A Class of Collisions of Plane Impulsive Light--Like Signals in General Relativity

We present a systematic study of collisions of homogeneous, plane--fronted, impulsive light--like signals which do not interact after head--on collision. For the head--on collision of two such signals, six real parameters are involved, three from each of the incoming signals. We find two necessary conditions to be satisfied by these six parameters for the signals to be non--interacting after collision. We then solve the collision problem in general when these necessary conditions hold. After collision the two signals focus each other at Weyl curvature singularities on each others signal front. Our family of solutions contains some known collision solutions as special cases.Comment: 14 pages, late

Evaporation and growth of crystals - propagation of step density compression waves at vicinal surfaces

We studied the step dynamics during crystal sublimation and growth in the limit of fast surface diffusion and slow kinetics of atom attachment-detachment at the steps. For this limit we formulate a model free of the quasi-static approximation in the calculation of the adatom concentration on the terraces at the crystal surface. Such a model provides a relatively simple way to study the linear stability of a step train in a presence of step-step repulsion and an absence of destabilizing factors (as Schwoebel effect, surface electromigration etc.). The central result is that a critical velocity of the steps in the train exists which separates the stability and instability regimes. When the step velocity exceeds its critical value the plot of these trajectories manifests clear space and time periodicity (step density compression waves propagate on the vicinal surface). This ordered motion of the steps is preceded by a relatively short transition period of disordered step dynamics.Comment: 18 pages, 6 figure

Shifted-windows transformers for the detection of cerebral aneurysms in microsurgery

Purpose: Microsurgical Aneurysm Clipping Surgery (MACS) carries a high risk for intraoperative aneurysm rupture. Automated recognition of instances when the aneurysm is exposed in the surgical video would be a valuable reference point for neuronavigation, indicating phase transitioning and more importantly designating moments of high risk for rupture. This article introduces the MACS dataset containing 16 surgical videos with frame-level expert annotations and proposes a learning methodology for surgical scene understanding identifying video frames with the aneurysm present in the operating microscope’s field-of-view./ Methods: Despite the dataset imbalance (80% no presence, 20% presence) and developed without explicit annotations, we demonstrate the applicability of Transformer-based deep learning architectures (MACSSwin-T, vidMACSSwin-T) to detect the aneurysm and classify MACS frames accordingly. We evaluate the proposed models in multiple-fold cross-validation experiments with independent sets and in an unseen set of 15 images against 10 human experts (neurosurgeons)./ Results: Average (across folds) accuracy of 80.8% (range 78.5–82.4%) and 87.1% (range 85.1–91.3%) is obtained for the image- and video-level approach, respectively, demonstrating that the models effectively learn the classification task. Qualitative evaluation of the models’ class activation maps shows these to be localized on the aneurysm’s actual location. Depending on the decision threshold, MACSWin-T achieves 66.7–86.7% accuracy in the unseen images, compared to 82% of human raters, with moderate to strong correlation./ Conclusions: Proposed architectures show robust performance and with an adjusted threshold promoting detection of the underrepresented (aneurysm presence) class, comparable to human expert accuracy. Our work represents the first step towards landmark detection in MACS with the aim to inform surgical teams to attend to high-risk moments, taking precautionary measures to avoid rupturing

Hand-eye calibration for rigid laparoscopes using an invariant point

PURPOSE: Laparoscopic liver resection has significant advantages over open surgery due to less patient trauma and faster recovery times, yet it can be difficult due to the restricted field of view and lack of haptic feedback. Image guidance provides a potential solution but one current challenge is in accurate "hand-eye" calibration, which determines the position and orientation of the laparoscope camera relative to the tracking markers. METHODS: In this paper, we propose a simple and clinically feasible calibration method based on a single invariant point. The method requires no additional hardware, can be constructed by theatre staff during surgical setup, requires minimal image processing and can be visualised in real time. Real-time visualisation allows the surgical team to assess the calibration accuracy before use in surgery. In addition, in the laboratory, we have developed a laparoscope with an electromagnetic tracking sensor attached to the camera end and an optical tracking marker attached to the distal end. This enables a comparison of tracking performance. RESULTS: We have evaluated our method in the laboratory and compared it to two widely used methods, "Tsai's method" and "direct" calibration. The new method is of comparable accuracy to existing methods, and we show RMS projected error due to calibration of 1.95 mm for optical tracking and 0.85 mm for EM tracking, versus 4.13 and 1.00 mm respectively, using existing methods. The new method has also been shown to be workable under sterile conditions in the operating room. CONCLUSION: We have proposed a new method of hand-eye calibration, based on a single invariant point. Initial experience has shown that the method provides visual feedback, satisfactory accuracy and can be performed during surgery. We also show that an EM sensor placed near the camera would provide significantly improved image overlay accuracy

