Current volumetric biomedical foundation models struggle to generalize as public 3D datasets are small and do not cover the broad diversity of medical procedures, conditions, anatomical regions, and imaging protocols. We address this by creating a representation learning method that instead anticipates strong domain shifts at training time itself. We first propose a data engine that synthesizes highly variable training samples that would enable generalization to new biomedical contexts. To then train a single 3D network for any voxel-level task, we develop a contrastive learning method that pretrains the network to be stable against nuisance imaging variation simulated by the data engine, a key inductive bias for generalization. This network's features can be used as robust representations of input images for downstream tasks and its weights provide a strong, _dataset-agnostic_ initialization for finetuning on new datasets. As a result, we set new standards across _both_ multimodality registration and few-shot segmentation, a first for any 3D biomedical vision model, all without (pre-)training on any existing dataset of real images.

The idea of representing a signal as the weights of a neural network, called *Implicit Neural Representations* (INRs), has led to exciting implications for compression, view synthesis and 3D volumetric data understanding. One problem in this setting pertains to the use of INRs for downstream processing tasks. Despite some conceptual results, this remains challenging because the INR for a given image/signal often exists in isolation. What does the neighborhood around a given INR correspond to? Based on this question, we offer an operator theoretic reformulation of the INR model, which we call Operator INR (or O-INR). At a high level, instead of mapping positional encodings to a signal, O-INR maps one function space to another function space. A practical form of this general casting is obtained by appealing to Integral Transforms. The resultant model does not need multi-layer perceptrons (MLPs), used in most existing INR models -- we show that convolutions are sufficient and offer benefits including numerically stable behavior. We show that O-INR can easily handle most problem settings in the literature, and offers a similar performance profile as baselines. These benefits come with minimal, if any, compromise. Our code is available at https://github.com/vsingh-group/oinr.

Image-to-image translation has seen major advances in computer vision but can be difficult to apply to medical images, where imaging artifacts and data scarcity degrade the performance of conditional generative adversarial networks. We develop the spatial-intensity transform (SIT) to improve output image quality while closely matching the target domain. SIT constrains the generator to a smooth spatial transform (diffeomorphism) composed with sparse intensity changes. SIT is a lightweight, modular network component that is effective on various architectures and training schemes. Relative to unconstrained baselines, this technique significantly improves image fidelity, and our models generalize robustly to different scanners. Additionally, SIT provides a disentangled view of anatomical and textural changes for each translation, making it easier to interpret the model's predictions in terms of physiological phenomena. We demonstrate SIT on two tasks: predicting longitudinal brain MRIs in patients with various stages of neurodegeneration, and visualizing changes with age and stroke severity in clinical brain scans of stroke patients. On the first task, our model accurately forecasts brain aging trajectories without supervised training on paired scans. On the second task, it captures associations between ventricle expansion and aging, as well as between white matter hyperintensities and stroke severity. As conditional generative models become increasingly versatile tools for visualization and forecasting, our approach demonstrates a simple and powerful technique for improving robustness, which is critical for translation to clinical settings. Source code is available at github.com/clintonjwang/spatial-intensity-transforms.