Application-driven Validation of Posteriors in Inverse Problems
Tim J. Adler Jan-Hinrich Nölke Annika Reinke Minu Dietlinde Tizabi Sebastian Gruber Dasha Trofimova Lynton Ardizzone Paul F. Jaeger Florian Buettner Ullrich Köthe Lena Maier-Hein
Current deep learning-based solutions for image analysis tasks are commonly
incapable of handling problems to which multiple different plausible solutions
exist. In response, posterior-based methods such as conditional Diffusion
Models and Invertible Neural Networks have emerged; however, their translation
is hampered by a lack of research on adequate validation. In other words, the
way progress is measured often does not reflect the needs of the driving
practical application. Closing this gap in the literature, we present the first
systematic framework for the application-driven validation of posterior-based
methods in inverse problems. As a methodological novelty, it adopts key
principles from the field of object detection validation, which has a long
history of addressing the question of how to locate and match multiple object
instances in an image. Treating modes as instances enables us to perform
mode-centric validation, using well-interpretable metrics from the application
perspective. We demonstrate the value of our framework through instantiations
for a synthetic toy example and two medical vision use cases: pose estimation
in surgery and imaging-based quantification of functional tissue parameters for
diagnostics. Our framework offers key advantages over common approaches to
posterior validation in all three examples and could thus revolutionize
performance assessment in inverse problems.