Stability and Generalizability in SDE Diffusion Models with Measure-Preserving Dynamics

Inverse problems describe the process of estimating the causal factors from a set of measurements or data. Mapping of often incomplete or degraded data to parameters is ill-posed, thus data-driven iterative solutions are required, for example when reconstructing clean images from poor signals. Diffusion models have shown promise as potent generative tools for solving inverse problems due to their superior reconstruction quality and their compatibility with iterative solvers. However, most existing approaches are limited to linear inverse problems represented as Stochastic Differential Equations (SDEs). This simplification falls short of addressing the challenging nature of real-world problems, leading to amplified cumulative errors and biases. We provide an explanation for this gap through the lens of measure-preserving dynamics of Random Dynamical Systems (RDS) with which we analyse Temporal Distribution Discrepancy and thus introduce a theoretical framework based on RDS for SDE diffusion models. We uncover several strategies that inherently enhance the stability and generalizability of diffusion models for inverse problems and introduce a novel score-based diffusion framework, the \textbf{D}ynamics-aware S\textbf{D}E \textbf{D}iffusion \textbf{G}enerative \textbf{M}odel (D$^3$GM). The \textit{Measure-preserving property} can return the degraded measurement to the original state despite complex degradation with the RDS concept of \textit{stability}. Our extensive experimental results corroborate the effectiveness of D$^3$GM across multiple benchmarks including a prominent application for inverse problems, magnetic resonance imaging. Code and data will be publicly available.

Weakly Supervised Learning of Cortical Surface Reconstruction from Segmentations

Existing learning-based cortical surface reconstruction approaches heavily rely on the supervision of pseudo ground truth (pGT) cortical surfaces for training. Such pGT surfaces are generated by traditional neuroimage processing pipelines, which are time consuming and difficult to generalize well to low-resolution brain MRI, e.g., from fetuses and neonates. In this work, we present CoSeg, a learning-based cortical surface reconstruction framework weakly supervised by brain segmentations without the need for pGT surfaces. CoSeg introduces temporal attention networks to learn time-varying velocity fields from brain MRI for diffeomorphic surface deformations, which fit an initial surface to target cortical surfaces within only 0.11 seconds for each brain hemisphere. A weakly supervised loss is designed to reconstruct pial surfaces by inflating the white surface along the normal direction towards the boundary of the cortical gray matter segmentation. This alleviates partial volume effects and encourages the pial surface to deform into deep and challenging cortical sulci. We evaluate CoSeg on 1,113 adult brain MRI at 1mm and 2mm resolution. CoSeg achieves superior geometric and morphological accuracy compared to existing learning-based approaches. We also verify that CoSeg can extract high-quality cortical surfaces from fetal brain MRI on which traditional pipelines fail to produce acceptable results.

The Developing Human Connectome Project: A Fast Deep Learning-based Pipeline for Neonatal Cortical Surface Reconstruction

The Developing Human Connectome Project (dHCP) aims to explore developmental patterns of the human brain during the perinatal period. An automated processing pipeline has been developed to extract high-quality cortical surfaces from structural brain magnetic resonance (MR) images for the dHCP neonatal dataset. However, the current implementation of the pipeline requires more than 6.5 hours to process a single MRI scan, making it expensive for large-scale neuroimaging studies. In this paper, we propose a fast deep learning (DL) based pipeline for dHCP neonatal cortical surface reconstruction, incorporating DL-based brain extraction, cortical surface reconstruction and spherical projection, as well as GPU-accelerated cortical surface inflation and cortical feature estimation. We introduce a multiscale deformation network to learn diffeomorphic cortical surface reconstruction end-to-end from T2-weighted brain MRI. A fast unsupervised spherical mapping approach is integrated to minimize metric distortions between cortical surfaces and projected spheres. The entire workflow of our DL-based dHCP pipeline completes within only 24 seconds on a modern GPU, which is nearly 1000 times faster than the original dHCP pipeline. Manual quality control demonstrates that for 82.5% of the test samples, our DL-based pipeline produces superior (54.2%) or equal quality (28.3%) cortical surfaces compared to the original dHCP pipeline.

