arXiv:2606. 00139v1 Announce Type: cross Abstract: Curvature-penalized geodesic models have proven their effectiveness in image segmentation by computing globally optimal curves.
arXiv:2609.08153v1 Announce Type: new Abstract: Generative diffusion models have emerged as a class of powerful techniques for various imaging applications, including but not limited to synthesis, re...
arXiv:2608. 19965v1 Announce Type: cross Abstract: Segmentation of curvilinear anatomical structures in 3D medical images remains challenging due to complex topology, severe class imbalance, weak contrast, and large variations in structure morphology.
arXiv:2608.20942v1 Announce Type: new Abstract: Motivated by the classical Chan-Vese model and the ability of deep priors to capture complex spatial structures, we develop a segmentation model that l...
The paper introduces a Deep Active Contour and Mean Curvature (DACMC) loss function for medical image segmentation. By incorporating mean curvature as a geometric constraint and approximating it with a convolution kernel, the method aims to improve the geometric characterization of segmented regions. Experiments on liver and spleen datasets show that DACMC achieves new state‑of‑the‑art performance across several segmentation benchmarks.
arXiv:2606. 14912v1 Announce Type: cross Abstract: Despite great advances, finding accurate segmentation remains a challenging task, especially in scenarios with cluttered backgrounds, complex intensity variations and topology appearance.
The paper introduces a Nested Inductive Bias framework that uses a two‑stage diffeomorphic composition to pull back non‑Euclidean target geometries onto symmetric positive definite (SPD) manifolds. This approach allows the construction of curvature‑aligned Riemannian classifiers that respect both matrix constraints and the intrinsic relational geometry of data. Empirical results on kinematic, signal processing, and synthetic benchmarks show that class separability degrades when metric curvature does not match the data distribution, and the authors also propose the Rational Conformal Metric (RCM) for robust vectorized architectures.
arXiv:2510. 21033v3 Announce Type: replace-cross Abstract: We develop a theory of iso-Riemannian optimization for problems constrained to learned data manifolds, a setting in which classical Riemannian optimization - and Riemannian gradient descent in particular - can be poorly suited.
arXiv:2510. 09468v3 Announce Type: replace Abstract: Latent manifolds of autoencoders provide low-dimensional representations of data, which can be studied from a geometric perspective.
Optimizing 3D shapes within the latent spaces of deep generative models is fundamental to computer assisted engineering, yet remains prone to a critical failure mode we term manifold drift: the tendency of gradient-based optimization to move latent vectors away from the manifold of valid shapes. This problem is exacerbated in state-of-the-art 3D shape generative models that operate in increasingly high-dimensional latent spaces where valid shapes occupy a vanishingly small fraction of the full space.
arXiv:2607. 19305v2 Announce Type: replace-cross Abstract: Deep neural networks on manifold-valued representations have attracted growing interest, but many basic components remain tied to specific manifolds, rely on Euclidean approximations, or require costly and numerically fragile geometric operations.
arXiv:2606. 17022v1 Announce Type: cross Abstract: A central objective of machine learning is to identify structure and patterns in data.
arXiv:2607. 19305v1 Announce Type: cross Abstract: Deep neural networks on manifold-valued representations have attracted growing interest, but many basic components remain tied to specific manifolds, rely on Euclidean approximations, or require costly and numerically fragile geometric operations.