A Proposed Device for Controlling the Flow of Information Based on Weyl Fermions.

In this work we propose a novel device for controlling the flow of information using Weyl fermions. Based on a previous work by our group, we show that it is possible to fully control the flow of Weyl fermions on several different channels by applying an electric field perpendicular to the direction of motion of the particles on each channel. In this way, we can transmit information as logical bits, depending on the existence or not of a Weyl current on each channel. We also show that the response time of this device is exceptionally low, less than 1 ps, for typical values of its parameters, allowing for the control of the flow of information at extremely high rates of the order of 100 Petabits per second. Alternatively, this device could also operate as an electric field sensor. In addition, we demonstrate that Weyl fermions can be efficiently guided through the proposed device using appropriate magnetic fields. Finally, we discuss some particularly interesting remarks regarding the electromagnetic interactions of high-energy particles.

A new formula for bivariate Hermite interpolation on variable step grids and its application to image interpolation.

In this paper, we present a novel formula of the bivariate Hermite interpolating (BHI) polynomial in the case of support points arranged on a grid with variable step. This expression is applicable when interpolation of a bivariate function is required, given its value and the values of its partial derivatives of arbitrarily high order, at the support points. The proposed formula is a generalization of an existing formula for the bivariate Hermite polynomial. It is also algebraically much simpler, thus can be computed more efficiently. In order to apply Hermite interpolation to image interpolation, we simplify the proposed (BHI) to handle support points on a regular unit-step grid. The values of image partial derivatives are arithmetically approximated using compact finite differences. The proposed method is being assessed in a number of image interpolation experiments that include a synthetic image, for which the values of the partial derivatives are computed analytically, as well as a collection of images from different medical modalities. The proposed BHI with up to second-order image partial derivatives, outperforms the convolution-based interpolation methods, as well as generalized interpolation methods with the same number of support points that was compared with, in the majority of image interpolation experiments. The computational load of the proposed BHI is calculated and its behaviour with respect to its controlling parameters is investigated.

An implicit evolution scheme for active contours and surfaces based on IIR filtering.

In this work, we present an approach for implementing an implicit scheme for the numerical solution of the partial differential equation of the evolution of an active contour/surface. The proposed scheme is applicable to any variant of the traditional active contour (AC), irrespectively of the calculation of the image-based force field and it is readily applicable to explicitly parameterized active surfaces (AS). The proposed approach is formulated as an infinite impulse response (IIR) filtering of the coordinates of the contour/surface points. The poles of the filter are determined by the parameters controlling the shape of the active contour/surface. We show that the proposed IIR-based implicit evolution scheme has very low complexity. Furthermore, the proposed scheme is numerically stable, thus it allows the convergence of the AC/AS with significantly fewer iterations than the explicit evolution scheme. It also possesses the separability property along the two parameters of the AS, thus it may be applied to deformable surfaces, without the need to store and invert large sparse matrices. We implemented the proposed IIR-based implicit evolution scheme in the Vector Field Convolution (VFC) AC/AS using synthetic and clinical volumetric data. We compared the segmentation results with those of the explicit AC/AS evolution, in terms of accuracy and efficiency. Results show that the VFC AC/AS with the proposed IIR-based implicit evolution scheme achieves the same segmentation results with the explicit scheme, with considerably less computation time.

A novel tool for segmenting 3D medical images based on generalized cylinders and active surfaces.

Three-dimensional (3D) medical imaging has been incorporated in routine clinical practice, since the required infrastructure has become increasingly affordable. New algorithms and applications are needed to serve the additional image processing and analysis functions in 3D space. In this work we propose a system for semi-automatic modeling and segmentation of elongated salient and anatomical objects in 3D medical images. The proposed methodology is based on a novel mathematical formalization of a well-known class of geometric primitives, namely generalized cylinders (GCs), which exhibits advantages over the existing parametric definition. Since the anatomical objects have to be modeled by their intersection with the transverse image planes, the proposed methodology includes also a new seeded region growing (SRG) segmentation algorithm for ellipse detection in 2D images, based on a priori shape knowledge. Finally, the resulting GC model is used to initialize an active surface (AS) segmentation method, in order to accurately delineate the required object. In this work we present the proposed algorithms in detail, along with the evaluation of the accuracy of the model-based segmentation by experts. Results show that elongated objects like the aorta and the trachea may be segmented with sensitivity between 90% and 95%. The proposed SRG-ellipse detector requires minimal user-initialization and its executions requires only few seconds for each image slice on an average laptop. The evolution of the AS requires less than one second per iteration for a typical CT image. Comparisons are provided with state of the art semi-automatic medical image processing software, which validate the merit of the proposed work.

Hermite kernels for slice interpolation in medical images.

Univariate Hermite interpolation of the total degree (HTD) is an algebraically demanding interpolation method that utilizes information of the values of the signal to be interpolated at distinct support positions, as well as the values of its derivatives up to a maximum available order. In this work the interpolation kernels of the univariate HTD are derived, using several approximations of the 1st and 2nd order of discrete signal derivative. We assess the derived Hermite kernels in the task of medical image slice interpolation, against several other well established interpolation techniques. Results show that specific Hermite kernels can outperform other established interpolation methods with similar computational complexity, in terms of root mean square error (RMSE), in a number of interpolation experiments, resulting in higher accuracy interpolated images.

Automatic model-based tracing algorithm for vessel segmentation and diameter estimation.

An automatic algorithm capable of segmenting the whole vessel tree and calculate vessel diameter and orientation in a digital ophthalmologic image is presented in this work. The algorithm is based on a parametric model of a vessel that can assume arbitrarily complex shape and a simple measure of match that quantifies how well the vessel model matches a given angiographic image. An automatic vessel tracing algorithm is described that exploits the geometric model and actively seeks vessel bifurcation, without user intervention. The proposed algorithm uses the geometric vessel model to determine the vessel diameter at each detected central axis pixel. For this reason, the algorithm is fine tuned using a subset of ophthalmologic images of the publically available DRIVE database, by maximizing vessel segmentation accuracy. The proposed algorithm is then applied to the remaining ophthalmological images of the DRIVE database. The segmentation results of the proposed algorithm compare favorably in terms of accuracy with six other well established vessel detection techniques, outperforming three of them in the majority of the available ophthalmologic images. The proposed algorithm achieves subpixel root mean square central axis positioning error that outperforms the non-expert based vessel segmentation, whereas the accuracy of vessel diameter estimation is comparable to that of the non-expert based vessel segmentation.