Left-invariant evolutions of wavelet transforms on the Similitude Group

Enhancement of multiple-scale elongated structures in noisy image data is relevant for many biomedical applications but commonly used PDE-based enhancement techniques often fail at crossings in an image. To get an overview of how an image is composed of local multiple-scale elongated structures we construct a multiple scale orientation score, which is a continuous wavelet transform on the similitude group, SIM(2). Our unitary transform maps the space of images onto a reproducing kernel space defined on SIM(2), allowing us to robustly relate Euclidean (and scaling) invariant operators on images to left-invariant operators on the corresponding continuous wavelet transform. Rather than often used wavelet (soft-)thresholding techniques, we employ the group structure in the wavelet domain to arrive at left-invariant evolutions and flows (diffusion), for contextual crossing preserving enhancement of multiple scale elongated structures in noisy images. We present experiments that display benefits of our work compared to recent PDE techniques acting directly on the images and to our previous work on left-invariant diffusions on orientation scores defined on Euclidean motion group.Comment: 40 page

Locally Adaptive Frames in the Roto-Translation Group and their Applications in Medical Imaging

Locally adaptive differential frames (gauge frames) are a well-known effective tool in image analysis, used in differential invariants and PDE-flows. However, at complex structures such as crossings or junctions, these frames are not well-defined. Therefore, we generalize the notion of gauge frames on images to gauge frames on data representations $U:\mathbb{R}^{d} \rtimes S^{d-1} \to \mathbb{R}$ defined on the extended space of positions and orientations, which we relate to data on the roto-translation group $SE(d)$, $d=2,3$. This allows to define multiple frames per position, one per orientation. We compute these frames via exponential curve fits in the extended data representations in $SE(d)$. These curve fits minimize first or second order variational problems which are solved by spectral decomposition of, respectively, a structure tensor or Hessian of data on $SE(d)$. We include these gauge frames in differential invariants and crossing preserving PDE-flows acting on extended data representation $U$ and we show their advantage compared to the standard left-invariant frame on $SE(d)$. Applications include crossing-preserving filtering and improved segmentations of the vascular tree in retinal images, and new 3D extensions of coherence-enhancing diffusion via invertible orientation scores

Coherence Filtering to Enhance the Mandibular Canal in Cone-Beam CT data

Segmenting the mandibular canal from cone beam CT data, is difficult due to low edge contrast and high image noise. We introduce 3D coherence filtering as a method to close the interrupted edges and denoise the structure of the mandibular canal. Coherence Filtering is an anisotropic non-linear tensor based diffusion algorithm for edge enhancing image filtering. We test different numerical schemes of the tensor diffusion equation, non-negative, standard discretization and also a rotation invariant scheme of Weickert [1]. Only the\ud scheme of Weickert did not blur the high spherical images frequencies on the image diagonals of our test volume. Thus this scheme is chosen to enhance the small curved mandibular canal structure. The best choice of the diffusion equation parameters c1 and c2, depends on the image noise. Coherence filtering on the CBCT-scan works well, the noise in the mandibular canal is gone and the edges are connected. Because the algorithm is tensor based it cannot deal with edge joints or splits, thus is less fit for more complex image structures

Vessel enhancing diffusion: a scale space representation of vessel

A method is proposed to enhance vascular structures within the framework of scale space theory. We combine a smooth vessel filter which is based on a geometrical analysis of the Hessian's eigensystem, with a non-linear anisotropic diffusion scheme. The amount and orientation of diffusion depend on the local vessel likeliness. Vessel enhancing diffusion (VED) is applied to patient and phantom data and compared to linear, regularized Perona-Malik, edge and coherence enhancing diffusion. The method performs better than most of the existing techniques in visualizing vessels with varying radii and in enhancing vessel appearance. A diameter study on phantom data shows that VED least affects the accuracy of diameter measurements. It is shown that using VED as a preprocessing step improves level set based segmentation of the cerebral vasculature, in particular segmentation of the smaller vessels of the vasculature

An Automated Liver Vasculature Segmentation from CT Scans for Hepatic Surgical Planning

