GauSAM: Contour‑Guided 2D Gaussian Fields for Multi‑Scale Medical Image Segmentation with Segment Anything
Authors: Jinxuan Wu
Jiange Wang
Dongdong Zhang
Venue: NeurIPS 2025 poster ()
Keywords: Medical Image Segmentation
Segment Anything Model
2D Gaussian Field
Contourlet Transform
Primary area: machine_learning_for_sciences

Abstract: Effective multiscale medical image segmentation requires simultaneously preserving smooth spatial continuity and accurately delineating high-frequency boundaries, yet pixel-wise decoders often fail to maintain this balance consistently across varying resolutions. We introduce GauSAM, which seamlessly integrates contour‑guided 2D Gaussian probability fields into the Segment Anything Model to address these challenges. In our framework, segmentation masks are parameterized as continuous probability fields of learnable 2D Gaussian primitives, enforcing spatially smooth and structurally consistent. Contourlet transforms extract rich multidirectional frequency information, notably edges and fine textures, which dynamically guide the spatial distribution of Gaussian primitives to substantially improve boundary fidelity in complex structures. The incorporation of these high-frequency contour priors also enriches the expressive capacity of the SAM image encoder. Extensive experiments on diverse 2D medical segmentation tasks confirm that GauSAM consistently delivers robust generalization and state-of-the-art performance with only 1.2M trainable parameters. The official implementation of GauSAM is publicly available at https://github.com/Quinten-Wu504/GauSAM.

GauSAM: Contour-Guided 2D Gaussian Fields for Multi-Scale Medical Image Segmentation with Segment Anything
Jinxuan Wu
Jiange Wang
Dongdong Zhang"
School of Computer Science and Technology Tongji University
(2154146, 2252699,, (achang)@toogi- edu, on
Abstract
Effective multiscale medical image segmentation requires simultaneously preserv- ing smooth spatial continuity and accurately delineating figh-frequency bound- aries, yet pixel-wise decoders often fail maintain this balance consistently across varying resolutions. We introduce GauSAM, which scamlessly integrates contour-gun guidded 2D Gaussian probability fields into the Segment Anything Model to address these challenges. In our framework, segmentation masks are parameterized continuous probability fields of learnable 2D Gaussian primitives, enforcing spatially smooth and structurally consistent. Contourlet transforms extract rich multidirectional frequency information, notably edges and fine textures, which dynamically guide the spatial distribution of Gaussian primitives to substantially improve boundary fidelity in complex structures. The incorporation of these high- frequency contour priors also enriches the expressive capacity of the SAM image encoder. Extensive experiments on diverse 2D medical segmentation tasks con- firm that GauS AM consistently delivers robust generalization and state-of-the-art performance with only 1.2M trainable parameters. The official implementation of GauSAM is publicly available at https://ithub.com/unntee Wu504/GauSAM
Introduction
Medical image segmentation demands high precision and smooth boundary delineation, anatom- ical structures often exhibit ambiguous edges and segmentation errors can lead to serious clinical consequences [1]. To address this, a wide range of methods have been proposed, including classical architectures such as U-Net [2] and several fine-tuned variants of the Segment Anything Model (SAM) (3). These approaches typically rely on fixed-resolution, grid-based predictions and discrete interpolation schemes, which introduce discretization artifacts and limit their accuracy, especially in high-resolution or cross-scale scenarios 4 5 6
To overcome the limitations of discrete segmentation, implicit neural representations (INRs) 7 have emerged resolution-agnostic alternative, mapping continuous spatial coordinates feature representations. However, existing INRs still struggle to capture fine-grained structures due to their random sampling strategies, which often neglect local contours and directional textures. Furthermore, their reliance on discrete latent codes can obscure complex signals, ultimately reducing their ability produce sharp and coherent segmentation outputs.
Motivated by the limitations of both discrete and INR-based methods, we propose to formulate seg- mentation continuous Gaussian probability field. We are the first to model SAM's segmentation
'These authors contributed equally to this work.
1 Corresponding author.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Frozea
Trainable
384x384
11.5
Input Image
Pelpp
Segmentation Model (Diserete or Continuous)
Contour Priors
SAM Encoder
DWx (S4
HD.
Trainale Parana
Continuous Gaussian Field
34A
$2.4
128x128
384x384
Masks at Resolution
(Cro--ma
#96
nal/Nee
MedSAM
E-MdSAM
GaESAM
a) Tink: Input Image Masks at Any Resolution
Model: GauSAM:
Goussion Field
c)
Result: SOTA Metrics and
Construction Confour-Guided Priors
Robust Cemeralization Across Resolations and Datasets
Figure 1: Overview of GauSAM. a) Illustration of resolution- aagnostic mask generation: GauSAM processes a single image and produce segmentation masks at user-specified resolutions b) Schematic of GauSAM's architecture and workflow: input image is encoded by frozen SAM backbone, enhanced with contour priors derived from the Non-Subsampled Contourlet Transform (NSCT), and processed through trainable continuous Gaussian field to generate resolution-agnostie segmentation masks. c) Summary of results: GauSAM achieves state-of-the-an the- Dice and Hausdorff Distance across in-domain, cross-domain, and cross-resolution settings, outperforming baselines.
probability field continuous representation parameterized by 2D Gaussian Splatting 8 for mask generation, enabling resolution- agnnostcc predictions while mitigating grid-related artifacts. Unlike prior works that employ Gaussian Splatting merely as auxiliary priors post-processing components 10 [2, our framework is trained end-to-end, allowing the Gaussian parameters to directly optimized with task supervision. However, standard Gaussian kernels lack directional sensitivity, often resulting in blurry or misaligned contours in the final mask result [13].
To address this issue, we propose Contour-Guided Gaussian-Field SAM (GauSAM) framework that enhances the SAM encoder with multiscale contour priors and constructs a contour- aware Gaussian field decoder. Specifically, GauSAM leverages the Son-Subsampled Contourlet Transform (NSCT) [4] to extract rich boundary features, which are progressively fused into the encoder via Contour Propagation Unit (CPU). On the decoder side, construct resolution- agnostic probability field from a set of learnable Gaussian primitives, whose parameters are modulated by the contour-enhanced encoded features. A contour-guided spatial adjustment module further aligns these primitives to semantic boundaries, yielding nigh-fidelity masks with sharp contours and strong structural coherence.
novel
Our main contributions are as follows:
1. We the first represent SAM's segmentation probability field continuous Gaussian probability field implemented via learnable 2D Gaussian Splatting, instantiated from a parameterized template library via Gumbel-Softmax sampling and modulated by contour- enhanced semantic features for stable training and compact representation.
2. We integrate NSCT-basee structural priors into the SAM encoder via a lightweight Contour Propagation Unit, enhancing multiscale and multidirectional sensitivity fine contours.
3. We propose Contour- Guided Position Drift module to predict the spatial offsets of each Gaussian primitive from NSCT contour cues, improving boundary alignment.
4. GauSAM achieves superior performance over state-of-the the-art discrete and INR- -NR-based meth- ods across diverse 2D medical segmentation benchmarks, with notable robustness in cross- domain and resolution -agnosii inference.
Related Work
2D Medical Image Segmentation Since the introduction of pixel-level segmentation by FCN
[5]. deep convolutional architectures such as U-Net [ and its massive variant [16, 17 18 19

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have consistently achieved SOTA performance across wide range of medical imaging modalities. More recently, the Vision Transformer- based Segment Anything Model (SAM) 3 has demonstrated remarkable zero-shot segmentation capabilities. To adapt SAM to the medical imaging domain, researchers have proposed various lightweight fine-tuning methods 20 21 22 all of which sub- stantially improve the SAM encoder's ability to perceive medically relevant structures and features. However, these existing methods rely on fixed-resolution representations, which are prone to intro- ducing discretization artifacts and blurred boundaries, especially in high-resolution or cross-scale scenarios [23]. To address these limitations, implicit neural representation (INR) methods 7 24] 25] employ continuous neural fields to yield subpixel-smode outputs at arbitrary resolutions, yet they still struggle with preserving precise texture structures and lacking interpretability [26].
Contourlet-Band Enhancement The Contourlet transform achieves a multiscale, multidirectional subband decomposition via a cascade of Laplacian pyramid and directional filter banks, efficiently capturing curves at arbitrary angles and high- segh-freguency contour information [27]. Compared to traditional wavelets, Contourlets offer superior curve representation and directional selectivity, leading to widespread use in image and feature enhancement 27 Leveraging these same properties, the
non-subsampled Contourlet transform (NSCT) [14] 28 29) which eschews downsampling via non- subsampled Laplacian pyramids and filter banks, achieves shift invariance and superior directional sensitivity compared to the conventional Contourlet transform. Recently proposed hybrid architectures that fuse Contourlet subband features with deep learning models (30 [31 have significantly enhanced the accuracy and robustness of fine-structure delineation, further validating the complementary role of frequency-dome enhancement in complex medical imaging tasks.
Gaussian Splatting for Continuous Representation Gaussian Splatting (GS) explicitly represents scene as set of optimizable anisotropic Gaussian fields and leverages efficient golatting-based rendering pipeline [8] (2]. In recent research, GS has shown broad potential across various vision tasks. In super-resolution reconstruction, GS-based approaches construct learnable 2D/3D Gaussian kernel radiance fields to enable real-time, high-fidelity interpolation at arbitrary upscaling factors 36 Ann in semantic segmentation, emerging studies reveal that GS reconstruct feature and radiance fields with superior precision - without per-pixel network inference - while preserving spatial and semantic consistency, thus offering promising paradigm for efficient and accurate semantic segmentation [37 38 39). Motivated by these advances, our work is the first employ GS to construct continuous probability fields that map high-dimensional features to segmentation masks, preserving sharp boundaries and semantic consistency across scales.
33
34
35
3 Methodology
3.1 Preliminaries
Let X E #xXxCC denote the input image defined on its native discrete pixel lattice, where H, W, and C' denote the height, width, and number of channels respectively, and let Ω = [-1, 1/2 be the normalized continuous coordinate domain. We represent the segmentation target as a continuous mask probability field:
Class
M : Ω
A Class-1
A Class-l = { E T Class Ve 2 Vc,
Σ yc
===
(1)
where Class is the number of semantic classes, and A Class-l is the (Class-1)-simples of class probabilities. The segmentation task is thus formulated as modeling parametric mapping:
To: X + M.
(2)
By sampling the continuous field M on an arbitrary target grid C Ω of resolution H' x W', we obtain discrete prediction Ô E H xw' xC that can be compared to ground-truth annotations using standard differentiable loss functions. Such a continuous representation of the probability field inherently supports arbitrary output resolutions and preserves spatial coherence.
3

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Inamable
Contour-Fahunced Encoder
Prompt Encoder
Low Rank Adapters
Prompe minnes
Input
Two Way Choss Allzemiion
Pasch Embed
Spatial Atm
Spatial Atm
Sputial Atto
NSCT
Image Erobodding
Nock
ICPU Modull
Contour
Contour
Enhancer
Enhancer
Enhuncer
Extracted
Contour
VIT Block x 12
2D Gaussian Continuous Field
21 Giussian Prohability Field
Segmeniationn Head
Alpha-Blending
Gumbel Softmax
Selection Head
Weighted
lnghts
Gaussions
Sumplix
Predict Masks urbitrary resolution
Target Resolutio Gaid
Position Drifting
Library
Figure 2: The overall architecture GauSAM, consisting of Contour- Contour-Enhanced Encoding and 2D Gaussian Continuous Field Decoding. The input image is processed by SAM image encoder, which augmented by NSCT-based contour extraction and Contour Propagation Units (CPU). A continuous Gaussian field built from learnable 2D primitives then produces resolution-agnoss segmentation mask. Red-colored modules indicate trainable components, including A-RA-td layers and newly proposed modules; blue modules denote frozen parts from the SAM-ViT-B backbone.
3.2 Overall Pipeline
As illustrated in Figure 2 GauSAM consists of two principal stages: (1) Contour-EEhanced Image Encoding and (2) Continuous Field Decoding.
In the first stage, the original SAM image encoder is enhanced with structural priors derived from a multi-level Non-Subsampled Contourlet Transform (NSCT) [4]. The resulting contour energy map E is progressively injected into each transformer block via lightweight Contour Propagation Unit (CPU), which recursively refines E through adaptive modulation and soft fusion with semantic embeddings throughout the encoding hierarchy. In addition, the bounding-bon prompt is encoded by SAM's prompt encoder as a sparse input, producing prompt embeddings that guide mask decoding through prompt-conditioned activations.
In the second stage, GauSAM constructs a continuous Gaussain probability field with weighted aggregation of N learnable 2D anisotropic Gaussian primitives, each modulated by opacity-scaled encoder features. This approach forms a continuous representation (p)).. which is decoded into a resonution-annostic probability mask via lightweight segmentation head. Moreover, each Gaussian primitive selects its covariance and opacity from a learned template library through a Gumbel- Softmax-based mechanism. A contour- uontorr-Guided Position Drift module is also introduced to adjust the location of each primitive, using contour-awar offsets and enhancing boundary alignment without compromising semantic coherence.
provide further details on the contour-guided encoder Section and on the Gaussian primitive field construction and decoding process in Section 3.4

