Nonrigid registration is conventionally divided into point set registration, which aligns sparse geometries, and image registration, which aligns continuous intensity fields on regular grids. However, this dichotomy creates a critical bottleneck for emerging scientific data, such as spatial transcriptomics, where high-dimensional vector-valued functions, e.g., gene expression, are defined on irregular, sparse manifolds. Consequently, researchers currently face a forced choice: either sacrifice single-cell resolution via voxelization to utilize image-based tools, or ignore the critical functional signal to utilize geometric tools. To resolve this dilemma, we propose Domain Elastic Transform (DET), a grid-free probabilistic framework that unifies geometric and functional alignment. By treating data as functions on irregular domains, DET registers high-dimensional signals directly without binning. We formulate the problem within a rigorous Bayesian framework, modeling domain deformation as an elastic motion guided by a joint spatial-functional likelihood. The method is fully unsupervised and scalable, utilizing feature-sensitive downsampling to handle massive atlases. We demonstrate that DET achieves 92\% topological preservation on MERFISH data where state-of-the-art optimal transport methods struggle ($<$5\%), and successfully registers whole-embryo Stereo-seq atlases across developmental stages -- a task involving massive scale and complex nonrigid growth. The implementation of DET is available on {https://github.com/ohirose/bcpd} (since Mar, 2025).

For classification tasks, the performance of a deep neural network is determined by the structure of its decision boundary, whose geometry directly affects essential properties of the model, including accuracy and robustness. Motivated by a classical tube formula due to Weyl, we introduce a method to measure the decision boundary of a neural network through local surface volumes, providing a theoretically justifiable and efficient measure enabling a geometric interpretation of the effectiveness of the model applicable to the high dimensional feature spaces considered in deep learning. A smaller surface volume is expected to correspond to lower model complexity and better generalisation. We verify, on a number of image processing tasks with convolutional architectures that decision boundary volume is inversely proportional to classification accuracy. Meanwhile, the relationship between local surface volume and generalisation for fully connected architecture is observed to be less stable between tasks. Therefore, for network architectures suited to a particular data structure, we demonstrate that smoother decision boundaries lead to better performance, as our intuition would suggest.

Your Out-of-Distribution Detection Method is Not Robust!

Reinforcement learning (RL) has become a standard technique for post-training diffusion-based image synthesis models, as it enables learning from reward signals to explicitly improve desirable aspects such as image quality and prompt alignment. In this paper, we propose an online RL variant that reduces the variance in the model updates by sampling paired trajectories and pulling the flow velocity in the direction of the more favorable image. Unlike existing methods that treat each sampling step as a separate policy action, we consider the entire sampling process as a single action. We experiment with both high-quality vision language models and off-the-shelf quality metrics for rewards, and evaluate the outputs using a broad set of metrics. Our method converges faster and yields higher output quality and prompt alignment than previous approaches.

We refer to the proposed solution as SA3D, for Segment Anything in 3D. It is only required to provide a manual segmentation prompt ( e.g., rough points) for the target object in a single view, which is used to generate its 2D mask in this view with SAM.

Estimating the 6D object pose is one of the core problems in computer vision and robotics. It predicts the full configurations of rotation, translation and size of a given object, which has wide applications including Virtual Reality (VR) [2], scene understanding [30], and [42, 57, 31, 49]. There are twodirections in 6D object pose estimation.