Modeling group actions on latent representations enables controllable transformations of high-dimensional image data. Prior works applying group-theoretic priors or modeling transformations typically operate in the high-dimensional data space, where group actions apply uniformly across the entire input, making it difficult to disentangle the subspace that varies under transformations. While latent-space methods offer greater flexibility, they still require manual partitioning of latent variables into equivariant and invariant subspaces, limiting the ability to robustly learn and operate group actions within the representation space. To address this, we introduce a novel end-to-end framework that for the first time learns group actions on latent image manifolds, automatically discovering transformation-relevant structures without manual intervention. Our method uses learnable binary masks with straight-through estimation to dynamically partition latent representations into transformation-sensitive and invariant components. We formulate this within a unified optimization framework that jointly learns latent disentanglement and group transformation mappings. The framework can be seamlessly integrated with any standard encoder-decoder architecture. We validate our approach on five 2D/3D image datasets, demonstrating its ability to automatically learn disentangled latent factors for group actions in diverse data, while downstream classification tasks confirm the effectiveness of the learned representations. Our code is publicly available at GitHub.

We introduce IrrMap, the first large-scale dataset (1.1 million patches) for irrigation method mapping across regions. IrrMap consists of multi-resolution satellite imagery from LandSat and Sentinel, along with key auxiliary data such as crop type, land use, and vegetation indices. The dataset spans 1,668,899 farms and 11,443,492 acres across multiple western U.S. states from 2013 to 2023, providing a rich and diverse foundation for irrigation analysis and ensuring geospatial alignment and quality control. The dataset is ML-ready, with standardized 224×224 GeoTIFF patches, the multiple input modalities, carefully chosen train-test-split data, and accompanying dataloaders for seamless deep learning model training and benchmarking in irrigation mapping. The dataset is also accompanied by a complete pipeline for dataset generation, enabling researchers to extend IrrMap to new regions for irrigation data collection or adapt it with minimal effort for other similar applications in agricultural and geospatial analysis. We also analyze the irrigation method distribution across crop groups, spatial irrigation patterns (using Shannon diversity indices), and irrigated area variations for both LandSat and Sentinel, providing insights into regional and resolution-based differences. To promote further exploration, we openly release IrrMap, along with the derived datasets, benchmark models, and pipeline code, through a GitHub repository: https://github.com/Nibir088/IrrMap and Data repository: https://huggingface.co/Nibir/IrrMap, providing comprehensive documentation and implementation details.

Geometric shape features have been widely used as strong predictors for image classification. Nevertheless, most existing classifiers such as deep neural networks (DNNs) directly leverage the statistical correlations between these shape features and target variables. However, these correlations can often be spurious and unstable across different environments (e.g., in different age groups, certain types of brain changes have unstable relations with neurodegenerative disease); hence leading to biased or inaccurate predictions. In this paper, we introduce a novel framework that for the first time develops invariant shape representation learning (ISRL) to further strengthen the robustness of image classifiers. In contrast to existing approaches that mainly derive features in the image space, our model ISRL is designed to jointly capture invariant features in latent shape spaces parameterized by deformable transformations. To achieve this goal, we develop a new learning paradigm based on invariant risk minimization (IRM) to learn invariant representations of image and shape features across multiple training distributions/environments. By embedding the features that are invariant with regard to target variables in different environments, our model consistently offers more accurate predictions. We validate our method by performing classification tasks on both simulated 2D images, real 3D brain and cine cardiovascular magnetic resonance images (MRIs). Our code is publicly available at https://github.com/tonmoy-hossain/ISRL.

Multi-contrast magnetic resonance imaging (MCMRI) super-resolution (SR) methods aims to leverage the complementary information present in multi-contrast images. However, existing methods encounter several limitations. Firstly, most current networks fail to appropriately model the correlations of multi-contrast images and lack certain interpretability. Secondly, they often overlook the negative impact of spatial misalignment between modalities in clinical practice. Thirdly, existing methods do not effectively constrain the complementary information learned between multi-contrast images, resulting in information redundancy and limiting their model performance. In this paper, we propose a robust alignment-assisted multi-contrast convolutional dictionary (A2-CDic) model to address these challenges. Specifically, we develop an observation model based on convolutional sparse coding to explicitly represent multi-contrast images as common (e.g., consistent textures) and unique (e.g., inconsistent structures and contrasts) components. Considering there are spatial misalignments in real-world multi-contrast images, we incorporate a spatial alignment module to compensate for the misaligned structures. This approach enables the proposed model to fully exploit the valuable information in the reference image while mitigating interference from inconsistent information. We employ the proximal gradient algorithm to optimize the model and unroll the iterative steps into a multi-scale convolutional dictionary network. Furthermore, we utilize mutual information losses to constrain the extracted common and unique components. This constraint reduces the redundancy between the decomposed components, allowing each sub-module to learn more representative features. We evaluate our model on four publicly available datasets comprising internal, external, spatially aligned, and misaligned MCMRI images. The experimental results demonstrate that our model surpasses existing state-of-the-art MCMRI SR methods in terms of both generalization ability and overall performance. Code is available at https://github.com/lpcccc-cv/A2-CDic.

