{\mathbf{m}}_{\ET}-\widehat{\mathbf{m}}_{\TC},0)\right\|_1
 + \left\|\max(\widehat{\mathbf{m}}_{\TC}-\widehat{\mathbf{m}}_{\WT},0)\right\|_1.
\end{equation}

\paragraph{MoE load balancing.}
To prevent routing collapse, we regularize the batch-average routing probabilities:
\begin{equation}
\mathcal{L}_{\mathrm{moe}} =
\sum_{m=1}^{M} \left(\overline{\gamma}_m - \frac{1}{M}\right)^2,
\end{equation}
where $\overline{\gamma}_m$ is the batch-average of $\gamma_m$.

\subsection{Inference and post-processing}
At inference, concept tokens are predicted by $h_{\mathrm{attr}}(\cdot)$ (no external LLM calls).
\ET probabilities are gated by $\pi_{\ET}$.
Optionally, we apply light post-processing for \ET to remove tiny isolated components below a small voxel threshold, mitigating HD95 sensitivity.

\begin{algorithm}[t]
\caption{GliomaSAM3D-MoE inference (fully automatic)}
\label{alg:infer}
\begin{algorithmic}[1]
\REQUIRE Volume $\mathbf{X}\in\R^{4\times H\times W\times D}$
\STATE HFDI-3D: $\mathbf{X}^{+}\leftarrow \mathrm{HFDI}(\mathbf{X})$
\STATE Slice encoding: $\mathbf{F}_t\leftarrow E_{\mathrm{img}}(\mathbf{x}^{+}_t)$ for $t=1..D$
\STATE Inter-slice aggregation: $\widetilde{\mathbf{F}}_{1:D} \leftarrow T_{\mathrm{seq}}(\mathbf{F}_{1:D})$
\STATE Concept prediction: $(\widehat{\mathbf{c}},\pi_{\ET}) \leftarrow h_{\mathrm{attr}}(\Pool(\widetilde{\mathbf{F}}_{1:D}))$
\STATE Prompt embeddings: $\mathbf{p}\leftarrow E_{\mathrm{prm}}(\mathrm{Embed}(\widehat{\mathbf{c}}))$
\STATE Direction-aware enhancement: MSDA-3D + FA + FCF + spectral modulation
\STATE Decode with sparse MoE: obtain logits $\{\mathbf{l}_{\WT},\mathbf{l}_{\TC},\mathbf{l}_{\ET}\}$
\STATE Region probabilities: $\widehat{\mathbf{m}}_{\WT} \leftarrow \sigma(\mathbf{l}_{\WT})$, $\widehat{\mathbf{m}}_{\TC} \leftarrow \sigma(\mathbf{l}_{\TC})$
\STATE \ET gating: $\widehat{\mathbf{m}}_{\ET} \leftarrow \sigma(\mathbf{l}_{\ET})\cdot \pi_{\ET}$
\STATE (Optional) post-process \ET: remove tiny isolated components
\STATE \textbf{return} $\{\widehat{\mathbf{m}}_{\WT},\widehat{\mathbf{m}}_{\TC},\widehat{\mathbf{m}}_{\ET}\}$
\end{algorithmic}
\end{algorithm}



\section{Experiments}\label{sec:experiments}

\subsection{Datasets}
We conduct experiments on the BraTS 2021 and BraTS 2023 adult glioma datasets~\cite{Baid2021BraTS,SynapseBraTS2023}.
Both releases provide co-registered, skull-stripped, and resampled mpMRI volumes, typically including T1, T1ce, T2, and FLAIR modalities, along with expert tumor annotations~\cite{Menze2015BraTS,Baid2021BraTS}.
Following the BraTS convention, we evaluate three derived regions: whole tumor (\WT), tumor core (\TC), and enhancing tumor (\ET)~\cite{Baid2021BraTS}.
In addition to in-domain evaluation (training and testing within the same BraTS edition), we consider \emph{cross-year generalization} (e.g., train on BraTS 2021 and evaluate on BraTS 2023) to quantify robustness to dataset shift.

