arXiv:2511.18679v1 Announce Type: new 
Abstract: Neural representations for 3D meshes are emerging as an effective solution for compact storage and efficient processing. Existing methods often rely on neural overfitting, where a coarse mesh is stored and progressively refined through multiple decoder networks. While this can restore high-quality surfaces, it is computationally expensive due to successive decoding passes and the irregular structure of mesh data. In contrast, images have a regular structure that enables powerful super-resolution and restoration frameworks, but applying these advantages to meshes is difficult because their irregular connectivity demands complex encoder-decoder architectures. Our key insight is that a geometry image-based representation transforms irregular meshes into a regular image grid, making efficient image-based neural processing directly applicable. Building on this idea, we introduce our neural geometry image-based representation, which is decoder-free, storage-efficient, and naturally suited for neural processing. It stores a low-resolution geometry-image mipmap of the surface, from which high-quality meshes are restored in a single forward pass. To construct geometry images, we leverage Optimal Transport (OT), which resolves oversampling in flat regions and undersampling in feature-rich regions, and enables continuous levels of detail (LoD) through geometry-image mipmapping. Experimental results demonstrate state-of-the-art storage efficiency and restoration accuracy, measured by compression ratio (CR), Chamfer distance (CD), and Hausdorff distance (HD).

تقدم دراسة جديدة تمثيلًا لصورة هندسية عصبية يحول الشبكات ثلاثية الأبعاد غير المنتظمة إلى شبكة صورة منتظمة، مما يسهل المعالجة العصبية الفعالة. تتناول هذه الطريقة القيود المفروضة على الأساليب الحالية التي تعتمد على الإفراط في التكيف العصبي وعمليات فك التشفير المتعددة، والتي تتطلب موارد حسابية كبيرة. تهدف الطريقة المقترحة إلى تحسين جودة وكفاءة تمثيل ومعالجة الشبكات ثلاثية الأبعاد.

Un nuevo estudio presenta una representación de imagen geométrica neuronal que transforma mallas 3D irregulares en una cuadrícula de imagen regular, facilitando así el procesamiento neuronal eficiente. Este enfoque aborda las limitaciones de los métodos existentes que dependen del sobreajuste neuronal y múltiples pasadas de decodificación, que son costosas en términos computacionales. El método propuesto busca mejorar la calidad y eficiencia de la representación y procesamiento de mallas 3D.

Une nouvelle étude présente une représentation d'image géométrique neuronale qui transforme les maillages 3D irréguliers en une grille d'image régulière, facilitant ainsi le traitement neuronal efficace. Cette approche répond aux limitations des méthodes existantes qui reposent sur le surajustement neuronal et plusieurs passes de décodage, coûteuses en termes de calcul. La méthode proposée vise à améliorer la qualité et l'efficacité de la représentation et du traitement des maillages 3D.

A new study introduces a neural geometry image-based representation that transforms irregular 3D meshes into a regular image grid, facilitating efficient neural processing. This approach addresses the limitations of existing methods that rely on neural overfitting and multiple decoding passes, which are computationally expensive. The proposed method aims to enhance the quality and efficiency of 3D mesh representation and processing.

Neural Geometry Image-Based Representations with Optimal Transport (OT)

arXiv:2511.19741v1 Announce Type: new 
Abstract: Optimal Transport (OT) offers a powerful framework for finding correspondences between distributions and addressing matching and alignment problems in various areas of computer vision, including shape analysis, image generation, and multimodal tasks. The computation cost of OT, however, hinders its scalability. Slice-based transport plans have recently shown promise for reducing the computational cost by leveraging the closed-form solutions of 1D OT problems. These methods optimize a one-dimensional projection (slice) to obtain a conditional transport plan that minimizes the transport cost in the ambient space. While efficient, these methods leave open the question of whether learned optimal slicers can transfer to new distribution pairs under distributional shift. Understanding this transferability is crucial in settings with evolving data or repeated OT computations across closely related distributions. In this paper, we study the min-Sliced Transport Plan (min-STP) framework and investigate the transferability of optimized slicers: can a slicer trained on one distribution pair yield effective transport plans for new, unseen pairs? Theoretically, we show that optimized slicers remain close under slight perturbations of the data distributions, enabling efficient transfer across related tasks. To further improve scalability, we introduce a minibatch formulation of min-STP and provide statistical guarantees on its accuracy. Empirically, we demonstrate that the transferable min-STP achieves strong one-shot matching performance and facilitates amortized training for point cloud alignment and flow-based generative modeling.

تقدم دراسة جديدة مفهوم النقل الأمثل القابل للنقل بكفاءة عبر خطط النقل المقطعية الدنيا، مما يعزز إطار النقل الأمثل (OT) من خلال تقليل التكاليف الحسابية المرتبطة بمطابقة التوزيعات في مهام رؤية الكمبيوتر. تستفيد هذه الطريقة من الإسقاطات أحادية الأبعاد لتحسين خطط النقل، مما يعالج مشكلات القابلية للتوسع في تطبيقات مثل تحليل الأشكال وتوليد الصور.

Un nuevo estudio presenta el Transporte Óptimo Transferible Eficiente a través de Planes de Transporte Min-Sliced, que mejora el marco del Transporte Óptimo (OT) al reducir los costos computacionales asociados con la correspondencia de distribuciones en tareas de visión por computadora. Este método aprovecha proyecciones unidimensionales para optimizar los planes de transporte, abordando problemas de escalabilidad en aplicaciones como el análisis de formas y la generación de imágenes.

Une nouvelle étude présente le Transport Optimal Transférable Efficace via des Plans de Transport Min-Sliced, qui améliore le cadre du Transport Optimal (OT) en réduisant les coûts computationnels associés à l'appariement de distributions dans les tâches de vision par ordinateur. Cette méthode s'appuie sur des projections unidimensionnelles pour optimiser les plans de transport, abordant ainsi les problèmes d'évolutivité dans des applications telles que l'analyse de formes et la génération d'images.

A new study introduces Efficient Transferable Optimal Transport via Min-Sliced Transport Plans, which enhances the Optimal Transport (OT) framework by reducing computational costs associated with matching distributions in computer vision tasks. This method leverages one-dimensional projections to optimize transport plans, addressing scalability issues in applications like shape analysis and image generation.

Neural Geometry Image-Based Representations with Optimal Transport (OT)

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