This dissertation studies a question that limits the clinical usefulness of imaging AI: how can a model remain usable when data are heterogeneous, target structures are irregular, and deployment conditions change after training? I argue that accessibility in radiology AI is not achieved by a single high-performing model. Rather, it emerges when the pipeline, from input preparation, to segmentation representation, to post-deployment adaptation, to quantitative reporting, is designed to tolerate realistic variability without imposing excessive operational burden on clinicians. The thesis develops this argument through three methodological contributions and two application-oriented chapters. First, I present Neural Pre-Processing (NPP), a weakly supervised framework for end-to-end brain MRI pre-processing. NPP jointly addresses skull stripping, intensity normalization, and affine spatial normalization while separating geometry-preserving appearance correction from spatial transformation. This formulation improves speed and accuracy relative to traditional stepwise pipelines and makes downstream model inputs more usable. Second, I introduce InstaBound, a shape-agnostic approach to instance segmentation based on regression of an instance-aware signed distance field. Unlike methods that assume star-convexity or require multi-branch gradient heads, InstaBound uses a single branch to encode semantic and geometric information. This representation improves separation of touching structures while keeping the architecture simple. Third, I develop Seg-NuSA, a replay-free continual adaptation strategy for medical image segmentation. Seg-NuSA constrains updates to low-interference subspaces derived from pretrained weights, reducing catastrophic forgetting under privacy-constrained deployment. Across cross-modality and sequential adaptation settings, it yields a stronger retention-adaptation trade-off than fine-tuning and regularization-based baselines. These methodological chapters are then connected to a translational program in autosomal dominant polycystic kidney disease (ADPKD). I synthesize work on test-retest reproducibility, MRI quality control, liver cyst segmentation, pancreatic cyst detection, and the TraceOrg platform for automated measurement of kidney, liver, and cyst volumes. I then show how these workflow advances enable biomarker studies including growth-rate modeling, water therapy, tolvaptan response assessment, pregnancy-associated cyst dynamics, and spleen contouring in myelofibrosis. Taken together, the dissertation advances a framework for accessible radiology AI in which technical robustness, deployment stability, and measurement reproducibility are treated as mutually dependent design goals rather than independent stages of a pipeline.