DiffDet4SAR: Diffusion-based Aircraft Target Detection Network for SAR Images

Aircraft target detection in SAR images is a challenging task due to the discrete scattering points and severe background clutter interference. Currently, methods with convolution-based or transformer-based paradigms cannot adequately address these issues. In this letter, we explore diffusion models for SAR image aircraft target detection for the first time and propose a novel \underline{Diff}usion-based aircraft target \underline{Det}ection network \underline{for} \underline{SAR} images (DiffDet4SAR). Specifically, the proposed DiffDet4SAR yields two main advantages for SAR aircraft target detection: 1) DiffDet4SAR maps the SAR aircraft target detection task to a denoising diffusion process of bounding boxes without heuristic anchor size selection, effectively enabling large variations in aircraft sizes to be accommodated; and 2) the dedicatedly designed Scattering Feature Enhancement (SFE) module further reduces the clutter intensity and enhances the target saliency during inference. Extensive experimental results on the SAR-AIRcraft-1.0 dataset show that the proposed DiffDet4SAR achieves 88.4\% mAP$_{50}$, outperforming the state-of-the-art methods by 6\%. Code is availabel at \href{https://github.com/JoyeZLearning/DiffDet4SAR}.

Multi-Center Fetal Brain Tissue Annotation (FeTA) Challenge 2022 Results

Segmentation is a critical step in analyzing the developing human fetal brain. There have been vast improvements in automatic segmentation methods in the past several years, and the Fetal Brain Tissue Annotation (FeTA) Challenge 2021 helped to establish an excellent standard of fetal brain segmentation. However, FeTA 2021 was a single center study, and the generalizability of algorithms across different imaging centers remains unsolved, limiting real-world clinical applicability. The multi-center FeTA Challenge 2022 focuses on advancing the generalizability of fetal brain segmentation algorithms for magnetic resonance imaging (MRI). In FeTA 2022, the training dataset contained images and corresponding manually annotated multi-class labels from two imaging centers, and the testing data contained images from these two imaging centers as well as two additional unseen centers. The data from different centers varied in many aspects, including scanners used, imaging parameters, and fetal brain super-resolution algorithms applied. 16 teams participated in the challenge, and 17 algorithms were evaluated. Here, a detailed overview and analysis of the challenge results are provided, focusing on the generalizability of the submissions. Both in- and out of domain, the white matter and ventricles were segmented with the highest accuracy, while the most challenging structure remains the cerebral cortex due to anatomical complexity. The FeTA Challenge 2022 was able to successfully evaluate and advance generalizability of multi-class fetal brain tissue segmentation algorithms for MRI and it continues to benchmark new algorithms. The resulting new methods contribute to improving the analysis of brain development in utero.

Conditional Temporal Attention Networks for Neonatal Cortical Surface Reconstruction

Cortical surface reconstruction plays a fundamental role in modeling the rapid brain development during the perinatal period. In this work, we propose Conditional Temporal Attention Network (CoTAN), a fast end-to-end framework for diffeomorphic neonatal cortical surface reconstruction. CoTAN predicts multi-resolution stationary velocity fields (SVF) from neonatal brain magnetic resonance images (MRI). Instead of integrating multiple SVFs, CoTAN introduces attention mechanisms to learn a conditional time-varying velocity field (CTVF) by computing the weighted sum of all SVFs at each integration step. The importance of each SVF, which is estimated by learned attention maps, is conditioned on the age of the neonates and varies with the time step of integration. The proposed CTVF defines a diffeomorphic surface deformation, which reduces mesh self-intersection errors effectively. It only requires 0.21 seconds to deform an initial template mesh to cortical white matter and pial surfaces for each brain hemisphere. CoTAN is validated on the Developing Human Connectome Project (dHCP) dataset with 877 3D brain MR images acquired from preterm and term born neonates. Compared to state-of-the-art baselines, CoTAN achieves superior performance with only 0.12mm geometric error and 0.07% self-intersecting faces. The visualization of our attention maps illustrates that CoTAN indeed learns coarse-to-fine surface deformations automatically without intermediate supervision.