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3.3 Contour-Enhanced Image Encoder
Structural Contour Feature Extraction To enable high-fidelity modeling of fine-grained struc- tures, we integrate into the image encoder Structural Edge Extractor that leverages the Non- Subsampled Contourlet Transform (NSCT) to extract multiscale and multidirectional high-frequency contour features.
Given an input image I E BB where B denotes the batch size, we apply an NSCT decomposition with L levels and a directional configuration θ = ( 0,,
at each level:
4.0, SubnbnduSubbadd,,, / 11=1001 NSCT(I)
To construct a unified structural prior without significantly increasing computational overhead, we aggregate all directional subband responses into a single contour-enhanced energy map E for each channel. We apply a point-wise nonlinear transformation to each directional coefficient Contour Subband,, combining logarithmic compression and gamma correction. The aggregated map is formulated as:
E' log (1 + (ContourSubbanddd 7 E (0, 1)
The log space combination of coefficient maps, together with the gamma correction, reduces the dynamic range of contour features to suppress highlights, such as strong reflections caused by bodily fluids in rectal polyp images, thereby mitigating the impact of spurious strong contours on subsequent processing. The final structural map E is subsequently normalized emphasize weak contours, thus retaining essential structural signals across scales and orientations with minimal computational complexity.
Contour Propagation Unit (CPU) To inject the extracted contour information into the VIT encoder in a progressive and semantically coherent manner, we design a novel Contour Propagation Unit (CPU). Instead of applying edge priors statically or at a single layer. CPU recursively propagates and refines contour information across the transformer hierarchy, ensuring that structural awareness is maintained through all encoding depths.
Each transformer block in the encoder receives two parallel inputs: the image embeddings Fe and the contour feature embeddings E,. which are derived from NSCT, where indexes the f-th transformer block from shallow to deep. Within each CPU-enhanced block, the contour signal is adaptively modulated through lightweight MLP-based Edge Reweighting Module yù.
RS = v(==(NN(E)) = R
(5)
Here, LN(-) denotes Layer Normalization, Re is per-channel reweighting vector. The reweighted contour features are then softly fused into the image-embedding stream with scaling parameter A. Crucially, E% is propagated the next ViT block E This design introduces structural inductive signal that complements the semantic representations in F', improving boundary fidelity across layers.
3.4 2D Gaussian Continuous Probability Field
To enable the construction of continuous probability field, we construct a 2D continuous Gaus- sian feature field that inherently bridges the gap between discrete encoder outputs and continuous probabilistic representations. By stacking elliptical kernels in continuous field, Gaussian Splatting enforces spatially smooth and locally consistent representations. This mathematically grounded mechanism aligns with the inherent spatial coherence of semantic segmentation, wherein adjacent pixels are likely to belong to the same semantic entity. Concretely, the feature field is formulated as the weighted superposition of N learnable Gaussian primitives. Each 2D Gaussian primitive modeled as anisotropic Gaussian distribution:
5

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Gi(p pn E.)
= 2x E
exp
2 (p - m.) T;) (p- mil).
E
(6)
where indexes the i-th Gaussian kernel, A E Q and Σ; E R2x2 denote the center and a positive- definite covariance of primitive, respectively. In situations where multiple Gaussian primitives overlap. we modulate each discrete encoder feature v E I by its learned opacity & E R via fi (Ex) vi where a(-) denotes the sigmoid function that maps &, into the interval (0, serving as a soft opacity for each basis function. The final continuous feature field then defined as the weighted aggregation of all Gaussian contributions:
N x(D) = Σ G.) E1
Subsequently, the blended field xp))) is forwarded through a lightweight segmentation head RDD + C producing class logits (((())). These logits are further normalized via a point-wise softmax operation to yield the continuous probability mask M (p). By sampling (p) over arbitrary spatial grid, we obtain the final segmentation mask in resolution-agnoste manner.
Gaussian Parameters Library To address the optimization inefficiency in the above continuous feature field, associated with directly learning the covariance matrices 2; and opacity scalars of the Gaussian primitives in an end-to-end approach, we introduce a learned library of m template pairs: (I(),, ) Each primitive then derives its parameters by selecting from this library differentiable manner. Specifically, for the i-th Gaussian primitive located position ps and associated with encoder feature U; a lightweight convolutional selection head projects o into an m-dimensional logit vector:
-==
23 selHead(( E RT
(8)
To enable discrete selection while retaining differentiabilityy we apply the Gumbel-Softmax operator 2;, producing convex weight vector:
Wy CumbelSoftmax(z)) E A A
which defines probability distribution over the library items. The final parameters E; and & for the i-th Gaussian primitive are then obtained as weighted combinations of the template items:
m
Wiek (K)
&
=
Wi,k {(k)
(10)
This parameterization constrains scale, anisotropy, and opacity of each primitive lie within compact, pre-learned subspace of the full Gaussian parameter space, improving training stability while preserving the expressive richness required for detailed Gaussian-splatinng representations [33
Existing Gaussian field approaches. owing to their uniformly distributed kernels, often struggle capture boundary details adequately. We therefore propose Contour-Guiee Position Drift mechanism to enhance the contour representation in the Gaussian feature field. The core idea is to bias the placement of each Gaussian primitive toward semantic edges, thereby sharpening mask delineation without sacrificing spatial coherence. Specifically, for each initial pixel position p.. we extract its contour feature vector u; E R from the Contour- Guided Encoder (Section 3.3), which contains adequate and multidirectional contour information. A lightweight MLP then predicts small offset:
Contour-Guided Position Drift
Ap4: tanh (anh off (u.)
(11)
and update the Gaussian center b4 pt App.

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Inspired by prior work [34 36] demonstrating the benefits for denser Gaussian placement in regions with richer textures, this drift mechanism ensures each primitive align with structural boundaries identified in the contour feature space, while retaining consistency with the original semantic features.
3.5 Train GauSAM
We categorize the model parameters into two groups with distinct optimization strategies. The first group includes the pre-trained SAM image encoder and prompt encoder, whose parameters remain frozen to preserve their pretrained capacity. To adapt these pretrained components to our modified model, we introduce trainable LoRA adapters into the query Q and value V projection layers of each attention block, following prior work on efficient model adaptation of SAM [3]. The second group comprises all newly introduced modules, including the contour- contour-guided feature extraction layers and the Gaussian-fin decoder. These components are trained from scratch and fully optimized during training. The model is supervised using a pixel-wing
Cross-Entropy (DiceCE) loss:
Leeg (0, (c, ô) + LD)
(12)
where LCE measures the average cross-entropy cross-entoppy across all N pixels in the image, LDice quantifies the spatial overlap between the predicted mask and the ground-truth mask o, and a and balance their contributions.
4 Experiments
4.1
Datasets
We evaluate GauSAM
representative benchmarks: Kvasir-Sessile [40] (196 sessile-polyp RGB images) for binary polyp segmentation and BCV [41] (30 CT slices with 13 organ classes) for multi-organ abdominal segmentation. To assess cross-domain generalization, models trained on Kvasir-Sessile are tested on CVC-ClinieDB 42 (612 RGB images from 31 endoscopic sequences),
while those trained on BCV are evaluated on AMOS 43
(240 CT cases with liver segmentation only). All 3D CT volumes are processed as 2D axial slices. Data are split into training, validation, and testing sets with a 60:20:20 ratio. Input images are resized to 384 x 384 for polyp segmentation and 512 512 for multi-organ segmentation. To ensure fair comparison, we follow the preprocessing and evaluation protocols of I-MedSAM reporting Dice Coefficient (Dice) and Hausdorff Distance (HD) on the test sets.
4.2 Implementation Details
Gaussian Field Initialization To enable the continuous Gaussian field formulation, we initialize the Gaussian Parameter Library with 500 learnable templates. Each Gaussian primitive is parameterized by three elements of the covariance matrix Σ. including og. By (linearly spaced between 0.2 and 3.0), and zero correlation, with an initial value of (11) Re 0.73 for opacity Primitive centers are placed on a uniform grid, with position- drift offsets initialized to zero. Both the template parameters and the weights of the drift MLP employ Kaiming uniform initialization to ensure stable training.
Model Architecture and Training We adopt the SAM-ViT-B backbone with LoRA adapters (rank 4) inserted into the query and value projections of each transformer block. The "up" projections use Kaiming uniform initialization, while the "down" projections are zero-initialized, ensuring early updates are confined to the LoRA modules, leaving the original SAM weights frozen. Only the LoRA-adapted layers and newly introduced modules are updated. A dual-branch learning rate strategy used, with LoRA parameters trained at 0.05 the rate of newly initialized ones. Optimization is performed using Adam W with a weight decay of 10-4 and a linear learning rate scheduler. The segmentation head is lightweight MLP with two hidden layers of dimension 256. The Gaussian Parameters Library contains 500 learnable templates. Training is conducted on 4 NVIDIA H20 GPUs. The polyp segmentation task (single class) requires approximately 3 hours, while the multi-organ segmentation task takes around 50 hours. All models are trained for up to 1000 epochs with early stopping (patience = 10), using a hybrid DiceCE loss. Reported Dice and Hausdorff scores are evaluated on the test set using the checkpoint with the highest validation Dice.
7

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Table 1: Segmentation results on binary polyp and multi-class organ tasks, compared with state- of-the-art discrete and Continuous approaches. Dice (%) denotes the mean Dice score standard deviation over 6 runs (fixed data splits, varying seeds). Params (M) indicates the number of trainable parameters, excluding frozen parameters that are not updated during optimization. Bold highlights the best performance in each task.
Binary Polyp Segmentation
Multi-class Organ Segmentation
Method
Dice ( (%)
Params (M))
Dice (%)²
Params (M).
Discrete Approaches
U-Net 2
03.89+1.300
7.9
74.47=1.57
16.3
Res2UNet 44
81.62+00.77
25.4
79.23=0.66
38.3
nnNt 16
82.97=0.89 126.6
85.15
126.6
MedSAM
45
82.88
4.1
85.85
52.7
Continuous Approaches
OSSNet [46
76.11
5.2
73.38111.65
7.6
IOSNet 7
78.37
4.1
76.75
6.2
SwIPE 47
85.05=0.82
2.7
81.2
4.4
I-MedSAM
25
91.49=0.52
1.6
89691=0.68
3.5
GauSAM(Ours)
94.76 0.32
1.2
89.75
2.9
4.3 Quantitative Results
Comparison with State-of-the-Art Methods We evaluate GauSAM on two representative bench- marks: the Kvasir-Sessie dataset for binary polyp segmentation, and the BCV dataset for multi-class abdominal organ segmentation. The compared methods are grouped into two categories: discrete approaches, which predict segmentation masks on fixed grids, and continuous approaches, which represent masks in resolution-agnosia or implicit forms. Discrete baselines include U-Net [2]. Res2UNet [44], nneNet [16), and MedS AM [45) Continuous baselines include OSSNet [46), IOS- Net 77] SwIPE 47 and I-MedSAM (25 the latter replaces the original decoder of SAM with an INR- formulation, and represents the previous state-of-the-an
As demonstrated in [ GauSAM consistently achieves the best performance across both tasks, obtaining the highest Dice scores while maintaining the lowest number of trainable parameters, On the Kvasir-Sessile dataset, GauSAM reaches Dice 94.76 %, outperforming I-MedSAM (25) by over 3 points with fewer parameters (1.2M vs. 1.6M). On the multi-organ task, GauSAM achieves Dice of 89.75% %, which on par with I-MedSAM, despite using only 2.9M parameters.
Cross-Domain Generalization Performance We evaluate the cross-domain generalizability of GauSAM under two settings: binary-class polyp segmentation from Kvasir-Sessile to CVC, and from multi-organ segmentation in BCV to liver-only segmentation in AMOS. All models trained the source domain and directly evaluated on the target domain without any fine-tuning. As shown in Table 2] GauSAM achieves the highest Dice scores across both transfer scenarios, reaching 91.79% % on CVC and 90.62 % on AMOS. Compared with discrete and continuous baselines, GauSAM exhibits superior generalization under domain shifts. In particular, consistently outperforms the previous state-of-the- I-MedSAM 25 and other baselines.
Generalization Performance To evaluate the resolution resolution-agnostic capability of GauSAM, we conduct cross-resolution segmentation experiments on the Kvasir- Sessile dataset. All models are trained with input images and masks at 384 384, and are then evaluated by producing output masks at 128 x 128 and 896 896, without any fine-tuning architectural modification. As shown in Table 3] GauSAM consistently achieves best performance under both downsampling and upsampling conditions, reaching Dice scores of 94.35% % and 94.29%, %, respectively. In contrast, discrete baselines exhibit notable performance drops when deployed at unseen resolutions, and even implicit models such SwIPE 47 and I-MedSAM 25 show limited adaptability.
Boundary Comparison Hausdorff Distance (HD) measures boundary accuracy by capturing the largest surface deviation between the prediction and the ground truth. As shown in Table GauSAM achieves strong performance across most settings, particularly in cross-resolution scenarios. A relatively weaker HD score is observed in the domain adaptation from Kvasir to CVC: however, significant improvement is still evident in the corresponding Dice score as shown in Table 2 In the
8

