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 2DGaussian probability fields into the Segment Anything Model to address these challenges. In our framework, segmentation masks are parameterized as continuous probability fields of learnable 2DGaussian 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.

This paper presents a novel approach to addressing the long-sequence problem in high-resolution medical images for Vision Transformers (ViTs). Using smaller patches as tokens can enhance ViT performance, but quadratically increases computation and memory requirements. Therefore, the common practice for applying ViTs to high-resolution images is either to: (a) employ complex sub-quadratic attention schemes or (b) use large to medium-sized patches and rely on additional mechanisms within the model to capture the spatial hierarchy of details. We propose Symmetrical Hierarchical Forest (SHF), a lightweight approach that adaptively patches the input image to increase token information density and encode hierarchical spatial structures into the input embedding. We then apply a reverse depatching scheme to the output embeddings of the transformer encoder, eliminating the need for convolution-based decoders. Unlike previous methods that modify attention mechanisms or use a complex hierarchy of interacting models, SHFcan be retrofitted to any ViT model to allow it to learn the hierarchical structure of details in high-resolution images without requiring architectural changes. Experimental results demonstrate significant gains in computational efficiency and performance: on the PAIPWSI dataset, we achieved a 3 32 speedup or a 2.95% 7.03% increase in accuracy (measured by Dice score) at a 64K2 resolution with the same computational budget, compared to state-of-the-art production models. On the 3D medical datasets BTCV and KiTS, training was 6 faster, with accuracy gains of 6.93% and 5.9%, respectively, compared to models without SHF.

Yet, training still treats these logits in isolation--either supervising only the final, highest-resolution logits or applying deep supervision with identical loss weights at every scale--without exploring mixed-scale combinations. Consequently, the decoder output misses the complementary cues that arise only when coarse and fine predictions are fused. To address this issue, we introduce LoMix (Logits Mixing), a Neural Architecture Search (NAS)-inspired, differentiable plug-and-play module that generates new mixed-scale outputs and learns how exactly each of them should guide the training process. More precisely, LoMix mixes the multi-scale decoder logits with four lightweight fusion operators: addition, multiplication, concatenation, and attentionbased weighted fusion, yielding a rich set of synthetic "mutant" maps. Every original or mutant map is given a softplus loss weight that is co-optimized with network parameters, mimicking a one-step architecture search that automatically discovers the most useful scales, mixtures, and operators. Plugging LoMix into recent U-shaped architectures (i.e., PVT-V2-B2 backbone with EMCAD decoder) on Synapse 8-organ dataset improves DICE by +4.2% over single-output supervision, +2.2% over deep supervision, and +1.5% over equally weighted additive fusion, all with zero inference overhead. When training data are scarce (e.g., one or two labeled scans, 5% of the trainset), the advantage grows to +9.23%, underscoring LoMix's data efficiency. Across four benchmarks and diverse U-shaped networks, LoMiX improves DICE by up to +13.5% over single-output supervision, confirming that learnable weighted mixed-scale fusion generalizes broadly while remaining data efficient, fully interpretable, and overhead-free at inference. Our implementation is available at https://github.com/SLDGroup/LoMix.

A.1 Broader impact Our work introduces a general method for unsupervised 3D segmentation that can be used for any 3D voxel-grid data. This line of work is especially useful for analyzing biomedical data, as many different types of biomedical data are in volumetric form and lack the ground truth annotations required for fully-or semi-supervised segmentation. For example, we may wish to study diseased tissue but do not have sufficient understanding to ensure that unexplored features of interests are labelled in training data. We illustrate the potential of our proposed approach for scientific discovery applications using our example of cryo-ET data in the Appendix. The discovered features can now be analyzed for their chemical identities and functions, in diseased vs. healthy cells.

Precise image segmentation provides clinical study with instructive information.

Neural Information Processing Systems http://nips.cc/

We do not use the background label when computing evaluation metrics.

Segmentation is the identification of anatomical regions of interest, such as organs, tissue, and lesions, serving as a fundamental task in computer-aided diagnosis in medical imaging. Although deep learning models have achieved remarkable performance in medical image segmentation, the need for explainability remains critical for ensuring their acceptance and integration in clinical practice, despite the growing research attention in this area. Our approach explored the use of contrast-level Shapley values, a systematic perturbation of model inputs to assess feature importance. While other studies have investigated gradient-based techniques through identifying influential regions in imaging inputs, Shapley values offer a broader, clinically aligned approach, explaining how model performance is fairly attributed to certain imaging contrasts over others. Using the BraTS 2024 dataset, we generated rankings for Shapley values for four MRI contrasts across four model architectures. Two metrics were proposed from the Shapley ranking: agreement between model and ``clinician" imaging ranking, and uncertainty quantified through Shapley ranking variance across cross-validation folds. Higher-performing cases (Dice \textgreater0.6) showed significantly greater agreement with clinical rankings. Increased Shapley ranking variance correlated with decreased performance (U-Net: $r=-0.581$). These metrics provide clinically interpretable proxies for model reliability, helping clinicians better understand state-of-the-art segmentation models.