Circle Detection Using the Image Ray Transform

Physical analogies are an exciting paradigm for creating techniques for image feature extraction. A transform using an analogy to light rays has been developed for the detection of circular and tubular features. It uses a 2D ray tracing algorithm to follow rays through an image, interacting at a low level, to emphasise higher level features. It has been empirically tested as a pre-processor to aid circle detection with the Hough Transform and has been shown to provide a clear improvement over standard techniques. The transform was also used on natural images and we show its ability to highlight circles even in complex scenes. We also show the flexibility available to the technique through adjustment of parameters

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

Efficient segmentation based on Eikonal and diffusion equations

Segmentation of regions of interest in an image has important applications in medical image analysis, particularly in computer aided diagnosis. Segmentation can enable further quantitative analysis of anatomical structures. We present efficient image segmentation schemes based on the solution of distinct partial differential equations (PDEs). For each known image region, a PDE is solved, the solution of which locally represents the weighted distance from a region known to have a certain segmentation label. To achieve this goal, we propose the use of two separate PDEs, the Eikonal equation and a diffusion equation. In each method, the segmentation labels are obtained by a competition criterion between the solutions to the PDEs corresponding to each region. We discuss how each method applies the concept of information propagation from the labelled image regions to the unknown image regions. Experimental results are presented on magnetic resonance, computed tomography, and ultrasound images and for both two-region and multi-region segmentation problems. These results demonstrate the high level of efficiency as well as the accuracy of the proposed methods

Efficient and Robust Segmentations Based on Eikonal and Diffusion PDEs

In this paper, we present efficient and simple image segmentations based on the solution of two separate Eikonal equations, each originating from a different region. Distance functions from the interior and exterior regions are computed, and final segmentation labels are determined by a competition criterion between the distance functions. We also consider applying a diffusion partial differential equation (PDE) based method to propagate information in a manner inspired by the information propagation feature of the Eikonal equation. Experimental results are presented in a particular medical image segmentation application, and demonstrate the proposed methods

Nilpotent Approximations of Sub-Riemannian Distances for Fast Perceptual Grouping of Blood Vessels in 2D and 3D

We propose an efficient approach for the grouping of local orientations (points on vessels) via nilpotent approximations of sub-Riemannian distances in the 2D and 3D roto-translation groups $SE(2)$ and $SE(3)$. In our distance approximations we consider homogeneous norms on nilpotent groups that locally approximate $SE(n)$, and which are obtained via the exponential and logarithmic map on $SE(n)$. In a qualitative validation we show that the norms provide accurate approximations of the true sub-Riemannian distances, and we discuss their relations to the fundamental solution of the sub-Laplacian on $SE(n)$. The quantitative experiments further confirm the accuracy of the approximations. Quantitative results are obtained by evaluating perceptual grouping performance of retinal blood vessels in 2D images and curves in challenging 3D synthetic volumes. The results show that 1) sub-Riemannian geometry is essential in achieving top performance and 2) that grouping via the fast analytic approximations performs almost equally, or better, than data-adaptive fast marching approaches on $\mathbb{R}^n$ and $SE(n)$.Comment: 18 pages, 9 figures, 3 tables, in review at JMI

Deformable Contour Models for Digitizing a Printed Brainstem Atlas

The brainstem is a part of the brain that is connected to the cerebrum and the spinal cord. Ten out of twelve pairs of cranial nerves emerge from the brainstem. The cranial nerves transmit information between the brain and various parts of the body. Due to its anatomical and physiological relevance, a descriptive digital brainstem is important for neurosurgery planning and simulation. For both of these neurosurgical applications, the complexity of the brainstem requires a digital atlas approach to segmentation that maps intensities to tissues rather than less descriptive voxel or surface-based approaches. However, a descriptive brainstem atlas with adequate details for neurosurgery planning and simulation has not been developed to date. Fortunately, various textbooks contain 2D representations of the brainstem at various longitudinal coordinates. The aim of this thesis is to describe a minimally supervised method to segment sketches coinciding with slices of the brainstem featuring labeled contours. This thesis also describes a deformable contour model approach, emphasizing a 1-simplex framework, to reconstruct a 3D volume from 2D slices

Long-range mechanical force enables self-assembly of epithelial tubular patterns

Enabling long-range transport of molecules, tubules are critical for human body homeostasis. One fundamental question in tubule formation is how individual cells coordinate their positioning over long spatial scales, which can be as long as the sizes of tubular organs. Recent studies indicate that type I collagen (COL) is important in the development of epithelial tubules. Nevertheless, how cell–COL interactions contribute to the initiation or the maintenance of long-scale tubular patterns is unclear. Using a two-step process to quantitatively control cell–COL interaction, we show that epithelial cells developed various patterns in response to fine-tuned percentages of COL in ECM. In contrast with conventional thoughts, these patterns were initiated and maintained by traction forces created by cells but not diffusive factors secreted by cells. In particular, COL-dependent transmission of force in the ECM led to long-scale (up to 600 μm) interactions between cells. A mechanical feedback effect was encountered when cells used forces to modify cell positioning and COL distribution and orientations. Such feedback led to a bistability in the formation of linear, tubule-like patterns. Using micro-patterning technique, we further show that the stability of tubule-like patterns depended on the lengths of tubules. Our results suggest a mechanical mechanism that cells can use to initiate and maintain long-scale tubular patterns