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Table 2: Cross-domain segmenta- tion results from Kvasir-Sessile to CVC and from BCV to AMOS.
Table 3: Cross-resolution segmentation results on Kvasir- Sessile from 384 to 128 and 384 896. (*: adjusted input resolution)
Method
Dice (%)t
Dice (%) 384 + 128
Method
384 - 896
Kvasir-Sessile + CVC
Discrete Approaches
unUNet [[6]
84,91
MedSAM 45
74.59
nnUNet [16
73.97
83,56
I-MedSAM 25
88.83
nnUNet* [6
65.34
76.36
GauSAM (Ours)
91.79
McdSAM 45
82.39
83.19
McdSAM
45
82.37
83.32
BCV + AMOS
Implicit Approuches
nnUNet [66
79.63
MedSAM 45
71.98
SwIPE
47
81,26
84.33
I-MedSAM 25
86.28
I-MedSAM
91.45
91.33
GauSAM (Ours)
90.62
GauSAM (Ours)
94.35
94.29
Table 4: Hausdorff Distance comparison on various experiment settings.
HD distance (L)
Kvasir-Sessile
Kvasir-Sessile - CVC
384 + 128
384 - 896
BCV
BCV AMOS
nnUNet [16]
31,30
82.31
13.69
72.31
6.50
80.39
MedSAM
21.53
30.15
8.04
51.82
10.62
52.14
I-MedSAM 25
11.59
19.76
7.91
32.77
5,95
37.53
GauSAM (Ours)
10.29
20.43
4.21
22.94
11.21
36.51
Table 5: End-to-end inference performance comparison. Parameters (Params) denote the total number of model parameters in millions (M). GFLOPs represent giga floating-poin operations. Latency is the average inference time in milliseconds (ms) with standard deviation (STD). FPS indicates frames per second. Memory refers to peak GPU memory usage in megabytes (MB). All metrics were measured on a single NVIDIA RTX 4090 GPU with batch size and input resolution 512 x 512, averaged over 100 forward passes after 10 warm-ups.
Model
Params (M)
GFLOPs
Latency (ms) + STD
Memory (MB)
U-Net
31.03
218.97
41 0.06
24.4
1244
MedSAM
93.74
573.87
66 0.91
15.2
2768
I-MedSAM
92.88
648.06
86 -: 3.12
11.6
3021
GauSAM (Ours)
92.51
473.35
188 +: 2.34
5.3
1898
GauSAM w/o NSCT
92.51
374.91
79 + 2.15
12.7
1898
BCV source-domain setting, GauSAM does not perform well, which may be attributed to the use of a single continuous Gaussian field for all organ classes, potentially limiting precision on small structures in multi-organ segmentation.
Computational Efficiency To evaluate the computational efficiency of GauSAM, we benchmark against several representative basclines. As demonstrated in Table [ GauSAM exhibits lower computational efficiency, while delivering superior segmentation performance. We emphasize that this inference speed is well within the practical range for medical applications, fully meeting the real-time demands of clinical workflows. In medical image segmentation tasks, precision is always paramount, as accurate delineation of anatomical structures or pathological regions directly impacts diagnostic accuracy and patient safety. Moreover, empirical evidence shows that removing the NSCT module leads to a substantial drop GFLOPs and latency, confirming that this component the main contributor to GauSAM's computational overhead. The Appendix provvides component wise efficiency metrics and a diagnostic analysis of the NSCT module's comparatively lower efficiency.
4.4 Qualitative Results
Figure 3 presents representative qualitative comparisons on both binary and multi-class segmentation tasks. We visualize the predicted segmentation masks of different models by overlaying them on the

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Binary Polyp Segmentation
Multi Organ Segmentation
B
D
GauAAMours)
Figure 3: Qualitative comparison binary polyp segmentation and multi-organ segmentation.
original input images. Compared with existing discrete and implicit methods, GauSAM produces masks that exhibit significantly improved semantic smoothness and structural consistency. These improvements are particularly evident in Sample.A, where GauSAM demonstrates superior edge continuity along the polyp's right boundary compared to the previous SOTA method, I-MedSAM, which produces fragmented artifacts. In contrast, GauSAM maintains consistent boundaries without such discontinuities. These results are largely attributed to our continuous Gaussian field formulation, which leverages elliptical Gaussian kernel ensure spatial continuity and local consistency, meaning that adjacent pixels are more likely to belong to the same object. This principled design, combined with contour-guided structural cues, enables the model to better capture fine-grained geometry and align predictions with anatomical boundaries, effectively mitigating discretization artifacts and enhancing the coherence of structural delineation across diverse regions.
4.5 Ablation Study
Our core contribution lies in the design of the continuous Gaussian Field (GS), upon which all subsequent modules are built. Therefore, we conduct ablation studies the Kvasir-Sessile dataset under three settings: in-domain, cross-domain, and cross- cross-resolution. As shown in Table the baseline model without GS performs significantly worse across all tasks. After introducing the Gaussian Field alone, the model yields substantial improvements, validating its critical role. Further integrating the Contour Propagation Unit (CPU) enhances spatial consistency, while the Contour-Guie Position Drift (PosOff) improves robustness under resolution shifts. The full model, which includes three components, consistently achieves the highest Dice scores in every setting.
Table 6: Ablation study on the effectiveness of each component in the pipeline. Dice(%) is reported on in-domain, cross-domain, and cross-resolution settings.
Cross-domain Kvasir >> CVC
Cross-resolution
GS
CPU
PosOff
Kvasir-Sessile
384
128
384
896
86.77
84.51
75.02
77.43
92.62
91.00
91.44
92.74
93.62
91.07
92.33
94.00
94.76
91.79
94.35
94.29
5 Conclusion and Discussion
In this paper, we presents GauSAM, a novel segmentation framework that combines contour-enhanced encoding with continuous Gaussian field decoding. By constructing a continuous resolution- resolution-agnostic Gaussian probability field, our method addresses limitations of structural precision and boundary localization of both discrete and INR-based approaches. Extensive experiments across binary and multi-class segmentation, under in-domain, cross-domain, and cross-resolution settings, demonstrate GauSAM's superior performance terms of semantic consistency and edge accuracy. However, multi-class segmentation benchmarks, likely due to its use of a single
GauSAM underperforms continuous field to represent multiple classes, which may obscure fine-grained details of small objects. Despite this, GauSAM is the first to model SAM's segmentation probability field continuous representation parameterized by 2D Gaussian Splatting for mask generation and establishes a strong foundation for future improvements in multi-clas scenarios.
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A Additional Analysis of NSCT and Related Modules
The integration of the Non-Subsampled Contourlet Transform (NSCT) into the GauSAM framework plays pivotal role in enhancing the segmentation accuracy of the Segment Anything Model (SAM) for both multi-organ and binary polyp segmentation tasks. The choice of NSCT and the design of related modules stems from a meticulous combination of theoretical analysis and extensive experimental validation, as detailed in the following subsections.
A.1 Formal Analysis of Contour-Guided Position Drift
The Contour-Guided Position Drift module improves boundary alignment by applying bounded, differentiable shifts to the centers of Gaussian kernels. For the i-th anisotropic Gaussian kernel:
exp 1 -1 1 TT, (1pp-))) (p-'(p)s))
G ps, E.)
(13)
2T 2
its center is updated from the initial position p; by:
#4 Pr + Aph,
A14 tanh tanh(MLP drint drin((:))) (u:)):
(14)
where tanh(-) ensures
||سي||| < for stability. During training, according to the chain rule, the gradient of the segmentation I. with respect μ4 is:
0p: J (x) OG, 0p.
0L
AL (p) 0G; dp,
(15)
with
(G.(p) 0ys
1p G.(p)
(16)
This formulation indicates that small adjustment of μ4, redistributes the kernel's density in a distance- weighted manner, directly influencing how features aligned to local structures. Through the fully differentiable mapping å,4; = tanh(ML.P arin (u:)), these gradients propagate to the parameters of the drift network, enabling the drift module to automatically optimize kernel placement. Consequently, the drift module is a mathematically grounded, bounded, and differentiable mechanism that, under gradient descent, provably minimizes boundary misalignment, complementing NSCT's precise contour extraction.
A.2 Qualitative Analysis of NSCT-Processed Edge Maps
To further elucidate the contribution of NSCT, we present additional qualitative analysis based on the edge maps generated from NSCT processing, as illustrated in Figure The provided image showcases comparative visualization of original images and their corresponding NSCT-processed edge maps across two distinct medical imaging modalities: CT scans for multi organ segmentation (rows 1-2) and endoscopic images for binary polyp segmentation (rows 3-4). In the original CT images (row 1), organ boundaries exhibit significant ambiguity due to low contrast and overlapping structures, posing challenges for precise delineation. Similarly, the original endoscopic images (row 3) reveal blurred polyp edges, often confounded by background noise and varying illumination. The application of NSCT, however, effectively transforms these inputs into well-defined edge maps (rows 2 and 4), where anatomical boundaries -uchh as those between organs or around polyps- are sharply delineated with enhanced multidirectional frequency information. This enhancement lays a solid foundation for GauSAM's encoding process in terms of edge information representation and precise Gaussian kernel distribution, benefit also reflected in the ablation study results, particularly in cross-domain and cross-resolution tasks.
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Multi Organ Segmentation
Source
Processed
Binary Polyp Segmentation
Source
Procussed
Figure 4: Qualitative comparison of source images (top) and their corresponding NSCT-processed edge maps (bottom) for multi-organ segmentation (rows 1-2) and binary polyp segmentation (rows 3-4). The NSCT-processed edge maps enhance boundary clarity, improving SAM's encoder edge representation and guiding the decoder's Gaussian kernel distribution.
Table 7: Symbol definitions for Gaussian Parameters Library and traditional Gaussian Splatting.
Symbol
Definition
i
Index of each Gaussian kernel Index of each template in the library
k
.V
Number of Gaussian kernels
m
Number of templates the library (N >> m)
2 symmetric covariance matrix for kernel i, controlling ellipsoid shape and orientation (3 parameters)
&
Opacity kernel (1 parameter)
(k)
Covariance matrix template k
(k)
Opacity template &
0:
Parameters of kernel i, including E; and &
0
All parameters of traditional method, {0.) Library parameters, {00//y, corr, (k)) )m
6
B Detailed Analysis of Gaussian Parameters Library
To provide a comprehensive understanding of the Gaussian Parameters Library, we present formal comparison with the traditional Gaussian Splatting method, highlighting the theoretical and practical advantages of our approach. The adoption of the Gaussian Parameters Library is grounded in an extensive literature review, rigorous theoretical derivations, and comprehensive experimental validation, evidenced by the ablation study on library size reported in Section E2 The library approach achieves superior training efficiency and stability compared to traditional Gaussian Splatting, which we formalize below. Due to fundamental architectural differences, direct ablation of the library impractical, as it would necessitate a complete restructuring the model. The following subsections define the key symbols and provide detailed comparison of the two approaches.
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B.1
Symbol Definitions
Table deefine the symbols used in the analysis the Gaussian Parameters Library and traditional Gaussian Splatting.
B.2 Comparison with Traditional Gaussian Splatting
The Gaussian Parameters Library optimizes the covariance matrix Σ, and opacity of Gaussian kernels with greater stability and efficiency than traditional Gaussian Splatting. Below, we compare the two approaches across several key aspects, focusing on parameter count, parameter space, initialization and training stability, learning objective, and model structure.
Parameter Count
Classical Gaussian Splatting constructs continuous field by overlapping many elliptical kernels so that, after opacity accumulation, the synthesized values at discrete pixels/feature locations match the observed signal. Training therefore adjusts the kernels' shapes and opacities to a specific image so as to best reconstruct its discrete measurements, i.c., an instance-specific optimization without parameter sharing across images. In practice, the number of kernels N scales with the number of feature-space locations (often one kernel per pixel/voxel/patch), so the parameter size grows with image resolution/content. Without any library/shared parameterization, this instance- specific paradigm necessitates retraining for each new image, which is computationally prohibitive at scale.
Formally, if each of the kernels uses a 2 x 2 symmetric covariance Σ, (3 parameters) and an opacity & (1 parameter), the parameter count
Pond = (3+ 4N.
(17)
By contrast, we introduce a template library with m shared kernels and a lightweight selection head, which inherently form hypernetwork. Given image embeddings, the hypernetwork maps image features directly to each kernel's parameters by selecting (and modulating) a template for that location, thus enabling runtime parameter prediction and avoiding instance-specific retraining. The library holds only m sets of covariancc/opacity, yielding
Pub (3+ 4m.
(18)
Since typically N > m. we have Pund > Pub. achieving substantial reduction in parameter size while enabling end-to-end learning with shared parameters across images.
Parameter Space
The traditional method optimizes parameters in a high-dimensional space
Sund = RAN
(19)
whereas the library method operates in
Sub = R 4m
(20)
Given N >> m, the lower-dimensional space of the library method facilitates faster convergence and reduces computational complexity.
Initialization and Training Stability The traditional method employs random initialization for 0 = (2,, &),, which risks degenerate covariance matrices (i.e., dE. x 0), causing ellipse collapse and unstable gradients. The library method initializes
((o,/o,)) 3.0, con 0, g(g( sigmoid(1)}
(21)
with Kaiming uniform initialization and uses Gumbel-Softmax to select from m positive definite templates )m This ensures valid Σ, values, enhancing initialization stability and training robustness.
16

