Medical image segmentation plays an important role in accurately identifying and isolating regions of interest within medical images. Generative approaches are particularly effective in modeling the statistical properties of segmentation masks that are closely related to the respective structures. In this work we introduce FlowSDF, an image-guided conditional flow matching framework, designed to represent the signed distance function (SDF), and, in turn, to represent an implicit distribution of segmentation masks. The advantage of leveraging the SDF is a more natural distortion when compared to that of binary masks. Through the learning of a vector field associated with the probability path of conditional SDF distributions, our framework enables accurate sampling of segmentation masks and the computation of relevant statistical measures. This probabilistic approach also facilitates the generation of uncertainty maps represented by the variance, thereby supporting enhanced robustness in prediction and further analysis. 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.

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.

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.

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 a conditional score-based generative modeling 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 the score function of the 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 potential utility in medical image segmentation applications.

The total generalized variation extends the total variation by incorporating higher-order smoothness. Thus, it can also suffer from similar discretization issues related to isotropy. Inspired by the success of novel discretization schemes of the total variation, there has been recent work to improve the second-order total generalized variation discretization, based on the same design idea. In this work, we propose to extend this to a general discretization scheme based on interpolation filters, for which we prove variational consistency. We then describe how to learn these interpolation filters to optimize the discretization for various imaging applications. We illustrate the performance of the method on a synthetic data set as well as for natural image denoising.

We analyze a ``piggyback""-style method for computing the derivative of a loss which depends on the solution of a convex-concave saddle-point problem, with respect to the bilinear term. We attempt to derive guarantees for the algorithm under minimal regularity assumptions on the functions. Our final convergence results include possibly nonsmooth objectives. We illustrate the versatility of the proposed piggyback algorithm by learning optimized shearlet transforms, which are a class of popular sparsifying transforms in the field of imaging.

Electron tomography allows one to obtain 3D reconstructions visualizing a tissue’s ultrastructure from a series of 2D projection images. An inherent problem with this imaging technique is that its projection images contain unwanted shifts, which must be corrected for to achieve reliable reconstructions. Commonly, the projection images are aligned with each other by means of fiducial markers prior to the reconstruction procedure. In this work, we propose a joint alignment and reconstruction algorithm that iteratively solves for both the unknown reconstruction and the unintentional shift and does not require any fiducial markers. We evaluate the approach first on synthetic phantom data where the focus is not only on the reconstruction quality but more importantly on the shift correction. Subsequently, we apply the algorithm to healthy C57BL/6J mice and then compare it with non-obese diabetic (NOD) mice, with the aim of visualizing the attack of immune cells on pancreatic beta cells within type 1 diabetic mice at a more profound level through 3D analysis. We empirically demonstrate that the proposed algorithm is able to compute the shift with a remaining error at only the sub-pixel level and yields high-quality reconstructions for the limited-angle inverse problem. By decreasing labour and material costs, the algorithm facilitates further research directed towards investigating the immune system’s attacks in pancreata of NOD mice for numerous samples at different stages of type 1 diabetes.