An Adaptively Inexact Method for Bilevel Learning Using Primal-Dual Style Differentiation

We consider a bilevel learning framework for learning linear operators. In this framework, the learnable parameters are optimized via a loss function that also depends on the minimizer of a convex optimization problem (denoted lower-level problem). We utilize an iterative algorithm called `piggyback' to compute the gradient of the loss and minimizer of the lower-level problem. Given that the lower-level problem is solved numerically, the loss function and thus its gradient can only be computed inexactly. To estimate the accuracy of the computed hypergradient, we derive an a-posteriori error bound, which provides guides for setting the tolerance for the lower-level problem, as well as the piggyback algorithm. To efficiently solve the upper-level optimization, we also propose an adaptive method for choosing a suitable step-size. To illustrate the proposed method, we consider a few learned regularizer problems, such as training an input-convex neural network.

Synthetic Augmentation for Anatomical Landmark Localization using DDPMs

Deep learning techniques for anatomical landmark localization (ALL) have shown great success, but their reliance on large annotated datasets remains a problem due to the tedious and costly nature of medical data acquisition and annotation. While traditional data augmentation, variational autoencoders (VAEs), and generative adversarial networks (GANs) have already been used to synthetically expand medical datasets, diffusion-based generative models have recently started to gain attention for their ability to generate high-quality synthetic images. In this study, we explore the use of denoising diffusion probabilistic models (DDPMs) for generating medical images and their corresponding heatmaps of landmarks to enhance the training of a supervised deep learning model for ALL. Our novel approach involves a DDPM with a 2-channel input, incorporating both the original medical image and its heatmap of annotated landmarks. We also propose a novel way to assess the quality of the generated images using a Markov Random Field (MRF) model for landmark matching and a Statistical Shape Model (SSM) to check landmark plausibility, before we evaluate the DDPM-augmented dataset in the context of an ALL task involving hand X-Rays.

FlowSDF: Flow Matching for Medical Image Segmentation Using Distance Transforms

Medical image segmentation is a crucial task that relies on the ability to accurately identify and isolate regions of interest in medical images. Thereby, generative approaches allow to capture the statistical properties of segmentation masks that are dependent on the respective structures. In this work we propose FlowSDF, an image-guided conditional flow matching framework to represent the signed distance function (SDF) leading to an implicit distribution of segmentation masks. The advantage of leveraging the SDF is a more natural distortion when compared to that of binary masks. By learning a vector field that is directly related to the probability path of a conditional distribution of SDFs, we can accurately sample from the distribution of segmentation masks, allowing for the evaluation of statistical quantities. Thus, this probabilistic representation allows for the generation of uncertainty maps represented by the variance, which can aid in further analysis and enhance the predictive robustness. We qualitatively and quantitatively illustrate competitive performance of the proposed method on a public nuclei and gland segmentation data set, highlighting its utility in medical image segmentation applications.

Score-Based Generative Models for Medical Image Segmentation using Signed Distance Functions

Medical image segmentation is a crucial task that relies on the ability to accurately identify and isolate regions of interest in images. Thereby, generative approaches allow to capture the statistical properties of segmentation masks that are dependent on the respective medical images. In this work we propose a conditional score-based generative modeling framework that leverages the signed distance function to represent an implicit and smoother distribution of segmentation masks. The score function of the conditional distribution of segmentation masks is learned in a conditional denoising process, which can be effectively used to generate accurate segmentation masks. Moreover, uncertainty maps can be generated, which can aid in further analysis and thus enhance the predictive robustness. We qualitatively and quantitatively illustrate competitive performance of the proposed method on a public nuclei and gland segmentation data set, highlighting its potential utility in medical image segmentation applications.