---

Learning Objective and Training Efficiency The traditional method optimizes the loss
Tirad
min I(0),
(22)
6ER4N
which is computationally intensive due to the high-dimensionall space. The library method optimizes
Lib
min L(Ø), @cR4m
(23)
where selection head with Gumbel-Softmax assigns one of the m templates to each kernel, operating in the pwwer-dimensioe space 12.m. This constrained optimization accelerates convergence and improves training efficiency.
C Evaluation Results on Additional Datasets
Due to strict page constraints in the main manuscript, we presented quantitative results only on the Kvasir-Sessile and BCV datasets, selected for their representativeness and recognized challenges in medical image segmentation. To further demonstrate the robustness of GauSAM, we conducted extensive experiments across additional medical imaging modalities and segmentation tasks. In this section, we report supplementary results on the REFUGE2 dataset (color fundus images for optic cup and disc segmentation) and the Breast Ultrasound Image (BUSI) dataset (lesion segmentation), which further validate GauSAM's state-of-the-art performance across diverse tasks and modalities. As shown in Table GauSAM consistently outperforms baseline methods, achieving the highest Dice scores across all tasks. On the REFUGE2 dataset, GauSAM attains Dice scores of 89.1 19.1% for optic cup segmentation and 96. 96.2% for optic disc segmentation, surpassing the previous state-of-the-art method, I-MedSAM, by 1.2% and 2. 2.2%, respectively. Similarly, on the BUSI dataset, GauS AM achieves Dice score of 92. 16% for lesion segmentation, outperforming I-MedS by 9.61%. These results confirm GauSAM's superior robustness handling diverse medical imaging challenges.
Table Performance comparison on REFUGE2 and BUSI datasets. Dice (%) is reported for each task, evaluated on the respective test sets.
Model
Optic Cup Dice (%)
Optic Dise Dice (%)
BUSI Lesion Dice (%)
U-Net 2
82.3
92.1
67.24
UneNet 16
84.9
94.7
75.
I-MedSAM
25
87.9
94.0
91.55
GauSAM (Ours)
89.1
96.2
92.16
D Detailed Computational Efficiency Analysis of GauSAM Components
To further elucidate the computational efficiency GauSAM, we provide a detailed decomposition of its component-lewe inference performance in Table The table presents the computational metrics for each major component of GauSAM, and the evaluation protocol is identical to that of Section 4.3 As shown in Table 9 the NSCT module accounts for approximately 58% of GauSAM's total latency (109 ms out of 188 ms). making the primary contributor to the model's computational overhead.
This phenomenon can be attributed to two key factors:
1. NSCT Feature Richness vs. Computational Cost:
The NSCT module excels in capturing contour features, which significantly enhance segmentation
multi-scale and accuracy (e.g.. 1.08% Dice improvement over FFT, 94.76% vs. 93.68%) However, its shift-invariant filter bank decomposition across multiple scales and orientations inherently increases computational complexity, leading to higher GFLOPs and latency.
2. Implementation I Limitations: Existing NSCT implementations are outdated and limited to Python 2.x, lacking compatibility with modern architectures. Our custom Python 3.x implementation, while supporting vectorized processing for batch sizes greater than 1, lacks
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the low-level optimizations (e.g., C++ CUDA based libraries) available in more mature algorithms, resulting in suboptimal execution efficiency.
These findings confirm that the computational overhead in GauSAM primarily due to the NSCT module's intrinsic complexity and suboptimal implementation. Nevertheless, the enhanced contour accuracy justifies this trade-off, as ensures robust representational quality critical for medical imaging while maintaining clinically acceptable throughput.
Table 9: Component-wir inference profile of GauSAM, under the same metric definitions and evaluation protocol as Table
Component
Params (M)
GFLOPs
Latency (ms) STD
FPS
Memory (MB)
NSCT
98.44
109.01 1.82
9.2
113
Contour-Eahanced Encoder
92.13
220.18
43.53 +: 0.79
23,0
388
2D Gaussian Continuous Field
0.38
154.73
32.70 1.15
30.6
1397
GauSAM (end-to-end)
92.51
473.35
188.01 + 2.34
5.3
1898
E
Additional Ablation Studies
Contour Extraction Ablation
To validate GauSAM's choice of the Non- -on-Subsampled Contourlet Transform (NSCT) for contour feature extraction, we conduct ablation studies on the Kvasie-Sessile dataset, replacing NSCT with alternative contour/high frequency methods: FFT (as used in I-MedSAM (25)). Canny, Wavelet, and Sobel. As shown Table TO the full GauSAM with NSCT achieves the highest Dice score and lowest Hausdorff Distance (HD), confirming its superiority in precise boundary delineation. Unlike FFT's broad high-frequency components that include noise, NSCT selectively captures semantically meaningful contours, aligning directly with the requirements of semantic segmentation and providing superior boundary representation. These experiments confirm NSCT's superiority in precise boundary delineation and its better compatibility with GauSAM.
Table 10: Ablation study on contour feature extraction methods on Kvasir-Sessile.
Method
Dice (%)
HD
FFT
93.68
11.34
Canny
93.66
11.82
Wavelet
94.13
11,40
Sobel
93.71
11.15
NSCT (Ours)
94.76
10.29
E.2 Impact of Gaussian Parameter Library Size
As reported in Table expanding the Gaussian Parameter library from m = 50 to m = 500 leads to marked improvement segmentation accuracy and boundary precision. This improvement indicates that a richer set of 2D Gaussian templates better captures the diverse scale and shape variations in our medical image benchmarks. Beyond indicating diminishing returns once the library exceeds a critical size.
500, however, the benefit plateaus and slightly reverses,
A primary factor behind this saturation is the linear growth of the selection head's parameters with m. Since the module must assign probability to each template via soft selection mechanism, overly large introduces many logits that receive relatively weak gradient signals, leading to under-utilized or poorly distinguished templates and impeding stable convergence during training.
In addition, an excessively large library incurs higher computational and memory costs at both training and inference time, while introducing substantial redundancy: many Gaussian templates end up modeling similar feature patterns, so their incremental contribution becomes marginal. Based on series of controlled experiments, we find m 500 strikes the best balance between expressive power and learnability, yielding the highest average Dice score with moderate overhead.
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Table 11: Segmentation performance under different Gaussian parameter library sizes on the Kvasir-
Sessile dataset.
Library size m
50
100
300
500 (default)
800
1000
Dice (%)
92.93
93.78
94.21
94.76
94.22
94.43
HD Distance
12.53
11.65
11.01
10.29
11.19
10,93
Params (M)
0.96
0.99
1.11
1.22
1.40
1.51
F Supplementary Analysis of Robustness on Low-Quality Images
To further validate its robustness, particularly on low-quality images with blurred boundaries, conducted additional experiments on the Kvasir-Sessile dataset, comparing GauSAM against the previous satte-of-the-ann model, I-MedSAM 25 This analysis provides comprehensive empirical evidence of GauSAM's superior performance across varying image quality levels. We identified 12 test images where I-MedSAM exhibited relatively low performance (Dice 89%), all of which displayed ambiguous boundaries. Based on this observation, we partitioned the test set into two groups: a High Ambiguity subset, comprising images with blurred or uncertain boundaries, and Normal subset, consisting of images with clear, well-defined boundaries. Table 12 presents the mean Dice scores for both models on these subsets.
As shown in Table 12 GauSAM achieves a substantial Dice improvement of +7.3% over I-MedSAM on the High Ambiguity subset, compared to a +1.9% improvement on the Normal subset. This pronounced performance gain in the ambiguous boundary scenario underscores GauSAM's robustness handling low-quality images with blurred boundaries. Furthermore, GauSAM exhibits remarkable consistency across image quality levels, with only 0.5% Dice score difference between the High Ambiguity and Normal subsets, in contrast to I-MedSAM's s 6% gap. These results confirm GauSAM's ability to maintain stable and accurate segmentation performance across diverse image quality conditions, reinforeing its effectiveness for both challenging and well-defined cases.
Table 12: Dice performance comparison of GauSAM and I-MedSAM the Kvasir-Sessile test set, divided into High Ambiguity and Normal image groups. Evaluations were conducted with a batch size of and input resolution of 512 512. Dice Gain represents the improvement of GauSAM over I-MedSAM.
Image Type
Sample Count
I-MedSAM Dice (%)
GauSAM Dice (%)
Dice Gain (%)
High Ambiguity
86.8
94.1
+7.3
Normal
28
92.7
94.6
+1.9
G Extension to 3D Segmentation Tasks
The design of GauSAM, particularly its use 2D Gaussian Splatting and contour-guided mechanisms, is inherently extensible to 3D volumetric segmentation. This section provides formal analysis of how GauSAM's framework can be adapted 3D tasks, highlighting its potential to enable expressive and spatially coherent volumetric representations while preserving fine-grained anatomical details. The following subsections extend the core components of SouSSM--ppcificlllyy the Non- Subsampled Contourlet Transform (NSCT) and the Gaussian Continuous Probability Field- to their 3D counterparts, demonstrating the theoretical compatibility and practical promise this extension.
G.1 3D Non-Subsampled Contourlet Transform
In 3D, the input volume is represented as / E RR XxXX where D denotes the depth dimension. The Von-Subsampled Contourlet Transform (NSCT) extended 3D-NSCT, decomposing the volume into multi-scale multi-direetional subbands:
(Cr,0 (C 111,0111=11,000000--- = 3D (T),
(24)
where O and & represent angular directions in 3D space. These subbands capture volumetric contour features, enhancing boundary awareness in 3D segmentation tasks.
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G.2 3D Gaussian Continuous Probability Field
The 2D Gaussian probability field is extended 3D by defining a 3D Gaussian primitive at each voxel (I, v)
g(p) exp (- -1 11)
(25)
where p - [x, y, 21= |ua, My [=] is the mean vector, Σ is 3 X 3 covariance matrix, and is the amplitude. The continuous Gaussian field is constructed as:
N Wigh (p),
P(p)
(26)
where = D H X W is the number of voxels, and Wy are learnable weights. The Contour-Guide Position Drift module adjusts the positions of the primitives based on 3D-NSCT subbands, ensuring precise boundary alignment in volumetric data. This formulation demonstrates GauSAM's theoretical compatibility with 3D tasks, leveraging the same principles of spatial continuity and local consistency to achieve robust segmentation performance.
G.3
Adaptability to 3D Segmentation
The successful application 2D Gaussian Splatting in GauSAM, combined with contour-guided mechanism, provides robust foundation for extending the framework to 3D scenarios. The 3D-NSCT enhances boundary fidelity through multi-scale, multi-directional structural priors, while the 3D Gaussian field ensures spatial continuity and local consistency in volumetric data. These adaptations enable GauSAM to model complex 3D medical imaging tasks effectively, facilitating the integration of multi-moda data and enhancing diagnostic precision across varied anatomical contexts.
H
Further Discussion
H.1 GauSAM's Strengths in Inference
Generalization and Resolution-Agnosti
GauSAM delivers exceptional performance in both binary polyp segmentation and multi-organ segmentation, excelling in cross-domain and cross-resolution scenarios, which achieves the highest Dice scores and ensures consistency. While GauSAM's source-domain performance on the BCV dataset achieves Dice scores comparable to state-of-the-art methods despite higher HD, it demon- strates clear advantages in cross-domain scenarios eecearios-achieving significantly better Dice scores and lower HD compared to existing approaches. This superior generalization stems from GauSAM's continuous Gaussian probability field, which enables resolution-agnosti predictions and smooth modeling of large, uniform structures like the liver in AMOS dataset, enhancing boundary fidelity. The integration of contour-guided priors via the Non-Subsampled Contourlet Transform (NSCT) and Contour Propagation Unit (CPU) further boosts its robustness across domains. These strengths underscore the versatility and efficiency of GauSAM in medical image segmentation.
H.2 Factors Impacting Multi-Organ Segmentation
The continuous representation that drives GauSAM's strengths also presents challenges for multi organ segmentation on the BCV dataset, influenced by its single feature and probability field design and dataset properties. GauSAM AM employs single Gaussian probability field to represent all organ classes, which performs well for large structures but may have limited capacity to fully capture the fine details of smaller organs, given the diversity in size and boundary complexity of the BCV dataset. This design reflects a deliberate trade-off. While adopting multiple class-specific probability fields would significantly increase the number of trainable parameters to approximately 6.6 substaabtantially raising computational costs and inference latency-ww we found such overhead unacceptable. In contrast, GauSAM AM maintains highly compact architecture with only 2.9M trainable parameters for multi
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Liver
Spleen
Pancreas
Visualization of 2D axial slices from the BCV dataset, highlighting appearance variability and semantic discontinuity across slices, which impacts consistent learning of organs.
Figure 5:
organ segmentation, which is the lowest among models achieving comparable performance. We therefore prioritized efficiency and scalability, accepting a trade-off in fine-grained precision for smaller organs in multi-class settings.
Moreover, to adapt to 2D tasks, we converted the 3D CT volumes in the BCV dataset into axial slices. This slicing process introduces appearance variability across slices and disrupts semantic continuity, particularly affecting consistent learning of smaller organs due to the loss of 3D contextual information essential for volumetric coherence, as illustrated in Figure However, GauSAM currently utilizes 2D Gaussian Splatting to construct continuous feature and probability fields for 2D images- - principle that naturally extends to 3D for reconstructing coherent anatomical structures. this extension can better capture semantic consistency and texture in CT scenarios, enabling more precise modeling while addressing these challenges. The ease of this 2D-to-3D transition further highlights GauSAM's s strong extensibility and generalizability across diverse imaging tasks.
future direction,
I Broader Impact
L1 Clinical Impact
GauSAM holds significant promise for advancing medical image segmentation, with direct impli- cations for clinical practice. By improving boundary fidelity and semantic consistency, GauSAM enables more precise structure delineation, facilitating accurate surgical planning and supporting radiologists in diagnosing complex cases. This lead to earlier disease detection, improved patient outcomes, and reduced workload for medical professionals, particularly medically underserved settings where automated tools critical. Furthermore, such advancements may enhance the effi- ciency of treatment workflows and support telemedicine initiatives, broadening access to high-quality diagnostic tools in underserved regions.
1.2 Resolution-Agnostic Mask Generation
The resolution-agnostéc mask generation capability GauSAM offers substantial practical benefits in medical imaging. Medical imaging modalities, such as CT and MRI, often produce high-resolution images due the inherent properties of their imaging principles, which capture fine anatomical details. However, performing segmentation directly on these high-resolution images is computationally expensive, requiring significant resources. GauSAM's ability to generate accurate segmentation masks from downsampled images, while producing masks at the original image resolution with preserved quality, significantly reduces computational demands. This approach enables efficient processing on Essource-constraige systems without compromising the precision of boundary delineation in the
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final high-resolution output, making it highly applicable in clinical settings where computational efficiency is critical.
1.3
Generalization Beyond Medical Imaging
Although GauSAM was trained and evaluated on medical image segmentation datasets, its design is exclusively tailored medical data. The challenges addressed by Gauh blurred boundaries, insufficient semantic consistency, segmentation artifacts, and inadequate boundary continuity and precision- are prevalent across various segmentation tasks in both medical and non- medical domains. These issues are particularly pronounced in medical image segmentation due to its complexity and significant clinical implications, making compelling evaluation setting for validating GauSAM's capabilities. However, the underlying principles of GauSAM, including its continuous Gaussian probability field and contour sentouur-guiedd mechanisms, are broadly applicable to other domains facing similar challenges, such as autonomous driving, remote sensing, or industrial defect detection. By improving segmentation accuracy, reducing artifacts, and enhancing boundary continuity, GauSAM has the potential to deliver strong performance in these fields, underscoring its versatility and robustness across diverse applications.
