Roto-Translation Invariant Metrics on Position-Orientation Space

Riemannian metrics on the position-orientation space M(3) that are roto-translation group SE(3) invariant play a key role in image analysis tasks like enhancement, denoising, and segmentation. These metrics enable roto-translation equivariant algorithms, with the associated Riemannian distance often used in implementation. However, computing the Riemannian distance is costly, which makes it unsuitable in situations where constant recomputation is needed. We propose the mav (minimal angular velocity) distance, defined as the Riemannian length of a geometrically meaningful curve, as a practical alternative. We see an application of the mav distance in geometric deep learning. Namely, neural networks architectures such as PONITA, relies on geometric invariants to create their roto-translation equivariant model. The mav distance offers a trainable invariant, with the parameters that determine the Riemannian metric acting as learnable weights. In this paper we: 1) classify and parametrize all SE(3) invariant metrics on M(3), 2) describes how to efficiently calculate the mav distance, and 3) investigate if including the mav distance within PONITA can positively impact its accuracy in predicting molecular properties.

GraphSeg: Segmented 3D Representations via Graph Edge Addition and Contraction

Robots operating in unstructured environments often require accurate and consistent object-level representations. This typically requires segmenting individual objects from the robot's surroundings. While recent large models such as Segment Anything (SAM) offer strong performance in 2D image segmentation. These advances do not translate directly to performance in the physical 3D world, where they often over-segment objects and fail to produce consistent mask correspondences across views. In this paper, we present GraphSeg, a framework for generating consistent 3D object segmentations from a sparse set of 2D images of the environment without any depth information. GraphSeg adds edges to graphs and constructs dual correspondence graphs: one from 2D pixel-level similarities and one from inferred 3D structure. We formulate segmentation as a problem of edge addition, then subsequent graph contraction, which merges multiple 2D masks into unified object-level segmentations. We can then leverage \emph{3D foundation models} to produce segmented 3D representations. GraphSeg achieves robust segmentation with significantly fewer images and greater accuracy than prior methods. We demonstrate state-of-the-art performance on tabletop scenes and show that GraphSeg enables improved performance on downstream robotic manipulation tasks. Code available at https://github.com/tomtang502/graphseg.git.

Analysis of the MICCAI Brain Tumor Segmentation -- Metastases (BraTS-METS) 2025 Lighthouse Challenge: Brain Metastasis Segmentation on Pre- and Post-treatment MRI

Despite continuous advancements in cancer treatment, brain metastatic disease remains a significant complication of primary cancer and is associated with an unfavorable prognosis. One approach for improving diagnosis, management, and outcomes is to implement algorithms based on artificial intelligence for the automated segmentation of both pre- and post-treatment MRI brain images. Such algorithms rely on volumetric criteria for lesion identification and treatment response assessment, which are still not available in clinical practice. Therefore, it is critical to establish tools for rapid volumetric segmentations methods that can be translated to clinical practice and that are trained on high quality annotated data. The BraTS-METS 2025 Lighthouse Challenge aims to address this critical need by establishing inter-rater and intra-rater variability in dataset annotation by generating high quality annotated datasets from four individual instances of segmentation by neuroradiologists while being recorded on video (two instances doing "from scratch" and two instances after AI pre-segmentation). This high-quality annotated dataset will be used for testing phase in 2025 Lighthouse challenge and will be publicly released at the completion of the challenge. The 2025 Lighthouse challenge will also release the 2023 and 2024 segmented datasets that were annotated using an established pipeline of pre-segmentation, student annotation, two neuroradiologists checking, and one neuroradiologist finalizing the process. It builds upon its previous edition by including post-treatment cases in the dataset. Using these high-quality annotated datasets, the 2025 Lighthouse challenge plans to test benchmark algorithms for automated segmentation of pre-and post-treatment brain metastases (BM), trained on diverse and multi-institutional datasets of MRI images obtained from patients with brain metastases.

LaPIG: Cross-Modal Generation of Paired Thermal and Visible Facial Images

The success of modern machine learning, particularly in facial translation networks, is highly dependent on the availability of high-quality, paired, large-scale datasets. However, acquiring sufficient data is often challenging and costly. Inspired by the recent success of diffusion models in high-quality image synthesis and advancements in Large Language Models (LLMs), we propose a novel framework called LLM-assisted Paired Image Generation (LaPIG). This framework enables the construction of comprehensive, high-quality paired visible and thermal images using captions generated by LLMs. Our method encompasses three parts: visible image synthesis with ArcFace embedding, thermal image translation using Latent Diffusion Models (LDMs), and caption generation with LLMs. Our approach not only generates multi-view paired visible and thermal images to increase data diversity but also produces high-quality paired data while maintaining their identity information. We evaluate our method on public datasets by comparing it with existing methods, demonstrating the superiority of LaPIG.

Self-Supervised Learning based on Transformed Image Reconstruction for Equivariance-Coherent Feature Representation

The equivariant behaviour of features is essential in many computer vision tasks, yet popular self-supervised learning (SSL) methods tend to constrain equivariance by design. We propose a self-supervised learning approach where the system learns transformations independently by reconstructing images that have undergone previously unseen transformations. Specifically, the model is tasked to reconstruct intermediate transformed images, e.g. translated or rotated images, without prior knowledge of these transformations. This auxiliary task encourages the model to develop equivariance-coherent features without relying on predefined transformation rules. To this end, we apply transformations to the input image, generating an image pair, and then split the extracted features into two sets per image. One set is used with a usual SSL loss encouraging invariance, the other with our loss based on the auxiliary task to reconstruct the intermediate transformed images. Our loss and the SSL loss are linearly combined with weighted terms. Evaluating on synthetic tasks with natural images, our proposed method strongly outperforms all competitors, regardless of whether they are designed to learn equivariance. Furthermore, when trained alongside augmentation-based methods as the invariance tasks, such as iBOT or DINOv2, we successfully learn a balanced combination of invariant and equivariant features. Our approach performs strong on a rich set of realistic computer vision downstream tasks, almost always improving over all baselines.