CAS-Net: Conditional Atlas Generation and Brain Segmentation for Fetal MRI

Fetal Magnetic Resonance Imaging (MRI) is used in prenatal diagnosis and to assess early brain development. Accurate segmentation of the different brain tissues is a vital step in several brain analysis tasks, such as cortical surface reconstruction and tissue thickness measurements. Fetal MRI scans, however, are prone to motion artifacts that can affect the correctness of both manual and automatic segmentation techniques. In this paper, we propose a novel network structure that can simultaneously generate conditional atlases and predict brain tissue segmentation, called CAS-Net. The conditional atlases provide anatomical priors that can constrain the segmentation connectivity, despite the heterogeneity of intensity values caused by motion or partial volume effects. The proposed method is trained and evaluated on 253 subjects from the developing Human Connectome Project (dHCP). The results demonstrate that the proposed method can generate conditional age-specific atlas with sharp boundary and shape variance. It also segment multi-category brain tissues for fetal MRI with a high overall Dice similarity coefficient (DSC) of $85.2\%$ for the selected 9 tissue labels.

Recovering medical images from CT film photos

While medical images such as computed tomography (CT) are stored in DICOM format in hospital PACS, it is still quite routine in many countries to print a film as a transferable medium for the purposes of self-storage and secondary consultation. Also, with the ubiquitousness of mobile phone cameras, it is quite common to take pictures of CT films, which unfortunately suffer from geometric deformation and illumination variation. In this work, we study the problem of recovering a CT film, which marks \textbf{the first attempt} in the literature, to the best of our knowledge. We start with building a large-scale head CT film database CTFilm20K, consisting of approximately 20,000 pictures, using the widely used computer graphics software Blender. We also record all accompanying information related to the geometric deformation (such as 3D coordinate, depth, normal, and UV maps) and illumination variation (such as albedo map). Then we propose a deep framework called \textbf{F}ilm \textbf{I}mage \textbf{Re}covery \textbf{Net}work (\textbf{FIReNet}) to tackle geometric deformation and illumination variation using the multiple maps extracted from the CT films to collaboratively guide the recovery process. Finally, we convert the dewarped images to DICOM files with our cascade model for further analysis such as radiomics feature extraction. Extensive experiments demonstrate the superiority of our approach over the previous approaches. We plan to open source the simulated images and deep models for promoting the research on CT film image analysis.

CortexODE: Learning Cortical Surface Reconstruction by Neural ODEs

We present CortexODE, a deep learning framework for cortical surface reconstruction. CortexODE leverages neural ordinary different equations (ODEs) to deform an input surface into a target shape by learning a diffeomorphic flow. The trajectories of the points on the surface are modeled as ODEs, where the derivatives of their coordinates are parameterized via a learnable Lipschitz-continuous deformation network. This provides theoretical guarantees for the prevention of self-intersections. CortexODE can be integrated to an automatic learning-based pipeline, which reconstructs cortical surfaces efficiently in less than 6 seconds. The pipeline utilizes a 3D U-Net to predict a white matter segmentation from brain Magnetic Resonance Imaging (MRI) scans, and further generates a signed distance function that represents an initial surface. Fast topology correction is introduced to guarantee homeomorphism to a sphere. Following the isosurface extraction step, two CortexODE models are trained to deform the initial surface to white matter and pial surfaces respectively. The proposed pipeline is evaluated on large-scale neuroimage datasets in various age groups including neonates (25-45 weeks), young adults (22-36 years) and elderly subjects (55-90 years). Our experiments demonstrate that the CortexODE-based pipeline can achieve less than 0.2mm average geometric error while being orders of magnitude faster compared to conventional processing pipelines.

CT Film Recovery via Disentangling Geometric Deformation and Illumination Variation: Simulated Datasets and Deep Models

While medical images such as computed tomography (CT) are stored in DICOM format in hospital PACS, it is still quite routine in many countries to print a film as a transferable medium for the purposes of self-storage and secondary consultation. Also, with the ubiquitousness of mobile phone cameras, it is quite common to take pictures of the CT films, which unfortunately suffer from geometric deformation and illumination variation. In this work, we study the problem of recovering a CT film, which marks the first attempt in the literature, to the best of our knowledge. We start with building a large-scale head CT film database CTFilm20K, consisting of approximately 20,000 pictures, using the widely used computer graphics software Blender. We also record all accompanying information related to the geometric deformation (such as 3D coordinate, depth, normal, and UV maps) and illumination variation (such as albedo map). Then we propose a deep framework to disentangle geometric deformation and illumination variation using the multiple maps extracted from the CT films to collaboratively guide the recovery process. Extensive experiments on simulated and real images demonstrate the superiority of our approach over the previous approaches. We plan to open source the simulated images and deep models for promoting the research on CT film recovery (https://anonymous.4open.science/r/e6b1f6e3-9b36-423f-a225-55b7d0b55523/).