\subsection{Preprocessing and data sampling}
Although BraTS provides standardized preprocessing, we apply additional normalization and sampling steps for stable training:
(i) per-modality z-score normalization within the brain mask,
(ii) foreground-aware random cropping to extract 3D patches centered on tumor regions with a fixed probability,
and (iii) standard geometric augmentations (random flips, rotations) and intensity perturbations.
We will release exact hyperparameters (patch size, sampling ratios, and augmentation strengths) in the final version.

\subsection{Evaluation metrics}
We report region-wise Dice similarity coefficient (Dice) and the 95th percentile Hausdorff distance (HD95) for \WT/\TC/\ET, consistent with BraTS evaluation practice~\cite{Baid2021BraTS}.
For \ET-absent volumes (i.e., empty \ET ground truth), we additionally report the false-positive \ET volume and the \ET-presence classification accuracy/AUROC of the proposed gate, since these directly reflect the intended behavior of existence-aware decoding.

\subsection{Implementation details}
All models are trained with the same data splits and preprocessing for fair comparison.
GliomaSAM3D-MoE uses a SAM-style 2D image encoder (initialized from SAM weights~\cite{Kirillov2023SAM}) applied slice-wise, followed by a 3D aggregation encoder and a task-structured sparse MoE decoder (Section~\ref{sec:method}).
We optimize the segmentation loss (Dice + cross-entropy) and the \ET-presence classification loss jointly; details of weighting and schedules will be included in the final version.
Unless otherwise stated, results are averaged over multiple runs (or folds) to reduce variance.

\subsection{Compared methods}
We compare against representative volumetric CNN/Transformer baselines and SAM-inspired volumetric models:
\begin{itemize}
    \item \textbf{3D U-Net}~\cite{Cicek2016} and \textbf{V-Net}~\cite{Milletari2016VNet} as classical volumetric encoder--decoders.
    \item \textbf{nnU-Net}~\cite{Isensee2021nnUNet} as a strong self-configuring medical segmentation baseline.
    \item \textbf{TransBTS}~\cite{Wang2021TransBTS}, \textbf{UNETR}~\cite{Hatamizadeh2022UNETR}, and \textbf{Swin UNETR}~\cite{Hatamizadeh2022SwinUNETR} as representative transformer-based volumetric models.
    \item \textbf{MedNeXt}~\cite{Roy2023MedNeXt} as a modern ConvNeXt-style volumetric baseline.
    \item \textbf{SAM3D}~\cite{Bui2023SAM3D} and \textbf{SAM-Med3D}~\cite{Wang2023SAMMed3D} as promptable volumetric SAM adaptations. For a \emph{fully automatic} setting, prompts are generated by a lightweight coarse segmentation network trained on the same data (details in the final version).
\end{itemize}

\subsection{Main quantitative results}
Tables~\ref{tab:brats21} and~\ref{tab:brats23} report the main comparisons on BraTS 2021 and BraTS 2023, respectively.
(Placeholders are included here and should be filled once experiments are completed.)

\begin{table}[t]
\centering
\caption{Quantitative comparison on \textbf{BraTS 2021}. Report Dice (\%) $\uparrow$ and HD95 (mm) $\downarrow$ for \WT/\TC/\ET.}
\label{tab:brats21}
\resizebox{\linewidth}{!}{
\begin{tabular}{lcccccc}
\toprule
Method & \WT Dice $\uparrow$ & \TC Dice $\uparrow$ & \ET Dice $\uparrow$ & \WT HD95 $\downarrow$ & \TC HD95 $\downarrow$ & \ET HD95 $\downarrow$ \\
\midrule
3D U-Net~\cite{Cicek2016} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} \\
V-Net~\cite{Milletari2016VNet} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} \\
nnU-Net~\cite{Isensee2021nnUNet} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} \\
TransBTS~\cite{Wang2021TransBTS} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} \\
UNETR~\cite{Hatamizadeh2022UNETR} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} \\
Swin UNETR~\cite{Hatamizadeh2022SwinUNETR} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} \\
MedNeXt~\cite{Roy2023MedNeXt} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} \\
SAM3D~\cite{Bui2023SAM3D} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} \\
SAM-Med3D~\cite{Wang2023SAMMed3D} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} \\
\midrule
\textbf{GliomaSAM3D-MoE (ours)} & \textbf{TBD} & \textbf{TBD} & \textbf{TBD} & \textbf{TBD} & \textbf{TBD} & \textbf{TBD} \\
\bottomrule
\end{tabular}}
\end{table}

