Mathematics and Algorithms in Tomography

This was the ninth Oberwolfach conference on the mathematics of tomography. Modalities represented at the workshop included X-ray tomography, radar, seismic imaging, ultrasound, electron microscopy, impedance imaging, photoacoustic tomography, elastography, emission tomography, X-ray CT, and vector tomography along with a wide range of mathematical analysis

Automatic Choroidal Layer Segmentation Using Markov Random Field And Level Set Method

The choroid is an important vascular layer that supplies oxygen and nourishment to the retina. The changes in thickness of the choroid have been hypothesised to relate to a number of retinal diseases in the pathophysiology. In this work, an automatic method is proposed for segmenting the choroidal layer from macular images by using the level set framework. The 3D nonlinear anisotropic diffusion filter is used to remove all the OCT imaging artifacts including the speckle noise and to enhance the contrast. The distance regularisation and edge constraint terms are embedded into the level set method to avoid the irregular and small regions and keep information about the boundary between the choroid and sclera. Besides, the Markov Random Field method models the region term into the framework by correlating the single pixel likelihood function with neighbour-hood information to compensate for the inhomogeneous texture and avoid the leakage due to the shadows cast by the blood vessels during imaging process. The effectiveness of this method is demonstrated by comparing against other segmentation methods on a dataset with manually labelled ground truth. The results show that our method can successfully and accurately estimate the posterior choroidal boundary

Nonlocal Graph-PDEs and Riemannian Gradient Flows for Image Labeling

In this thesis, we focus on the image labeling problem which is the task of performing unique pixel-wise label decisions to simplify the image while reducing its redundant information. We build upon a recently introduced geometric approach for data labeling by assignment flows [ APSS17 ] that comprises a smooth dynamical system for data processing on weighted graphs. Hereby we pursue two lines of research that give new application and theoretically-oriented insights on the underlying segmentation task. We demonstrate using the example of Optical Coherence Tomography (OCT), which is the mostly used non-invasive acquisition method of large volumetric scans of human retinal tis- sues, how incorporation of constraints on the geometry of statistical manifold results in a novel purely data driven geometric approach for order-constrained segmentation of volumetric data in any metric space. In particular, making diagnostic analysis for human eye diseases requires decisive information in form of exact measurement of retinal layer thicknesses that has be done for each patient separately resulting in an demanding and time consuming task. To ease the clinical diagnosis we will introduce a fully automated segmentation algorithm that comes up with a high segmentation accuracy and a high level of built-in-parallelism. As opposed to many established retinal layer segmentation methods, we use only local information as input without incorporation of additional global shape priors. Instead, we achieve physiological order of reti- nal cell layers and membranes including a new formulation of ordered pair of distributions in an smoothed energy term. This systematically avoids bias pertaining to global shape and is hence suited for the detection of anatomical changes of retinal tissue structure. To access the perfor- mance of our approach we compare two different choices of features on a data set of manually annotated 3 D OCT volumes of healthy human retina and evaluate our method against state of the art in automatic retinal layer segmentation as well as to manually annotated ground truth data using different metrics. We generalize the recent work [ SS21 ] on a variational perspective on assignment flows and introduce a novel nonlocal partial difference equation (G-PDE) for labeling metric data on graphs. The G-PDE is derived as nonlocal reparametrization of the assignment flow approach that was introduced in J. Math. Imaging & Vision 58(2), 2017. Due to this parameterization, solving the G-PDE numerically is shown to be equivalent to computing the Riemannian gradient flow with re- spect to a nonconvex potential. We devise an entropy-regularized difference-of-convex-functions (DC) decomposition of this potential and show that the basic geometric Euler scheme for inte- grating the assignment flow is equivalent to solving the G-PDE by an established DC program- ming scheme. Moreover, the viewpoint of geometric integration reveals a basic way to exploit higher-order information of the vector field that drives the assignment flow, in order to devise a novel accelerated DC programming scheme. A detailed convergence analysis of both numerical schemes is provided and illustrated by numerical experiments