Liver vasculature segmentation is a crucial step for liver surgical planning. Segmentation of liver vasculature is an important part of the 3D visualisation of the liver anatomy. The spatial relationship between vessels and other liver structures, like tumors and liver anatomic segments, helps in reducing the surgical treatment risks. However, liver vessels segmentation is a challenging task, that is due to low contrast with neighboring parenchyma, the complex anatomy, the very thin branches and very small vessels. This paper introduces a fully automated framework consist of four steps to segment the vessels inside the liver organ. Firstly, in the preprocessing step, a combination of two filtering techniques are used to extract and enhance vessels inside the liver region, first the vesselness filter is used to extract the vessels structure, and then the anisotropic coherence enhancing diffusion (CED) filter is used to enhance the intensity within the tubular vessels structure. This step is followed by a smart multiple thresholding to extract the initial vasculature segmentation. The liver vasculature structures, including hepatic veins connected to the inferior vena cava and the portal veins, are extracted. Finally, the inferior vena cava is segmented and excluded from the vessels segmentation, as it is not considered as part of the liver vasculature structure. The liver vessel segmentation method is validated on the publically available 3DIRCAD datasets. Dice coefficient (DSC) is used to evaluate the method, the average DSC score achieved a score 68.5%. The proposed approach succeeded to segment liver vasculature from the liver envelope accurately, which makes it as potential tool for clinical preoperative planning

Application of a Mamdani-type fuzzy rule-based system to segment periventricular cerebral veins in susceptibility-weighted images

This paper presents an algorithm designed to segment veins in the periventricular region of the brain in susceptibility-weighted magnetic resonance images. The proposed algorithm is based on a Mamdani-type fuzzy rule-based system that enables enhancement of veins within periventricular regions of interest as the first step. Segmentation is achieved after determining the cut-off value providing the best trade-off between sensitivity and specificity to establish the suitability of each pixel to belong to a cerebral vein. Performance of the algorithm in susceptibility-weighted images acquired in healthy volunteers showed very good segmentation, with a small number of false positives. The results were not affected by small changes in the size and location of the regions of interest. The algorithm also enabled detection of differences in the visibility of periventricular veins between healthy subjects and multiple sclerosis patients. © Springer International Publishing Switzerland 2016.Postprint (author's final draft

Coronary Artery Segmentation and Motion Modelling

Conventional coronary artery bypass surgery requires invasive sternotomy and the use of a cardiopulmonary bypass, which leads to long recovery period and has high infectious potential. Totally endoscopic coronary artery bypass (TECAB) surgery based on image guided robotic surgical approaches have been developed to allow the clinicians to conduct the bypass surgery off-pump with only three pin holes incisions in the chest cavity, through which two robotic arms and one stereo endoscopic camera are inserted. However, the restricted field of view of the stereo endoscopic images leads to possible vessel misidentification and coronary artery mis-localization. This results in 20-30% conversion rates from TECAB surgery to the conventional approach. We have constructed patient-specific 3D + time coronary artery and left ventricle motion models from preoperative 4D Computed Tomography Angiography (CTA) scans. Through temporally and spatially aligning this model with the intraoperative endoscopic views of the patient's beating heart, this work assists the surgeon to identify and locate the correct coronaries during the TECAB precedures. Thus this work has the prospect of reducing the conversion rate from TECAB to conventional coronary bypass procedures. This thesis mainly focus on designing segmentation and motion tracking methods of the coronary arteries in order to build pre-operative patient-specific motion models. Various vessel centreline extraction and lumen segmentation algorithms are presented, including intensity based approaches, geometric model matching method and morphology-based method. A probabilistic atlas of the coronary arteries is formed from a group of subjects to facilitate the vascular segmentation and registration procedures. Non-rigid registration framework based on a free-form deformation model and multi-level multi-channel large deformation diffeomorphic metric mapping are proposed to track the coronary motion. The methods are applied to 4D CTA images acquired from various groups of patients and quantitatively evaluated

Direction-adaptive grey-level morphology. Application to 3D vascular brain imaging

International audienceSegmentation and analysis of blood vessels is an important issue in medical imaging. In 3D cerebral angiographic data, the vascular signal is however hard to accurately detect and can, in particular, be disconnected. In this article, we present a procedure utilising both linear, Hessian-based and morphological methods for blood vessel edge enhancement and reconnection. More specifically, multi-scale second-order derivative analysis is performed to detect candidate vessels as well as their orientation. This information is then fed to a spatially-variant morphological filter for reconnection and reconstruction. The result is a fast and effective vessel-reconnecting method

VTrails: Inferring Vessels with Geodesic Connectivity Trees

The analysis of vessel morphology and connectivity has an impact on a number of cardiovascular and neurovascular applications by providing patient-specific high-level quantitative features such as spatial location, direction and scale. In this paper we present an end-to-end approach to extract an acyclic vascular tree from angiographic data by solving a connectivity-enforcing anisotropic fast marching over a voxel-wise tensor field representing the orientation of the underlying vascular tree. The method is validated using synthetic and real vascular images. We compare VTrails against classical and state-of-the-art ridge detectors for tubular structures by assessing the connectedness of the vesselness map and inspecting the synthesized tensor field as proof of concept. VTrails performance is evaluated on images with different levels of degradation: we verify that the extracted vascular network is an acyclic graph (i.e. a tree), and we report the extraction accuracy, precision and recall