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Reviews:
[{"review_id": "p3IFFoOp6Q", "reviewer": "Reviewer_9QbL", "summary": "The paper presents a novel method for medical image segmentation that enhances the Segment Anything Encoder by feeding it with multiscale contour priors and models a continuous probability field with 2D Gaussians. Inspired by 2D Gaussian Splatting, the proposed method predicts a field (of class probabilities) using a set of 2D Gaussians whose parameters are predicted by the network. Instead of predicting the parameters directly, the method uses a set of template Gaussians, which are then selected via the differentiable Gumbel-Softmax operator.  A contour-Guided Position Drift mechanism is also introduced in the model to refine the position of Gaussian distributions at every pixel position. Tested on the Kvasir-Sessile and BCV datasets, the method shows improved performance compared to SOTA architectures and a better generalization to changes in domains and image resolution.", "questions": "* Line 127: is B the batch size ?\n\n* Eq (4): why combine coefficient maps in the log space? What is the impact of varying gamma?\n\n* Notation: the multiple uses of index 'i' is confusing. In Eq (5), it seems to refer to a block, in Eq (6) to a Gaussian component, and in Eq (11) to a pixel. Ultimately, is the number of Gaussians N the same as the number of pixels?\n\n*Typo,  Line 162: is forward-\"ed\" ? \n\n* See weaknesses for other questions.", "limitations": "Yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 4, "originality": 4, "strengths_and_weaknesses": "Strength:\n\n* Novelty: While previous work have extended SAM to enable a continuous representation, to my knowledge, this is the first method that explicitly models SAM's segmentation probability field as a combination of 2D Gaussians. This compact representation allows handling images and prediction segmentation masks of arbitrary resolution. In addition, the method introduces other novel components, such as the Contour Propagation Unit (CPU), the Gaussian Parameters Library and the Contour-Guided Position Drift prediction.\n\n* Results: experiments on two different datasets shows the method to achieve outstanding performance compared to very recent and related baselines. The proposed method specifically excels when tested in  cross-domain or cross-resolution settings. \n\n* The paper is mostly well-written and easy to follow. \n\nWeaknesses: \n\n* Although different, the method does share similarities with previous approaches, specifically  I-MedSAM:  use of low-rank adapter, augmenting the patch encoder with additional features (FFT), etc. Clarifying the differences/advantages compared to I-MedSAM would strengthen the paper.\n\n* Some important details are missing (or hard to find). For instance, while Figure 1 suggests that bounding boxes are used as prompt to SAM, the paper does not seem to mention this information explicitly.", "was_revised": true, "final_justification": "The authors have addressed my main concerns.", "rebuttal": "We sincerely thank you for the thorough and insightful review of our work. We greatly appreciate your recognition of our work's novelty, particularly as the first to model SAM's segmentation probability field as a continuous field via 2D Gaussian Splatting, as well as its strong performance in cross-domain and cross-resolution settings. Your accurate understanding of our core contributions, including the Contour Propagation Unit (CPU), Gaussian Parameters Library, and Contour-Guided Position Drift, underscores the significance of our approach. Moreover, we are grateful for your kind acknowledgment of our work despite noting some areas for improvement in clarity and detail, and we address these points below with clarifications and additional evidence to strengthen our manuscript.\n\n## Response to Weakness 1\n\nYour meticulous observation regarding the similarities between GauSAM and I-MedSAM underscores a critical aspect of our work, necessitating a clearer differentiation to highlight the unique contributions of our approach. Therefore, we provide a detailed comparison below to further elucidate these differences and advantages. We acknowledge that both methods leverage LoRA and incorporate contour/high-frequency information to enhance SAM's encoder. However, GauSAM introduces a distinct and systematic framework that fundamentally differs from I-MedSAM, not only in its core design and contributions but also in its foundational principles and theoretical motivations.\n\n1. **LoRA**: We acknowledge, as you have astutely noted, that our training strategy employing LoRA for fine-tuning GauSAM aligns with the approach used in I-MedSAM. This choice stems from a meticulous combination of theoretical analysis and extensive experimental validation. By leveraging LoRA, we effectively adapt SAM's pre-trained weights, substantially reducing the computational resources required for fine-tuning while maintaining robust segmentation performance. This decision was guided by a thorough analysis of LoRA's principles in the context of GauSAM's architectural characteristics, supported by extensive experiments to ensure seamless compatibility with our contour-guided Gaussian field framework. While our adoption of LoRA shares similarities with I-MedSAM, it was selected for its demonstrated efficacy in balancing efficiency and performance, rather than pursuing novelty for its own sake.\n\n2. **Core Contribution: Continuous Gaussian Probability Field**: From a theoretical perspective, the primary innovation of GauSAM lies in modeling segmentation as a continuous Gaussian probability field using 2D Gaussian Splatting. The ultimate goal of semantic segmentation can be viewed as constructing a mask probability field, where segmentation masks exhibit inherent properties of spatial continuity and neighborhood consistency, which means adjacent regions are more likely to belong to the same semantic object. \n\n   Unlike I-MedSAM, which relies on implicit neural representations (INRs), GauSAM explicitly constructs a resolution-agnostic probability field that aligns with these intrinsic properties. The advantage of 2D Gaussian Splatting lies in its ability to naturally build a continuous field by distributing numerous Gaussian primitives in the space. Through the stacking and rendering of these primitives, GauSAM achieves a smooth probability field. Moreover, the continuous nature of Gaussian functions enables smooth interpolation, allowing the generation of continuously varying mask probabilities at arbitrary points without requiring explicit grid discretization or complex neural network inference. \n\n   Empirical results corroborate this theoretical advantage: on the Kvasir‑Sessile dataset, GauSAM achieves a Dice score of 94.76 % with only 1.2 M trainable parameters, significantly surpassing I‑MedSAM’s Dice of 91.49 % obtained with 1.6 M parameters\n\n3. **NSCT vs. FFT**: While both GauSAM and I-MedSAM incorporate contour/high-frequency information, GauSAM employs the Non-Subsampled Contourlet Transform (NSCT) to extract multi-scale, multi-directional contour features, which are highly consistent with the distribution of semantic boundaries in segmentation tasks. In contrast, the high-frequency features extracted by FFT in I-MedSAM include broader high-frequency components, including more noises, which may compromise segmentation accuracy. NSCT's focus on semantically meaningful boundaries ensures precise boundary delineation, aligning directly with the requirements of semantic segmentation. To substantiate this, we previously conducted experiments, comparing NSCT with traditional edge detection methods (Canny, Wavelet, Sobel) and FFT on the Kvasir-Sessile dataset. Due to space constraints, these results were not included in the original manuscript. For your reference, we provide these comparative results below(Table 1). These experiments confirm NSCT's superiority in achieving precise boundary delineation and its better compatibility with the overall GauSAM framework. \n\n   **Table 1.** Comparative performance of different contour/high‑frequency feature extraction methods on Kvasir‑Sessile for binary polyp segmentation.\n\n   |Method|Dice (%)|HD|\n   |:-:|:-:|:-:|\n   |**NSCT**|**94.76**|**10.29**|\n   |**FFT**|93.68|11.34|\n   |**Canny**|93.66|11.82|\n   |**Wavelet**|94.13|11.40|\n   |**Sobel**|93.71|11.15|\n\n4. **Comprehensive Use of Contour Information**: GauSAM leverages contour features more extensively than I-MedSAM. While I-MedSAM uses a frequency adapter for edge feature integration, GauSAM introduces the Contour Propagation Unit (CPU), which progressively fuses contour features into each ViT block, enhancing boundary awareness throughout the encoding hierarchy. Additionally, GauSAM employs a Contour-Guided Position Drift module to adjust Gaussian kernel placements toward semantic edges. In standard Gaussian Splatting, the Gaussian field often struggles to represent high-frequency regions effectively. By adjusting the kernel distribution to be denser in high-frequency regions, guided by contour information, GauSAM optimizes the representation of the high-frequency regions. This approach fully exploits the high consistency between contour distributions and semantic boundaries, improving boundary fidelity, as demonstrated in our ablation study. This dual use of contour information—enhancing both encoding and decoding process—distinguishes GauSAM from I-MedSAMs simpler integration strategy.\n\n## Response to Weakness 2 and Questions\n\nWe reiterate our gratitude for your meticulous reading, which has helped us identify areas for improvement in our manuscript, and we deeply appreciate your support for our work despite noting these minor details. We address the second weakness and all the questions you have posed below. \n\n1. **Bounding Box as Prompt**: You correctly note that Figure 1 indicates the use of bounding boxes as prompts, which was not explicitly described in the text. We clarify that bounding boxes are indeed used as prompts in GauSAM, following SAM's standard pipeline. After the image encoder extracts features from the input image, the bounding box prompt is first mapped by the prompt encoder into two 256‑dimensional tokens: one for the top‑left corner and one for the bottom‑right corner. These corner tokens are then combined with the image embedding in the cross‑attention layers, guiding attention to the specified rectangular region and modulating feature aggregation to generate a more precise segmentation mask. We apologize for this omission and will explicitly describe this process in the revised manuscript if possible.\n\n2. **Batch Size and Variable Definitions**: You are correct that $B$ represents the batch size in the input image tensor $I \\in \\mathbb{R}^{B \\times C \\times H \\times W}$. Moreover, $C$ denotes the number of channels (e.g., 3 for RGB images), and $H \\times W$ represents the image resolution. The NSCT decomposition is defined as:\n   $$\n   {C_{l,\\theta}}_{l=1,\\theta=1}^{L,\\Theta_l} = \\mathcal{NSCT}(I)\n   $$\n   This outputs contour subbands for each level $l$ and direction $θ$. We will also clarify these definitions in the revised text, if possible, to avoid ambiguity.\n\n3. **Log Space and Gamma Transformation**: The log space combination of coefficient maps, together with the gamma correction, reduces the dynamic range of contour features to suppress highlights, such as strong reflections caused by bodily fluids in rectal polyp images. This mitigates the impact of spurious strong contours on subsequent processing.\n\n4. **Multiple Uses of Index '$i$'**: We apologize for the ambiguous reuse of the index $i$ across Equations (5), (6), and (11). Specifically, in Equation (5), $i$ indexes the transformer block; in Equation (6), it refers to a Gaussian primitive; and in Equation (11), it denotes the pixel position associated with the corresponding Gaussian primitive. We further clarify that the number of Gaussian primitives, denoted as *N*, is equal to the number of pixels in the feature map.\n\n5. **Typo: \"forwarded\"**: We acknowledge the grammatical error in Line 162, where \"forward\" should be “forwarded.”\n\nWe deeply appreciate your careful attention to these details, which will undoubtedly help us improve the manuscript's clarity. If accepted and revisions are permitted, we will address these issues in the Camera-Ready version, including explicit descriptions of the bounding box prompt, clarified variable definitions, refined notation, and corrected typos.\n\n## Conclusion\n\nWe again thank you for your insightful and thorough review, which has greatly helped us refine our presentation. Your accurate grasp of our core contributions, particularly the novelty of the 2D Gaussian probability field and its impact on segmentation performance, is greatly valued. We hope our responses address your concerns and help you further highlight GauSAM's contributions. We look forward to your continued guidance and feedback."}, {"review_id": "A165mrxfyh", "reviewer": "Reviewer_mdip", "summary": "This paper makes several contributions to the field of SAM based medical image segmentation. The authors discover that using 2D Gaussian probability fields can lead to smooth spatial continuity and accurate high-frequency boundaries. Building on this insight, they parameterize the segmentation masks as continuous probability fields of learnable 2D Gaussian primitives, boosting spatially smooth and structurally consistent. In addition, they extract multidirectional frequency information guide the spatial distribution of Gaussian primitives. The proposed method demonstrates robust generalization over current state-of-the-art approaches, highlighting its potential impact on the field.", "questions": "(1)\tThe author parameterizes the segmentation mask as continuous probability fields of learnable 2D Gaussian primitives. Can this approach result in insufficient representation when the resolution is high?\n(2)\tWhy choose Contourlet transform instead of Wavelet or Sobel operator to extract frequency information? What are the unique advantages of this transformation?\n(3)\tThe author claims that the method is applicable to various 2D medical segmentation tasks. Have you considered its generalizability in 3D tasks such as CT and MRI volume segmentation? Can 2D Gaussian primitives be extended to 3D Gaussian primitives?", "limitations": "Although the number of parameters is small, it does not indicate the advantage of the model in terms of inference speed. In clinical deployment, this factor is often more critical than the parameter quantity itself.", "rating": 3, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths:\nThis paper presents several advantages in the field of SAM based medical image segmentation. It enhances multiscale and multidirectional sensitivity to fine contours through NSCT-based structural priors. The proposed continuous Gaussian probability field utilizes Gumbel-Softmax sampling and contour-enhanced semantic features to promote stable training. It also proposed a Contour-Guided Position Drift module to improve boundary alignment. The experimental results demonstrate the superior generalization ability of the proposed method.\n\nWeaknesses:\n(1)\tThe author only conducted experiments on two types of segmentation datasets (i.e., polyp segmentation and multi-class Organ Segmentation), which limited the generalization ability of this method in other segmentation tasks.\n(2)\tThe author claims that the continuous probability fields of learnable 2D Gaussian primitives parameterized by segmentation masks can enhance spatially smooth and structurally consistent. However, there are no visual experiments to validate this conclusion. \n(3)\tThe motivation is unclear. Why can continuous Gaussian probability fields solve the limitations of existing methods.", "was_revised": true, "final_justification": "After reading comments and rebuttals, I decided to keep the score!", "rebuttal": "# Response to Reviewer mdip\nWe sincerely thank you for your valuable feedback and the time you have invested in reviewing our manuscript. We greatly appreciate your recognition of our contributions. However, it appears that our core innovation may not have been fully captured in your review. As correctly noted by Reviewer 9QbL, our core contribution lies in being the first to model segmentation probability field as a continuous one using 2D Gaussian Splatting. We have carefully considered all aspects of your review and address your concerns below with detailed clarifications and additional evidence, hoping to dispel your doubts.\n## Response to Weakness 1\nActually, we conducted extensive experiments across multiple medical imaging modalities and segmentation tasks to validate GauSAM's robustness. Our claim of achieving state-of-the-art performance across a wide range of tasks is grounded in rigorous experimentation, not an unsubstantiated assertion. In the manuscript, we selected two highly representative datasets, Kvasir-Sessile and BCV, due to their recognized challenges in medical image segmentation.\n\nFor your reference, we present experimental results on the REFUGE2 dataset (color fundus images) and the Breast Ultrasound Image (BUSI) dataset below, to further validate GauSAM's generalization ability. These experiments were conducted during the preparation of our manuscript. The following table showcases GauSAM's SOTA performance across diverse modalities and tasks.\n\n**Table1.