\begin{table}[t]
\centering
\caption{Quantitative comparison on \textbf{BraTS 2023}. Report Dice (\%) $\uparrow$ and HD95 (mm) $\downarrow$ for \WT/\TC/\ET.}
\label{tab:brats23}
\resizebox{\linewidth}{!}{
\begin{tabular}{lcccccc}
\toprule
Method & \WT Dice $\uparrow$ & \TC Dice $\uparrow$ & \ET Dice $\uparrow$ & \WT HD95 $\downarrow$ & \TC HD95 $\downarrow$ & \ET HD95 $\downarrow$ \\
\midrule
3D U-Net~\cite{Cicek2016} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} \\
V-Net~\cite{Milletari2016VNet} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} \\
nnU-Net~\cite{Isensee2021nnUNet} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} \\
TransBTS~\cite{Wang2021TransBTS} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} \\
UNETR~\cite{Hatamizadeh2022UNETR} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} \\
Swin UNETR~\cite{Hatamizadeh2022SwinUNETR} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} \\
MedNeXt~\cite{Roy2023MedNeXt} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} \\
SAM3D~\cite{Bui2023SAM3D} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} \\
SAM-Med3D~\cite{Wang2023SAMMed3D} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} \\
\midrule
\textbf{GliomaSAM3D-MoE (ours)} & \textbf{TBD} & \textbf{TBD} & \textbf{TBD} & \textbf{TBD} & \textbf{TBD} & \textbf{TBD} \\
\bottomrule
\end{tabular}}
\end{table}

\subsection{Cross-year generalization}
To explicitly measure robustness to dataset shift, we evaluate cross-year transfer without re-training.
Table~\ref{tab:crossyear} summarizes the cross-year performance when training on one BraTS edition and evaluating on the other.

\begin{table}[t]
\centering
\caption{Cross-year generalization between BraTS 2021 and BraTS 2023. ``Mean'' denotes the average over \WT/\TC/\ET.}
\label{tab:crossyear}
\resizebox{\linewidth}{!}{
\begin{tabular}{lcccc}
\toprule
Train $\rightarrow$ Test & Method & Mean Dice $\uparrow$ & Mean HD95 $\downarrow$ & \ET FP Vol. $\downarrow$ \\
\midrule
\multirow{2}{*}{2021 $\rightarrow$ 2023} 
& nnU-Net~\cite{Isensee2021nnUNet} & \textit{TBD} & \textit{TBD} & \textit{TBD} \\
& \textbf{GliomaSAM3D-MoE (ours)} & \textbf{TBD} & \textbf{TBD} & \textbf{TBD} \\
\midrule
\multirow{2}{*}{2023 $\rightarrow$ 2021} 
& nnU-Net~\cite{Isensee2021nnUNet} & \textit{TBD} & \textit{TBD} & \textit{TBD} \\
& \textbf{GliomaSAM3D-MoE (ours)} & \textbf{TBD} & \textbf{TBD} & \textbf{TBD} \\
\bottomrule
\end{tabular}}
\end{table}

\subsection{Ablation studies}
We perform ablations to isolate the impact of each proposed component: (i) concept prompting, (ii) \ET-presence gating, (iii) direction-aware dual-domain enhancement, and (iv) task-structured sparse MoE decoding.
Table~\ref{tab:ablation} provides a template for reporting these results.

\begin{table}[t]
\centering
\caption{Ablation study on a validation split (e.g., BraTS 2021). ``Mean'' denotes the average over \WT/\TC/\ET.}
\label{tab:ablation}
\resizebox{\linewidth}{!}{
\begin{tabular}{lcccc}
\toprule
Variant & Mean Dice $\uparrow$ & Mean HD95 $\downarrow$ & \ET Dice $\uparrow$ & \ET FP Vol. $\downarrow$ \\
\midrule
w/o concept tokens & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} \\
w/o \ET gate & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} \\
w/o dual-domain enhancement & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} \\
w/o MoE (single decoder) & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} \\
\midrule
\textbf{Full model (ours)} & \textbf{TBD} & \textbf{TBD} & \textbf{TBD} & \textbf{TBD} \\
\bottomrule
\end{tabular}}
\end{table}

\subsection{Visualization and qualitative analysis}\label{sec:vis}
In addition to quantitative metrics, we include qualitative comparisons to highlight boundary quality, \ET false-positive suppression, and expert specialization behavior.
The following subsections describe the planned visualizations; figures should be inserted once generated.