More unlabelled data or label more data? A study on semi-supervised laparoscopic image segmentation

Improving a semi-supervised image segmentation task has the option of adding more unlabelled images, labelling the unlabelled images or combining both, as neither image acquisition nor expert labelling can be considered trivial in most clinical applications. With a laparoscopic liver image segmentation application, we investigate the performance impact by altering the quantities of labelled and unlabelled training data, using a semi-supervised segmentation algorithm based on the mean teacher learning paradigm. We first report a significantly higher segmentation accuracy, compared with supervised learning. Interestingly, this comparison reveals that the training strategy adopted in the semi-supervised algorithm is also responsible for this observed improvement, in addition to the added unlabelled data. We then compare different combinations of labelled and unlabelled data set sizes for training semi-supervised segmentation networks, to provide a quantitative example of the practically useful trade-off between the two data planning strategies in this surgical guidance application

Lattice Effects in Crystal Evaporation

We study the dynamics of a stepped crystal surface during evaporation, using the classical model of Burton, Cabrera and Frank, in which the dynamics of the surface is represented as a motion of parallel, monoatomic steps. The validity of the continuum approximation treated by Frank is checked against numerical calculations and simple, qualitative arguments. The continuum approximation is found to suffer from limitations related, in particular, to the existence of angular points. These limitations are often related to an adatom detachment rate of adatoms which is higher on the lower side of each step than on the upper side ("Schwoebel effect").Comment: DRFMC/SPSMS/MDN, Centre d'Etudes Nucleaires de Grenoble, 25 pages, LaTex, revtex style. 8 Figures, available upon request, report# UBFF30119

Electromigration-Induced Propagation of Nonlinear Surface Waves

Due to the effects of surface electromigration, waves can propagate over the free surface of a current-carrying metallic or semiconducting film of thickness h_0. In this paper, waves of finite amplitude, and slow modulations of these waves, are studied. Periodic wave trains of finite amplitude are found, as well as their dispersion relation. If the film material is isotropic, a wave train with wavelength lambda is unstable if lambda/h_0 < 3.9027..., and is otherwise marginally stable. The equation of motion for slow modulations of a finite amplitude, periodic wave train is shown to be the nonlinear Schrodinger equation. As a result, envelope solitons can travel over the film's surface.Comment: 13 pages, 2 figures. To appear in Phys. Rev.

Learned optical flow for intra-operative tracking of the retinal fundus

Purpose: Sustained delivery of regenerative retinal therapies by robotic systems requires intra-operative tracking of the retinal fundus. We propose a supervised deep convolutional neural network to densely predict semantic segmentation and optical flow of the retina as mutually supportive tasks, implicitly inpainting retinal flow information missing due to occlusion by surgical tools. / Methods: As manual annotation of optical flow is infeasible, we propose a flexible algorithm for generation of large synthetic training datasets on the basis of given intra-operative retinal images. We evaluate optical flow estimation by tracking a grid and sparsely annotated ground truth points on a benchmark of challenging real intra-operative clips obtained from an extensive internally acquired dataset encompassing representative vitreoretinal surgical cases. / Results: The U-Net-based network trained on the synthetic dataset is shown to generalise well to the benchmark of real surgical videos. When used to track retinal points of interest, our flow estimation outperforms variational baseline methods on clips containing tool motions which occlude the points of interest, as is routinely observed in intra-operatively recorded surgery videos. / Conclusions: The results indicate that complex synthetic training datasets can be used to specifically guide optical flow estimation. Our proposed algorithm therefore lays the foundation for a robust system which can assist with intra-operative tracking of moving surgical targets even when occluded

A quantitative theory of current-induced step bunching on Si(111)

We use a one-dimensional step model to study quantitatively the growth of step bunches on Si(111) surfaces induced by a direct heating current. Parameters in the model are fixed from experimental measurements near 900 deg C under the assumption that there is local mass transport through surface diffusion and that step motion is limited by the attachment rate of adatoms to step edges. The direct heating current is treated as an external driving force acting on each adatom. Numerical calculations show both qualitative and quantitative agreement with experiment. A force in the step down direction will destabilize the uniform step train towards step bunching. The average size of the step bunches grows with electromigration time as t^beta, with beta = 0.5, in agreement with experiment and with an analytical treatment of the steady states. The model is extended to include the effect of direct hopping of adatoms between different terraces. Monte-Carlo simulations of a solid-on-solid model, using physically motivated assumptions about the dynamics of surface diffusion and attachment at step edges, are carried out to study two dimensional features that are left out of the present step model and to test its validity. These simulations give much better agreement with experiment than previous work. We find a new step bending instability when the driving force is along the step edge direction. This instability causes the formation of step bunches and antisteps that is similar to that observed in experiment.Comment: 11 pages, 7 figure