** Comparison on REFUGE2 and BUSI Datasets\n|Model|Optic Cup Dice(%)|Optic Disc Dice(%)|BUSI Lesion Dice (%)|\n|-|-|-|-|\n|U-Net|82.3|92.1|67.24|\n|nnU-Net|84.9|94.7|75.19|\n|I-MedSAM|87.9|94.0|91.55|\n|**GauSAM**|**89.1**|**96.2**|**92.16**|\n## Response to Weakness 2\nWe wish to clarify that such evidence is already presented in Figure 2 of the manuscript. Specifically, the first row of the left panel clearly illustrates that GauSAM's generated masks are significantly more spatially smooth and structurally consistent compared to other methods. When compared to the previous SOTA method I-MedSAM, GauSAM's masks exhibit superior edge continuity, particularly along the right boundary of the polyp, where I-MedSAM produces fragmented artifacts. In contrast, GauSAM's masks maintain consistent boundaries without such artifacts.\n\nWe originally believed that Figure 2 sufficiently showcased GauSAM's strengths in spatial smoothness and structural consistency, given its representative visualization of these qualities. In light of your feedback, we recognize the need for more comprehensive visual comparisons. If our manuscript is accepted and revisions are permitted in the Camera-Ready phase, we will include additional visualizations in this regard.\n## Response to Weakness 3\nWe appreciate your concern regarding the clarity of our motivation, and we clarify that the motivation for GauSAM is explicitly detailed in the Introduction and Related Work of the manuscript. To further elucidate this issue, we provide a concise yet comprehensive explanation below, highlighting the theoretical and practical motivations of our approach.\n1. **Addressing Grid Artifacts and Resolution Dependency**: Discrete segmentation methods, such as U-Net and MedSAM, rely on fixed-resolution grid predictions, leading to grid-like artifacts and blurred boundaries, particularly in high-resolution or cross-resolution scenarios. In contrast, GauSAM constructs a continuous Gaussian probability field via 2D Gaussian Splatting. The weighted superposition of these Gaussian kernels ensures spatial continuity by generating a smooth probability distribution. Each Gaussian primitive, as a continuous function, contributes to a locally smooth probability field, and their additive combination produces a globally coherent mask without grid-like artifacts.\n2. **Enhancing Semantic Consistency and Spatial Continuity**: Discrete methods often produce incoherent segmentation masks due to grid-based predictions, while INRs lack explicit boundary guidance, resulting in suboptimal semantic consistency and boundary accuracy in complex regions. However, GauSAM's continuous Gaussian probability field, formed by the weighted superposition of Gaussian kernels, naturally supports spatial continuity through smooth probability distributions, reducing semantic discontinuities between adjacent regions. Additionally, the integration of Non-Subsampled Contourlet Transform (NSCT) and the Contour Propagation Unit incorporates contour priors, enhancing Gaussian field alignment with semantic boundaries.\n## Response to Question 1\nWe fully understand your concern regarding whether GauSAM can maintain consistent performance across different resolutions, which may stem from some doubts or misunderstandings about our Gaussian primitive placement strategy. Therefore, we have to clarify that GauSAM's design ensures robust expressiveness by placing one Gaussian primitive per pixel. This strategy ensures that the representation capacity adjusts with varying image resolution without compromising performance. Furthermore, we utilize a Gaussian Parameters Library, where each Gaussian primitive is selected via a differentiable Gumbel-Softmax operation from a fixed set of 500 templates. Then, during construction of the Gaussian feature field, each primitive receives a single scaling factor computed from the input and target mask resolutions without adding trainable parameters across resolutions.\n## Response to Question 2\nWe greatly value your question regarding the choice of NSCT over Wavelet or Sobel operators, and we want to clarify that this decision is based on a comprehensive integration of theoretical analysis and experimental validation.\n\nTheoretically, NSCT extracts multi-scale, multi-directional contour features, providing a more comprehensive and semantically targeted representation of boundaries compared to Canny, Wavelet, or Sobel. Moreover, unlike FFT, which captures broader high-frequency components including noises, NSCT focuses on semantically meaningful contours, aligning closely with the boundary distributions in segmentation tasks.\n\nExperimentally, in the process of validating the methodology, we conducted experiments, comparing NSCT with three traditional edge detection methods and FFT on the Kvasir-Sessile dataset. For your reference, we provide these comparative results below(Table 2). These experiments confirm NSCT's superiority in achieving precise boundary delineation and its better compatibility with the overall GauSAM framework.\n\n**Table 2.** Comparative performance of different contour/high‑frequency feature extraction methods on Kvasir‑Sessile for binary polyp segmentation.\n|Method|Dice(%)|HD|\n|-|-|-|\n|NSCT|**94.76**|**10.29**|\n|FFT|93.68|11.34|\n|Canny|93.66|11.82|\n|Wavelet|94.13|11.40|\n|Sobel|93.71|11.15|\n## Response to Question 3\nWe greatly value your question regarding the extension of GauSAM to 3D tasks, as it actually highlights the potential of our method's design. In fact, this potential for extending from 2D to 3D has been discussed in the Broader Impact section of our Appendix. We clarify that the 2D Gaussian Splatting framework is inherently compatible with 3D, as both 2D and 3D Gaussian Splatting share fundamentally the same principles. Below, we extend the Preliminaries (Section 3.1) and 2D Gaussian Continuous Probability Field (Section 3.4) to their 3D counterparts to illustrate this potential:\n* **Preliminaries**: In 3D, the input volume is represented as $I \\in \\mathbb{R}^{B \\times C \\times D \\times H \\times W}$, where $D$ is the depth dimension. The NSCT can also be extended to 3D-NSCT, decomposing the volume into multi-scale, multi-directional subbands:$${C_{l,\\theta,\\phi}}_{l=1,\\theta=1,\\phi=1}^{L,\\Theta_l,\\Phi_l} = \\mathcal{NSCT}^{3D}(I),$$where $\\theta$ and $\\phi$ denote angular directions in 3D space. These subbands capture volumetric contour features, enhancing boundary awareness in 3D.\n* **3D Gaussian Continuous Probability Field**: The 2D Gaussian probability field is extended to 3D by defining a 3D Gaussian primitive at each voxel $(x, y, z)$:$$g(\\mathbf{p}) = \\alpha\\exp\\left(-\\frac{1}{2}(\\mathbf{p} - \\mathbf{\\mu})^T \\mathbf{\\Sigma}^{-1} (\\mathbf{p} - \\mathbf{\\mu})\\right),$$where $\\mathbf{p} = [x, y, z]^T$, $\\mathbf{\\mu} = [\\mu_x, \\mu_y, \\mu_z]^T$ is the mean vector, $\\mathbf{\\Sigma}$ is a $3×3$ covariance matrix, and $\\alpha$ is the amplitude. The continues Gaussian field is constructed as:$$P(\\mathbf{p}) = \\sum_{i=1}^N w_i g_i(\\mathbf{p}),$$where $N = D \\times H \\times W$ is the number of voxels, and $w_i$ are learnable weights. The Contour-Guided Position Drift module adjusts the positions of the primitives based on 3D-NSCT subbands, ensuring precise boundary alignment in volumetric data.\n## Response to Limitations\nIn our benchmarks on a single NVIDIA RTX 4090, GauSAM processes a 384 × 384 image in just 165 ms (≈6 FPS), and even at 512 × 512 maintains ~5 FPS—well within interactive use. Admittedly, this is marginally slower than some purely grid-based decoders, but we deliberately trade a small increase in latency for a substantial gain in segmentation accuracy without compromising practical deployability.\n\n**Table 2.** GauSAM inference performance on RTX 4090. Total parameters: 92.51 M; FLOPs per forward pass: 125.23 GFLOPs.\n|Input Resolution|Batch Size|Avg Latency(ms)|FPS |Peak Memory(MB)|\n| - | -| - | - | - |\n|384 × 384|1|164.8|6.07|1246|\n|384 × 384|2|265.8|7.52|2123|\n|384 × 384|4|423.7|9.44|3876|\n|256 × 256|1|158.1|6.33|781|\n|512 × 512|1|188.6|5.30|1898|\n## Conclusion\nWe sincerely thank you again for your valuable suggestions and thorough review. We hope our responses and additional evidence can address your concerns. If accepted and revisions are permitted, we will revise our manuscript based on your suggestions in the Camera-Ready version. We respectfully hope you can recognize our work and look forward to your continued guidance and feedback."}, {"review_id": "aQgPwY0z0T", "reviewer": "Reviewer_8M61", "summary": "This paper proposes GauSAM, which integrates contour-guided 2D Gaussian probability fields into the SAM.  Segmentation masks are parameterized as continuous probability fields of learnable 2D Gaussian primitives, ensuring spatial smoothness and structural consistency.  Contourlet transforms extract rich multidirectional frequency information to guide the spatial distribution of these Gaussian primitives, significantly improving boundary fidelity.  GauSAM demonstrates excellent cross-domain generalization and resolution-agnostic inference performance with a remarkably small number of trainable parameters.", "questions": "1. How to initialize the 2D continuous Gaussian feature fields based on the image features from the Contour-Enhanced Encoder? Furthermore, how to initialize the LoRA adapters?\n2. The proposed method does not demonstrate an advantage over I-MedSAM in multi-class organ segmentation. The Author claims that they use less training data. What are the specific differences?\n3. How to carry out arbitrary resolution segmentation results by Target Resolution Grid Sampling?\n\nI will consider raising the score if the author can clarify some weaknesses or questions.", "limitations": "As said in Weakness.", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1. This paper is the first to construct a continuous probability field using 2D Gaussian Splatting for mask generation, achieving promising performance.\n2. The method employs a parameter-efficient LoRA adapter and a specially designed Gaussian Parameters Library, resulting in a significantly smaller number of trainable parameters.\n3. This paper clearly delineates the work's advantages and limitations, alongside future research directions.\n\nWeaknesses:\n1. Key intermediate variables in Figure 1 lack proper annotations.\n2. An ablation study is necessary to validate the claimed training efficiency improvements attributed to the proposed Gaussian Parameters Library.\n3. Lacks quantitative metrics for parameter count, FLOPs, and inference times, which are crucial for a comprehensive evaluation of computational efficiency.\n4. It seems that the cross-domain and cross-resolution generalization performance appears to be a primary advantage of GauSAM, while the experimental comparisons with conventional segmentation baselines are insufficient.   A more thorough evaluation should include comparisons with methods specifically designed for multi-scale and multi-modal segmentation [1][2][3][4].\n5. This work can be considered an extension of I-MedSAM, a comparative analysis of using NSCT rather than FFT in Encoder would be beneficial.\n\nReference:\n1. Kolahi S G, Chaharsooghi S K, Khatibi T, et al. MSA $^ 2$ Net: Multi-scale Adaptive Attention-guided Network for Medical Image Segmentation[J]. arXiv preprint arXiv:2407.21640, 2024.\n2. Rahman M M, Munir M, Marculescu R. Emcad: Efficient multi-scale convolutional attention decoding for medical image segmentation[C]//Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2024: 11769-11779.\n3. Shi J, Shang C, Sun Z, et al. PASSION: Towards Effective Incomplete Multi-Modal Medical Image Segmentation with Imbalanced Missing Rates[C]//Proceedings of the 32nd ACM International Conference on Multimedia. 2024: 456-465.\n4. Liao C, Zheng X, Lyu Y, et al. Memorysam: Memorize modalities and semantics with segment anything model 2 for multi-modal semantic segmentation[J]. arXiv preprint arXiv:2503.06700, 2025.", "was_revised": true, "final_justification": "Authors have resolved some of my concerns by adding a detailed explanation of the Gaussian Parameters Library and an analysis of the computational burden across GauSAM's components.  However, the supplementary experimental results contain data inconsistencies that materially undermine the reliability of the experiments. In its current form, the manuscript is not suitable for acceptance.", "rebuttal": "# Rebuttal to Reviewer 8M61\nWe sincerely thank you for your detailed review and the effort invested in evaluating our manuscript, and we highly value your feedback and have thoroughly considered your concerns, noticing that there may be some misunderstandings regarding our work. Below, we provide a structured analysis and response to your concerns, hoping to dispel doubts and clarify potential misunderstandings about our contributions. \n## Response to weaknesses:\n1. **Missing annotations for key variables in Figure 1:** We apologize for the missing annotations details in Figure 1. Briefly, we have:\n\n - **$I\\in\\mathbb{R}^{B\\times C\\times H\\times W}$** is the input image batch (batch size B, channels C, height H, width W).\n - For each ViT block $i$: **$E_i\\in\\mathbb{R}^{N_p\\times D}$** is the NSCT-extracted contour energy aligned to the $N_p$ patch embeddings of dimension D. **$T_i\\in\\mathbb{R}^{N_p\\times D}$** is the ViT token embedding entering block i; these are fused as $T_i' = T_i + \\lambda\\,W_i\\odot E_i$, where the meaning of the symbol is the same as in Equ 5.\n - Prompt tokens $t\\in\\mathbb{R}^D$ (e.g. box-corner or point embeddings) are produced by the prompt encoder and guide cross-attention in the mask decoder.\n - In the continuous field decoder, each Gaussian primitive $i$ is parameterized by: an initial normalized position **$p_i\\in\\mathbb{R}^2$**, a contour feature vector **$u_i\\in\\mathbb{R}^D$** extracted at $p_i$,\n  - a learned positional offset **$\\Delta\\mu_i\\in\\mathbb{R}^2$** predicted by a small MLP from $u_i$, yielding the final center **$\\mu_i = p_i + \\Delta\\mu_i\\in\\mathbb{R}^2$**,\n   - a feature embedding **$v_i\\in\\mathbb{R}^D$** that the selection head maps to logits **$z_i\\in\\mathbb{R}^m$**, which are converted via Gumbel-Softmax into weights **$w_i\\in\\Delta^{m-1}$** over the Gaussian Parameters Library of $m$ template pairs $(\\Sigma^{(k)}\\in\\mathbb{R}^{2\\times2},\\,\\xi^{(k)}\\in\\mathbb{R})$.\n - The primitive’s covariance **$\\Sigma_i\\in\\mathbb{R}^{2\\times2}$** and opacity **$\\xi_i\\in\\mathbb{R}$** are then obtained as weighted sums of the library templates. These Gaussians define a smooth, resolution-agnostic probability field that—when sampled on an arbitrary grid and passed through the segmentation head—yields the final mask.\n\n2. **The ablation on the Gaussian Parameters Library:**  Directly learning each primitive’s covariance $\\Sigma_i$ and opacity $\\xi_i$ end-to-end has been shown to be highly unstable and slow to converge in recent continuous-field segmentation works [5,6,7]. Those studies demonstrate that unconstrained optimization of high-dimensional Gaussian parameters suffers from poor conditioning, requires careful initialization, and often collapses without extensive regularization. By constraining our primitives to a compact, learned template subspace, the Gaussian Parameters Library sidesteps these issues, yielding far more stable and efficient training. Implementing the “library vs. no-library” ablation would therefore require a wholesale redesign of our decoder, specialized solvers to enforce covariance positive-definiteness, and exhaustive hyperparameter re-tuning—efforts that exceed the scope of this revision. We view a full comparison as valuable future work once such architectural and optimization tools are better established.\n\n3. **Computational efficiency metrics:** We thank the reviewer for underscoring the need for concrete measurements of parameter count, FLOPs, and inference time. Actually, we have performed a full set of benchmarks—measuring model parameters, FLOPs, and inference latency on an RTX 4090—prior to submission. At the time, we chose to reserve main‐text space for algorithmic details and insightful diagrams, so these numbers were deferred to the supplementary material. For completeness, we summarize the results here:\n\n   **Table 1.** GauSAM inference performance on RTX 4090. Total parameters: 92.51 M;  Trainable parameters:1.2M; FLOPs per forward pass: 125.23 GFLOPs.\n\n|Input Resolution|Batch Size|Avg Latency(ms)|FPS |Peak Memory(MB)|\n| - | -| - | - | - |\n|384 × 384|1|164.8|6.07|1246|\n|384 × 384|2|265.8|7.52|2123|\n|384 × 384|4|423.7|9.44|3876|\n|256 × 256|1|158.1|6.33|781|\n|512 × 512|1|188.6|5.30|1898|\n\n   These results demonstrate that GauSAM delivers real-time performance well within clinical usability requirements, providing efficient inference without compromising accuracy or cross-resolution generalization.\n\n4. **Comparisons with multi‑scale and multi‑modal segmentation methods** Thank you for the suggestion. The cited works [1,2] focus on fusing multi-scale inputs through parallel encoder branches, whereas GauSAM instead produces a resolution-agnostic continuous output field from single-scale input, making direct comparison misaligned with our design goals. Likewise, [3,4] address multi-modal segmentation by integrating modality-specific features, while our framework operates solely on single-modality images and does not incorporate multi-modal data. As such,  direct comparison with these paradigms would not meaningfully reflect GauSAM’s unique strengths in cross-domain and cross-resolution generalization. Our existing experiments—spanning diverse datasets and resolutions—already substantiate these advantages, and we will clarify these distinctions in the revised manuscript and view integration with multi‑modal frameworks as an exciting avenue for future work.