\subsubsection{Qualitative comparison on representative cases}
We will visualize representative axial/coronal/sagittal slices with overlays of predicted \WT/\TC/\ET masks for competing methods.
A typical figure includes (i) the four modalities (T1, T1ce, T2, FLAIR), (ii) ground truth, and (iii) predictions from each baseline and our method.

\begin{figure}[t]
\centering
\fbox{\parbox[c][0.22\textheight][c]{0.95\linewidth}{\centering \small Placeholder: qualitative comparison figure.}}
\caption{Qualitative comparison on representative BraTS cases. Each row corresponds to one subject; columns show modalities, ground truth, and predictions from baselines and GliomaSAM3D-MoE.}
\label{fig:qualitative}
\end{figure}

\subsubsection{\ET-absent case study and false-positive analysis}
To directly evaluate existence-aware decoding, we will curate a subset of \ET-absent volumes and visualize:
(i) predicted \ET masks before/after applying the \ET gate, (ii) the predicted \ET-presence probability $\pi_{\ET}$, and (iii) the resulting reduction in false-positive \ET regions.

\begin{figure}[t]
\centering
\fbox{\parbox[c][0.18\textheight][c]{0.95\linewidth}{\centering \small Placeholder: \ET-absent gating case study.}}
\caption{Case study on \ET-absent volumes. The proposed \ET gate suppresses spurious \ET predictions while preserving \WT/\TC.}
\label{fig:et_gate}
\end{figure}

\subsubsection{Boundary error maps and surface-distance visualization}
We will visualize boundary errors using signed distance transforms between prediction and ground truth, highlighting where improvements in HD95 arise.
In addition, 3D surface renderings can be used to show topological artifacts and boundary smoothness.

\begin{figure}[t]
\centering
\fbox{\parbox[c][0.18\textheight][c]{0.95\linewidth}{\centering \small Placeholder: boundary error maps / surface-distance visualization.}}
\caption{Boundary error visualization via distance-transform maps. Warmer colors indicate larger surface discrepancies.}
\label{fig:boundary}
\end{figure}

\subsubsection{Expert routing and concept token interpretability}
To interpret the MoE behavior, we will visualize the routing weights over experts for each region (\WT/\TC/\ET) and correlate routing patterns with tumor morphology (e.g., size/fragmentation).
For concept tokens, we will plot the predicted discrete concept indices and analyze their association with observable properties (e.g., \ET presence, boundary complexity).

\begin{figure}[t]
\centering
\fbox{\parbox[c][0.18\textheight][c]{0.95\linewidth}{\centering \small Placeholder: MoE routing and concept token visualization.}}
\caption{Visualization of MoE routing. We show expert assignment histograms per region and per case, illustrating specialization patterns.}
\label{fig:moe}
\end{figure}

\subsubsection{Frequency-domain analysis}
To motivate dual-domain enhancement, we will visualize amplitude spectra of input modalities and the effect of spectral modulation.
Additionally, we will include qualitative examples under synthetic intensity/style perturbations (e.g., amplitude mixing~\cite{Xu2023AmpMix}) to illustrate robustness.

\begin{figure}[t]
\centering
\fbox{\parbox[c][0.18\textheight][c]{0.95\linewidth}{\centering \small Placeholder: frequency-domain analysis visualization.}}
\caption{Frequency-domain visualization. We illustrate amplitude spectra and the effect of spectral modulation/augmentation on segmentation robustness.}
\label{fig:freq}
\end{figure}

\section{Conclusion}
We introduced GliomaSAM3D-MoE, a SAM-style fully automatic 3D glioma segmentation framework with concept prompting, \ET-aware existence gating, direction-aware dual-domain enhancement, and a task-structured sparse MoE decoder.
The final version will include complete quantitative results and visual analyses on BraTS 2021 and BraTS 2023.



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\end{document}