Deformable shapes provide important and complex geometric features of objects presented in images. However, such information is oftentimes missing or underutilized as implicit knowledge in many image analysis tasks. This paper presents Geo-SIC, the first deep learning model to learn deformable shapes in a deformation space for an improved performance of image classification. We introduce a newly designed framework that (i) simultaneously derives features from both image and latent shape spaces with large intra-class variations; and (ii) gains increased model interpretability by allowing direct access to the underlying geometric features of image data. In particular, we develop a boosted classification network, equipped with an unsupervised learning of geometric shape representations characterized by diffeomorphic transformations within each class. In contrast to previous approaches using pre-extracted shapes, our model provides a more fundamental approach by naturally learning the most relevant shape features jointly with an image classifier. We demonstrate the effectiveness of our method on both simulated 2D images and real 3D brain magnetic resonance (MR) images. Experimental results show that our model substantially improves the image classification accuracy with an additional benefit of increased model interpretability. Our code is publicly available at https://github.com/jw4hv/Geo-SIC.

This paper presents DeepFLASH, a novel network with efficient training and inference for learning-based medical image registration. In contrast to existing approaches that learn spatial transformations from training data in the high dimensional imaging space, we develop a new registration network entirely in a low dimensional bandlimited space. This dramatically reduces the computational cost and memory footprint of an expensive training and inference. To achieve this goal, we first introduce complex-valued operations and representations of neural architectures that provide key components for learning-based registration models. We then construct an explicit loss function of transformation fields fully characterized in a bandlimited space with much fewer parameterizations. Experimental results show that our method is significantly faster than the state-of-the-art deep learning based image registration methods, while producing equally accurate alignment. We demonstrate our algorithm in two different applications of image registration: 2D synthetic data and 3D real brain magnetic resonance (MR) images.

We present a robust method to correct for motion and deformations in in-utero volumetric MRI time series. Spatio-temporal analysis of dynamic MRI requires robust alignment across time in the presence of substantial and unpredictable motion. We make a Markov assumption on the nature of deformations to take advantage of the temporal structure in the image data. Forward message passing in the corresponding hidden Markov model (HMM) yields an estimation algorithm that only has to account for relatively small motion between consecutive frames. We demonstrate the utility of the temporal model by showing that its use improves the accuracy of the segmentation propagation through temporal registration. Our results suggest that the proposed model captures accurately the temporal dynamics of deformations in in-utero MRI time series.

Using image-based descriptors to investigate clinical hypotheses and therapeutic implications is challenging due to the notorious "curse of dimensionality" coupled with a small sample size. In this paper, we present a low-dimensional analysis of anatomical shape variability in the space of diffeomorphisms and demonstrate its benefits for clinical studies. To combat the high dimensionality of the deformation descriptors, we develop a probabilistic model of principal geodesic analysis in a bandlimited low-dimensional space that still captures the underlying variability of image data. We demonstrate the performance of our model on a set of 3D brain MRI scans from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database. Our model yields a more compact representation of group variation at substantially lower computational cost than models based on the high-dimensional state-of-the-art approaches such as tangent space PCA (TPCA) and probabilistic principal geodesic analysis (PPGA).

Principal geodesic analysis (PGA) is a generalization of principal component analysis (PCA) for dimensionality reduction of data on a Riemannian manifold. Currently PGA is defined as a geometric fit to the data, rather than as a probabilistic model. Inspired by probabilistic PCA, we present a latent variable model for PGA that provides a probabilistic framework for factor analysis on manifolds. To compute maximum likelihood estimates of the parameters in our model, we develop a Monte Carlo Expectation Maximization algorithm, where the expectation is approximated by Hamiltonian Monte Carlo sampling of the latent variables. We demonstrate the ability of our method to recover the ground truth parameters in simulated sphere data, as well as its effectiveness in analyzing shape variability of a corpus callosum data set from human brain images.