Learning Conditionally Independent Transformations using Normal Subgroups in Group Theory

Humans develop certain cognitive abilities to recognize objects and their transformations without explicit supervision, highlighting the importance of unsupervised representation learning. A fundamental challenge in unsupervised representation learning is to separate different transformations in learned feature representations. Although algebraic approaches have been explored, a comprehensive theoretical framework remains underdeveloped. Existing methods decompose transformations based on algebraic independence, but these methods primarily focus on commutative transformations and do not extend to cases where transformations are conditionally independent but noncommutative. To extend current representation learning frameworks, we draw inspiration from Galois theory, where the decomposition of groups through normal subgroups provides an approach for the analysis of structured transformations. Normal subgroups naturally extend commutativity under certain conditions and offer a foundation for the categorization of transformations, even when they do not commute. In this paper, we propose a novel approach that leverages normal subgroups to enable the separation of conditionally independent transformations, even in the absence of commutativity. Through experiments on geometric transformations in images, we show that our method successfully categorizes conditionally independent transformations, such as rotation and translation, in an unsupervised manner, suggesting a close link between group decomposition via normal subgroups and transformation categorization in representation learning.

CM-Diff: A Single Generative Network for Bidirectional Cross-Modality Translation Diffusion Model Between Infrared and Visible Images

The image translation method represents a crucial approach for mitigating information deficiencies in the infrared and visible modalities, while also facilitating the enhancement of modality-specific datasets. However, existing methods for infrared and visible image translation either achieve unidirectional modality translation or rely on cycle consistency for bidirectional modality translation, which may result in suboptimal performance. In this work, we present the cross-modality translation diffusion model (CM-Diff) for simultaneously modeling data distributions in both the infrared and visible modalities. We address this challenge by combining translation direction labels for guidance during training with cross-modality feature control. Specifically, we view the establishment of the mapping relationship between the two modalities as the process of learning data distributions and understanding modality differences, achieved through a novel Bidirectional Diffusion Training (BDT) strategy. Additionally, we propose a Statistical Constraint Inference (SCI) strategy to ensure the generated image closely adheres to the data distribution of the target modality. Experimental results demonstrate the superiority of our CM-Diff over state-of-the-art methods, highlighting its potential for generating dual-modality datasets.

ShapeShift: Towards Text-to-Shape Arrangement Synthesis with Content-Aware Geometric Constraints

While diffusion-based models excel at generating photorealistic images from text, a more nuanced challenge emerges when constrained to using only a fixed set of rigid shapes, akin to solving tangram puzzles or arranging real-world objects to match semantic descriptions. We formalize this problem as shape-based image generation, a new text-guided image-to-image translation task that requires rearranging the input set of rigid shapes into non-overlapping configurations and visually communicating the target concept. Unlike pixel-manipulation approaches, our method, ShapeShift, explicitly parameterizes each shape within a differentiable vector graphics pipeline, iteratively optimizing placement and orientation through score distillation sampling from pretrained diffusion models. To preserve arrangement clarity, we introduce a content-aware collision resolution mechanism that applies minimal semantically coherent adjustments when overlaps occur, ensuring smooth convergence toward physically valid configurations. By bridging diffusion-based semantic guidance with explicit geometric constraints, our approach yields interpretable compositions where spatial relationships clearly embody the textual prompt. Extensive experiments demonstrate compelling results across diverse scenarios, with quantitative and qualitative advantages over alternative techniques.

Ultrasound Image-to-Video Synthesis via Latent Dynamic Diffusion Models

Ultrasound video classification enables automated diagnosis and has emerged as an important research area. However, publicly available ultrasound video datasets remain scarce, hindering progress in developing effective video classification models. We propose addressing this shortage by synthesizing plausible ultrasound videos from readily available, abundant ultrasound images. To this end, we introduce a latent dynamic diffusion model (LDDM) to efficiently translate static images to dynamic sequences with realistic video characteristics. We demonstrate strong quantitative results and visually appealing synthesized videos on the BUSV benchmark. Notably, training video classification models on combinations of real and LDDM-synthesized videos substantially improves performance over using real data alone, indicating our method successfully emulates dynamics critical for discrimination. Our image-to-video approach provides an effective data augmentation solution to advance ultrasound video analysis. Code is available at https://github.com/MedAITech/U_I2V.

Flash Sculptor: Modular 3D Worlds from Objects

Existing text-to-3D and image-to-3D models often struggle with complex scenes involving multiple objects and intricate interactions. Although some recent attempts have explored such compositional scenarios, they still require an extensive process of optimizing the entire layout, which is highly cumbersome if not infeasible at all. To overcome these challenges, we propose Flash Sculptor in this paper, a simple yet effective framework for compositional 3D scene/object reconstruction from a single image. At the heart of Flash Sculptor lies a divide-and-conquer strategy, which decouples compositional scene reconstruction into a sequence of sub-tasks, including handling the appearance, rotation, scale, and translation of each individual instance. Specifically, for rotation, we introduce a coarse-to-fine scheme that brings the best of both worlds--efficiency and accuracy--while for translation, we develop an outlier-removal-based algorithm that ensures robust and precise parameters in a single step, without any iterative optimization. Extensive experiments demonstrate that Flash Sculptor achieves at least a 3 times speedup over existing compositional 3D methods, while setting new benchmarks in compositional 3D reconstruction performance. Codes are available at https://github.com/YujiaHu1109/Flash-Sculptor.