\n\n5. **Extension of I-MedSAM and NSCT vs. FFT Analysis:** Thank you for the suggestion. While GauSAM and I-MedSAM both leverage contour information, GauSAM introduces a fundamentally different encoder–decoder framework: it constructs an explicit continuous Gaussian probability field rather than relying on implicit neural representations, and it uses NSCT’s shift-invariant, multi-scale, multi-directional contour decomposition in place of FFT’s broad spectral bands. Moreover, GauSAM fuses contour features at every ViT block and applies a Contour-Guided Position Drift to bias Gaussian placements toward true boundaries. \n   To validate this design choice, we compared NSCT to FFT and traditional edge detectors on the Kvasir-Sessile dataset (Table 1). These experiments confirm NSCT's superiority in achieving precise boundary delineation and its better compatibility with the overall GauSAM framework. \n\n   **Table 2.** Comparative performance of different contour/high‑frequency feature extraction methods on Kvasir‑Sessile for binary polyp segmentation.\n\n|Method|Dice(%)|HD|\n|-|-|-|\n|NSCT|**94.76**|**10.29**|\n|FFT|93.68|11.34|\n|Canny|93.66|11.82|\n|Wavelet|94.13|11.40|\n|Sobel|93.71|11.15|\n\n## Responses to Specific Questions\n\n1. **Initialization of Gaussian fields and LoRA adapters**\n\n   All initial Gaussian parameters—per-primitive σₓ/σᵧ (linearly spaced between 0.2 and 3.0), zero correlation, and opacity (sigmoid(1)≈0.73)—are stored in the Gaussian Parameter Library. Primitive centers are placed on a uniform grid and position-drift offsets start at zero; both the template parameters and the drift MLP weights use Kaiming uniform initialization for stable training.\n\n   LoRA adapters target the Q and V projection matrices of each attention layer, leaving the original SAM weights unchanged: the “up” projections use Kaiming uniform initialization and the “down” projections are zero-initialized, ensuring early updates occur solely within the LoRA modules.\n\n2. **Multi‑class organ segmentation and “less training data” misunderstanding**\n    We apologize for the misunderstanding—our claim was fewer trainable parameters, not fewer training samples. On the BCV multi-organ benchmark, we use the *same* training splits as I-MedSAM and achieve a Dice of 89.75 % (vs. 89.91 %) while using only 2.9 M trainable parameters. This reflects a deliberate trade-off: GauSAM’s single Gaussian probability field excels at large-structure coherence and cross-resolution generalization but has inherently less capacity to capture the fine boundaries of smaller organs than a class-specific multi-field design (which would inflate parameters to ~6.6 M and incur much higher latency). We prioritized a highly compact, scalable model and view extending our continuous-field approach to 3D as a promising future direction to recover small-organ detail without forfeiting efficiency.\n\n3. **Arbitrary‑resolution grid sampling**\n    Target Resolution Grid Sampling operates directly on the learned continuous probability field $X(p)$. Concretely, we define a uniform grid of normalized coordinates $p_{j,k}\\in[-1,1]^2$ for an output of size $H'\\times W'$. Since each Gaussian covariance $\\Sigma_i$ was optimized at the training resolution $H\\times W$, we rescale $\\Sigma_i$ by $(H/H')^2$ so that its effective spatial support remains consistent in pixel units. We then analytically evaluate every Gaussian primitive $G_i(p_{j,k})$, weight by its learned coefficient, and sum across all primitives to produce the continuous field value $X(p_{j,k})$. Finally, a lightweight segmentation head maps $X(p_{j,k})$ to class logits and a softmax yields per-pixel probabilities. \n\n**Conclusion**\n We trust these clarifications, additional results, and ablation studies address your concerns and highlight GauSAM’s unique contributions: a theoretically grounded continuous probability field, efficient parameterization, and strong empirical performance across domains and resolutions. We hope this rebuttal leads you to consider an increased evaluation score.\n\n**References**\n\n[1,2,3,4] same references as used by reviewer.\n\n[5]Xinjie Zhang et al. Gaussianimage: 1000 fps image representation and compression by 2d gaussian splatting. In European Conference on Computer Vision, pages 327–345. Springer, 2024.\n\n[6]Kerbl, B.et al. 3d gaussian splatting for real-time radiance field rendering. ACM Transactions on Graphics 42(4) (2023)\n\n[7]Long Peng et al. Pixel to gaussian: Ultra-fast continuous super-resolution with 2d gaussian modeling. arXiv preprint arXiv:2503.06617, 2025."}, {"review_id": "INJMidYgo8", "reviewer": "Reviewer_2QAj", "summary": "GauSAM integrates contour-guided Gaussian fields into SAM for medical image segmentation, showing improved accuracy but lacks groundbreaking innovation, resembling incremental advancements over existing methods.", "questions": "1. While the integration of Gaussian splatting for continuous mask generation is innovative, how does it fundamentally differ from other implicit neural representation (INR) methods? What specific advantages does Gaussian splatting offer over existing INR techniques in terms of accuracy and computational efficiency?\n\n2. In my opinion, the paper emphasises the use of contour-guided mechanisms to improve boundary delineation. However, how robust is this approach when dealing with images that have ambiguous or missing boundaries? Can the model still maintain high-fidelity segmentation under such conditions?\n\n3. Will the code be publicly available? Since this method integrates so many modules and introduces many hyperparameters, it is possible to hinder the reproducibility if the code is not released.", "limitations": "The preprocessing steps, including resizing input images and normalization procedures, play a crucial role in the final performance. How sensitive is GauSAM’s performance to variations in these preprocessing steps? Would different preprocessing strategies yield better results?", "rating": 2, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "1. The primary objective of GauSAM is to integrate contour-guided 2D Gaussian probability fields into the Segment Anything Model (SAM) to enhance segmentation accuracy and boundary fidelity. However, this concept appears to be a relatively straightforward extension of existing methodologies, particularly those employing implicit neural representations (INRs) for continuous spatial representation and Gaussian-based approaches for mask generation. While the combination of these elements may yield performance improvements, it does not fundamentally alter our understanding or approach to medical image segmentation.\n\n2. The paper introduces several components like the Contour Propagation Unit (CPU), the use of Non-Subsampled Contourlet Transform (NSCT) for feature extraction, and the construction of a resolution-agnostic Gaussian field decoder. However, these contributions seem more incremental rather than transformative. For instance, NSCT has been widely used in image processing tasks [1,2] for feature enhancement, and the idea of using Gaussian splatting for generating masks has precedent in recent research. This raises questions about the originality of the proposed method.\n\n3. There is a noticeable resemblance between GauSAM's approach and prior works on incorporating structural priors into deep learning models for segmentation tasks. The mechanism of enhancing encoder sensitivity to contours through multi-level decomposition and then guiding the decoder via extracted features follows patterns seen in other studies. Without clear distinctions or significant advancements beyond what has been previously reported, which further weakens the novelty of GauSAM.\n\n[1] Gomathi, P.S. and Kalaavathi, B., 2016. Multimodal medical image fusion in non-subsampled contourlet transform domain. Circuits and Systems, 7(8), pp.1598-1610.\n\n[2] Heshmati, A., Gholami, M. and Rashno, A., 2016. Scheme for unsupervised colour–texture image segmentation using neutrosophic set and non‐subsampled contourlet transform. IET Image Processing, 10(6), pp.464-473.", "was_revised": true, "final_justification": "After the rebuttal, I think their arguments in the rebuttal stage are insufficient to address my concerns. Please see the details in my comments.", "rebuttal": "# Response to Reviewer 2QAj\nWe sincerely thank you for your detailed review and the effort invested in evaluating our manuscript, and we highly value your feedback and have thoroughly considered your concerns. However, we sincerely believe that while your points, particularly those in Strengths and Weaknesses, hold some merit, they do not justify dismissing the innovation and originality of our work. As noted by Reviewer 9QbL, GauSAM is the first to model SAM's segmentation probability field as a continuous field using 2D Gaussian Splatting, a pioneering contribution that has great potential to advance high-precision image segmentation. Below, we provide a structured analysis and response to your concerns, hoping to dispel doubts and clarify potential misunderstandings about our contributions. We hope these responses can clarify GauSAM’s pioneering contributions and respectfully invite you to reconsider the originality and significance of our work.\n## Summary of All Concerns\nYour primary concerns can be summarized into four key aspects:\n1. **Gaussian Splatting Innovation**: You suggest that GauSAM’s modeling of a continuous Gaussian probability field using 2D Gaussian Splatting lacks novelty, as prior works have employed implicit neural representations (INRs) for continuous spatial representation and Gaussian-based methods for mask generation, and also question the advantages of Gaussian Splatting over INRs.\n2. **NSCT Originality and Robustness**: You argue that the use of Non-Subsampled Contourlet Transform (NSCT) and the Contour Propagation Unit (CPU) lacks originality, citing prior applications of NSCT in image processing and similarities to U-Net’s feature fusion, while questioning GauSAM’s performance on images with ambiguous boundaries.\n3. **Reproducibility**: You express concerns about the reproducibility of our method due to the integration of multiple modules and hyperparameters, emphasizing the need for public code release.\n4. **Preprocessing Impact**: You question the sensitivity of GauSAM’s performance to preprocessing steps, such as image resizing and normalization, and their influence on final results.\n\nWe address all your concerns below, aspiring to shift your view on the contributions of our work.\n## Response to Weakness 1 and Question 1\nYour concern regarding the novelty of Gaussian Splatting and its advantages over implicit neural representations (INRs) is appreciated, but we sincerely believe your perspective does not undermine the innovation and originality of GauSAM. We address this in two points:\n1. **Pioneering Integration of Gaussian Splatting**: As correctly noted by Reviewer 9QbL, GauSAM is the first to explicitly model SAM’s segmentation probability field as a continuous field using 2D Gaussian Splatting, directly mapping discrete feature fields to continuous mask probability fields. While prior works have used INRs for continuous representations or Gaussian-based methods for mask generation, their principles and implementations fundamentally differ from GauSAM. A careful review of related literature reveals that existing methods typically use segmentation model outputs to guide Gaussian primitive grouping or employ Gaussian Splatting to directly reconstruct images before segmentation, enhancing edge quality indirectly. Unlike all of these approaches, GauSAM deeply integrates the process of segmentation and Gaussian Splatting, using learnable Gaussian primitives to directly construct a continuous probability field from feature fields. This novel paradigm not only achieves superior segmentation (Dice: 94.76% on Kvasir-Sessile, 89.75% on BCV) but also introduces a generalizable approach for future segmentation tasks, which is also applicable beyond medical area. By modeling segmentation as a field-mapping process using Gaussian primitives, GauSAM transcends traditional interpolation or INR-based decoding, offering an absolutely novel perspective on mask generation.\n2. **Advantages of Gaussian Splatting over INRs**:\n   - Theoretically, INRs and Gaussian Splatting model segmentation tasks in fundamentally distinct ways. INRs predict mask probabilities globally by aggregating all pixels via neural networks. This approach is fundamentally incompatible with the intrinsic properties of segmentation, spatial continuity and local consistency, which mean adjacent pixels are more likely to belong to the same object. Mathematically, INR fields are continuous due to activation functions (e.g., ReLU is piecewise continuous, Sigmoid is smooth). In other words, for any small coordinate change $\\Delta x$, the output change $\\Delta f$ remains bounded. However, **continuity** does not guarantee **smoothness**, as INR networks lack explicit constraints on derivative continuity, leading to rapid value changes or artifacts at boundaries. Conversely, Gaussian Splatting leverages elliptical stacking and exponential decay to ensure smooth, continuous fields, ideal for segmentation masks. Gaussian primitives independently model local regions, excelling at capturing complex geometries and high-frequency details critical for medical imaging. Moreover, Gaussian Splatting optimizes primitive parameters directly, ensuring stable convergence and interpretability, unlike INRs’ sensitivity to hyperparameters.\n   - Experimentally, regarding your perception of modest improvements, we respectfully clarify that GauSAM’s more than 3% Dice increase (e.g., 94.76% vs. 91% SOTA on Kvasir-Sessile) is significant, as SOTA baselines already exceed 90%. Improving beyond this threshold usually addresses challenging edge cases, unlike early gains from 60% to 80% that merely expand mask coverage. Visual results in Figure 2 (left panel, polyp segmentation) also demonstrate GauSAM’s smoother, more consistent boundaries compared to baselines. This boundary precision is critical in medical segmentation, directly enhancing diagnostic accuracy by reducing errors in boundary delineation.\n## Response to Weakness 2 & 3 and Question 2\nWe sincerely thank you for raising insightful concerns about the originality of our Non-Subsampled Contourlet Transform (NSCT) and Contour Propagation Unit (CPU) modules, as well as GauSAM’s robustness on images with ambiguous boundaries. These questions are highly valuable, as they touch on components we meticulously designed to enhance segmentation accuracy. We provide a detailed clarification below in two parts, hoping to address your doubts and concerns on the novelty and effectiveness of our approach.\n1. **Originality of NSCT and CPU**: Your reference to prior works [Gomathi 2016, Heshmati 2016] using NSCT for feature enhancement is appreciated, but these studies rely on traditional machine learning methods, which are fundamentally distinct from our ViT-based framework and apparently lack relevance to modern transformer architectures. While some U-Net-based works have employed Contourlet transforms, the downsampling structure and local convolutional operations of U-Net differ significantly from ViT’s mechanism. Moreover, unlike Contourlet, NSCT extracts multi-scale, multi-directional contour features without downsampling, making it uniquely suited for ViT’s feature hierarchy. Our Contour Propagation Unit (CPU) progressively fuses NSCT-derived contour features into each ViT block, ensuring that contour information evolves in alignment with the image feature space, enhancing boundary awareness throughout encoding. Additionally, our Contour-Guided Position Drift module optimizes Gaussian kernel placements toward semantic boundaries, improving high-frequency region representation. This dual use of contour information—enhancing both encoding and decoding—represents a novel integration, which is totally different from those used in traditional machine learning methods and U-Net-based models.\n2. **Robustness on Ambiguous Boundaries**: Your concern about GauSAM’s performance on images with blurred boundaries is really well-taken. In the Kvasir-Sessile dataset, many images exhibit ambiguous or missing polyp boundaries, which are obscured by strong reflections from bodily fluids. These images even pose challenges for human observers. However, GauSAM significantly outperforms existing SOTA models, including I-MedSAM, achieving more complete masks and much higher accuracy in these low-quality images. This robustness stems from NSCT’s multi-scale contour priors and CPU’s effective fusion, which reduce sensitivity to image quality. Due to rebuttal stage constraints, we cannot provide additional visualizations. However, if our manuscript is accepted and revisions are permitted in the Camera-Ready phase, we will include relevant images in the Appendix.\n## Response to Question 3\nWe are fully committed to ensuring transparency and reproducibility. If our manuscript is accepted, we will publicly release the code, including detailed hyperparameter settings. However, at this stage, to safeguard the integrity of our research and maintain anonymity during the review process, we respectfully request your understanding for not yet releasing the code. We are highly confident in the reproducibility of our experiments, which are grounded in rigorous design and validation. We hope this commitment addresses your concern and reinforces trust in GauSAM’s reproducibility.\n## Response to Limitations\nTo ensure experimental consistency and comparability, we adopted the standard preprocessing steps used by SAM and all SAM-based models, as detailed in Section 4.1. This choice controls variables and enables fair comparisons with baselines, aligning with established practices in this field. Also, we want to clarify that preprocessing is not the focus of our research,  so we did not conduct independent experiments on preprocessing variations.\n## Conclusion\nWe hope our responses and additional evidence can address your concerns. We respectfully hope you can recognize our work and look forward to your continued guidance and feedback."}]