DESIGN, DEVELOPMENT, AND EVALUATION OF A DISCRETELY ACTUATED STEERABLE CANNULA

Needle-based procedures require the guidance of the needle to a target region to deliver therapy or to remove tissue samples for diagnosis. During needle insertion, needle deflection occurs due to needle-tissue interaction which deviates the needle from its insertion direction. Manipulating the needle at the base provides limited control over the needle trajectory after the insertion. Furthermore, some sites are inaccessible using straight-line trajectories due to delicate structures that need to be avoided. The goal of this research is to develop a discretely actuated steerable cannula to enable active trajectory corrections and achieve accurate targeting in needle-based procedures. The cannula is composed of straight segments connected by shape memory alloy (SMA) actuators and has multiple degrees-of-freedom. To control the motion of the cannula two approaches have been explored. One approach is to measure the cannula configuration directly from the imaging modality and to use this information as a feedback to control the joint motion. The second approach is a model-based controller where the strain of the SMA actuator is controlled by controlling the temperature of the SMA actuator. The constitutive model relates the stress, strain and the temperature of the SMA actuator. The uniaxial constitutive model of the SMA that describes the tensile behavior was extended to one-dimensional pure- bending case to model the phase transformation of the arc-shaped SMA wire. An experimental characterization procedure was devised to obtain the parameters of the SMA that are used in the constitutive model. Experimental results demonstrate that temperature feedback can be effectively used to control the strain of the SMA actuator and image feedback can be reliably used to control the joint motion. Using tools from differential geometry and the configuration control approach, motion planning algorithms were developed to create pre-operative plans that steer the cannula to a desired surgical site (nodule or suspicious tissue). Ultrasound-based tracking algorithms were developed to automate the needle insertion procedure using 2D ultrasound guidance. The effectiveness of the proposed in-plane and out-of-plane tracking methods were demonstrated through experiments inside tissue phantom made of gelatin and ex-vivo experiments. An optical coherence tomography probe was integrated into the cannula and in-situ microscale imaging was performed. The results demonstrate the use of the cannula as a delivery mechanism for diagnostic applications. The tools that were developed in this dissertation form the foundations of developing a complete steerable-cannula system. It is anticipated that the cannula could be used as a delivery mechanism in image-guided needle-based interventions to introduce therapeutic and diagnostic tools to a target region

Deep learning in medical image registration: introduction and survey

Image registration (IR) is a process that deforms images to align them with respect to a reference space, making it easier for medical practitioners to examine various medical images in a standardized reference frame, such as having the same rotation and scale. This document introduces image registration using a simple numeric example. It provides a definition of image registration along with a space-oriented symbolic representation. This review covers various aspects of image transformations, including affine, deformable, invertible, and bidirectional transformations, as well as medical image registration algorithms such as Voxelmorph, Demons, SyN, Iterative Closest Point, and SynthMorph. It also explores atlas-based registration and multistage image registration techniques, including coarse-fine and pyramid approaches. Furthermore, this survey paper discusses medical image registration taxonomies, datasets, evaluation measures, such as correlation-based metrics, segmentation-based metrics, processing time, and model size. It also explores applications in image-guided surgery, motion tracking, and tumor diagnosis. Finally, the document addresses future research directions, including the further development of transformers

Pixel-level semantic understanding of ophthalmic images and beyond

Computer-assisted semantic image understanding constitutes the substrate of applications that range from biomarker detection to intraoperative guidance or street scene understanding for self-driving systems. This PhD thesis is on the development of deep learning-based, pixel-level, semantic segmentation methods for medical and natural images. For vessel segmentation in OCT-A, a method comprising iterative refinement of the extracted vessel maps and an auxiliary loss function that penalizes structural inaccuracies, is proposed and tested on data captured from real clinical conditions comprising various pathological cases. Ultimately, the presented method enables the extraction of a detailed vessel map of the retina with potential applications to diagnostics or intraoperative localization. Furthermore, for scene segmentation in cataract surgery, the major challenge of class imbalance is identified among several factors. Subsequently, a method addressing it is proposed, achieving state-of-the-art performance on a challenging public dataset. Accurate semantic segmentation in this domain can be used to monitor interactions between tools and anatomical parts for intraoperative guidance and safety. Finally, this thesis proposes a novel contrastive learning framework for supervised semantic segmentation, that aims to improve the discriminative power of features in deep neural networks. The proposed approach leverages contrastive loss function applied both at multiple model layers and across them. Importantly, the proposed framework is easy to combine with various model architectures and is experimentally shown to significantly improve performance on both natural and medical domain