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

Geodesic Tracking via New Data-driven Connections of Cartan Type for Vascular Tree Tracking

We introduce a data-driven version of the plus Cartan connection on the homogeneous space $\mathbb{M}_2$ of 2D positions and orientations. We formulate a theorem that describes all shortest and straight curves (parallel velocity and parallel momentum, respectively) with respect to this new data-driven connection and corresponding Riemannian manifold. Then we use these shortest curves for geodesic tracking of complex vasculature in multi-orientation image representations defined on $\mathbb{M}_{2}$. The data-driven Cartan connection characterizes the Hamiltonian flow of all geodesics. It also allows for improved adaptation to curvature and misalignment of the (lifted) vessel structure that we track via globally optimal geodesics. We compute these geodesics numerically via steepest descent on distance maps on $\mathbb{M}_2$ that we compute by a new modified anisotropic fast-marching method. Our experiments range from tracking single blood vessels with fixed endpoints to tracking complete vascular trees in retinal images. Single vessel tracking is performed in a single run in the multi-orientation image representation, where we project the resulting geodesics back onto the underlying image. The complete vascular tree tracking requires only two runs and avoids prior segmentation, placement of extra anchor points, and dynamic switching between geodesic models. Altogether we provide a geodesic tracking method using a single, flexible, transparent, data-driven geodesic model providing globally optimal curves which correctly follow highly complex vascular structures in retinal images. All experiments in this article can be reproduced via documented Mathematica notebooks available at GitHub (https://github.com/NickyvdBerg/DataDrivenTracking)

A Multi-Anatomical Retinal Structure Segmentation System For Automatic Eye Screening Using Morphological Adaptive Fuzzy Thresholding

Eye exam can be as efficacious as physical one in determining health concerns. Retina screening can be the very first clue to detecting a variety of hidden health issues including pre-diabetes and diabetes. Through the process of clinical diagnosis and prognosis; ophthalmologists rely heavily on the binary segmented version of retina fundus image; where the accuracy of segmented vessels, optic disc and abnormal lesions extremely affects the diagnosis accuracy which in turn affect the subsequent clinical treatment steps. This thesis proposes an automated retinal fundus image segmentation system composed of three segmentation subsystems follow same core segmentation algorithm. Despite of broad difference in features and characteristics; retinal vessels, optic disc and exudate lesions are extracted by each subsystem without the need for texture analysis or synthesis. For sake of compact diagnosis and complete clinical insight, our proposed system can detect these anatomical structures in one session with high accuracy even in pathological retina images. The proposed system uses a robust hybrid segmentation algorithm combines adaptive fuzzy thresholding and mathematical morphology. The proposed system is validated using four benchmark datasets: DRIVE and STARE (vessels), DRISHTI-GS (optic disc), and DIARETDB1 (exudates lesions). Competitive segmentation performance is achieved, outperforming a variety of up-to-date systems and demonstrating the capacity to deal with other heterogenous anatomical structures

Retinal Vessels Segmentation Techniques and Algorithms: A Survey

Retinal vessels identification and localization aim to separate the different retinal vasculature structure tissues, either wide or narrow ones, from the fundus image background and other retinal anatomical structures such as optic disc, macula, and abnormal lesions. Retinal vessels identification studies are attracting more and more attention in recent years due to non-invasive fundus imaging and the crucial information contained in vasculature structure which is helpful for the detection and diagnosis of a variety of retinal pathologies included but not limited to: Diabetic Retinopathy (DR), glaucoma, hypertension, and Age-related Macular Degeneration (AMD). With the development of almost two decades, the innovative approaches applying computer-aided techniques for segmenting retinal vessels are becoming more and more crucial and coming closer to routine clinical applications. The purpose of this paper is to provide a comprehensive overview for retinal vessels segmentation techniques. Firstly, a brief introduction to retinal fundus photography and imaging modalities of retinal images is given. Then, the preprocessing operations and the state of the art methods of retinal vessels identification are introduced. Moreover, the evaluation and validation of the results of retinal vessels segmentation are discussed. Finally, an objective assessment is presented and future developments and trends are addressed for retinal vessels identification techniques.https://doi.org/10.3390/app802015

The assessment of visual behaviour and depth perception in surgery

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On Improving Generalization of CNN-Based Image Classification with Delineation Maps Using the CORF Push-Pull Inhibition Operator

Deployed image classification pipelines are typically dependent on the images captured in real-world environments. This means that images might be affected by different sources of perturbations (e.g. sensor noise in low-light environments). The main challenge arises by the fact that image quality directly impacts the reliability and consistency of classification tasks. This challenge has, hence, attracted wide interest within the computer vision communities. We propose a transformation step that attempts to enhance the generalization ability of CNN models in the presence of unseen noise in the test set. Concretely, the delineation maps of given images are determined using the CORF push-pull inhibition operator. Such an operation transforms an input image into a space that is more robust to noise before being processed by a CNN. We evaluated our approach on the Fashion MNIST data set with an AlexNet model. It turned out that the proposed CORF-augmented pipeline achieved comparable results on noise-free images to those of a conventional AlexNet classification model without CORF delineation maps, but it consistently achieved significantly superior performance on test images perturbed with different levels of Gaussian and uniform noise

Handbook of Vascular Biometrics

This open access handbook provides the first comprehensive overview of biometrics exploiting the shape of human blood vessels for biometric recognition, i.e. vascular biometrics, including finger vein recognition, hand/palm vein recognition, retina recognition, and sclera recognition. After an introductory chapter summarizing the state of the art in and availability of commercial systems and open datasets/open source software, individual chapters focus on specific aspects of one of the biometric modalities, including questions of usability, security, and privacy. The book features contributions from both academia and major industrial manufacturers