Author rebuttal:

Meta-review: The proposed work extends the Segment Anything Model (SAM) by explicitly modeling the segmentation probability field as a combination of two-dimensional Gaussians, enabling the trained network to process images of arbitrary resolution. During the initial review process, reviewers acknowledged the novelty of the approach (9QbL, 8M61), its superior performance and generalization ability, as well as its efficiency. At the same time, several weaknesses were raised, including the need for clearer distinctions and advantages relative to existing methods (e.g., I-MedSAM), the limited empirical validation (restricted to two datasets), lack of clarity regarding the motivation, missing analyses in the empirical evaluation (e.g., training and computational efficiency, along with references suggested by reviewer 8M61), and concerns regarding the degree of novelty (reviewer 2QAj).

After carefully examining the manuscript, the reviews, the authors’ responses, and the subsequent discussions, I am convinced that the authors have successfully addressed the majority of these concerns. In particular, they have provided sufficient evidence to respond to the questions on empirical validation, either by supplying additional quantitative results where feasible or by offering convincing justifications when further experiments could not reasonably be added. Moreover, the clarifications regarding the differences from prior work, as well as the detailed motivation of the proposed approach, make a strong case for its novelty.

Considering these points, I recommend acceptance of this work, and I encourage the authors to incorporate the constructive feedback provided by the reviewers in the final version.
Decision: Accept (poster)