Variational Multi-Objective Coordination

In this paper, we propose variational optimistic linear support (VOLS), a novel algorithm that finds bounded approximate solutions for multi-objective coordination graphs (MO-CoGs). VOLS builds and improves upon an existing exact algorithm called variable elimination linear support (VELS). Like VELS, VOLS solves a MO-CoG as a series of scalarized single-objective coordination graphs. We improve upon VELS in two important ways. Firstly, where VELS uses a single-objective solver called variable elimination (VE) as a subroutine, VOLS uses a variational method called weighted mini-buckets (WMB). Because variational methods scale much better than VE, VOLS can be used to solve much larger MO-CoGs than was previously possible. Furthermore, we show that because WMB computes bounded approximations, so does VOLS. Secondly, we leverage the insight that VOLS can hot-start each call to WMB by reusing the reparameterizations output by WMB on earlier calls. We show empirically that VOLS scales much better than VELS and introduces only negligle error. Our experimental results indicate that the reuse of reparameterizations keeps the runtime low and the approximation quality high

Deep-learning-based 2.5D flow field estimation for maximum intensity projections of 4D optical coherence tomography

In microsurgery, lasers have emerged as precise tools for bone ablation. A challenge is automatic control of laser bone ablation with 4D optical coherence tomography (OCT). OCT as high resolution imaging modality provides volumetric images of tissue and foresees information of bone position and orientation (pose) as well as thickness. However, existing approaches for OCT based laser ablation control rely on external tracking systems or invasively ablated artificial landmarks for tracking the pose of the OCT probe relative to the tissue. This can be superseded by estimating the scene flow caused by relative movement between OCT-based laser ablation system and patient. Therefore, this paper deals with 2.5D scene flow estimation of volumetric OCT images for application in laser ablation. We present a semi-supervised convolutional neural network based tracking scheme for subsequent 3D OCT volumes and apply it to a realistic semi-synthetic data set of ex vivo human temporal bone specimen. The scene flow is estimated in a two-stage approach. In the first stage, 2D lateral scene flow is computed on census-transformed en-face arguments-of-maximum intensity projections. Subsequent to this, the projections are warped by predicted lateral flow and 1D depth flow is estimated. The neural network is trained semi-supervised by combining error to ground truth and the reconstruction error of warped images with assumptions of spatial flow smoothness. Quantitative evaluation reveals a mean endpoint error of (4.7 ± 3.5) voxel or (27.5 ± 20.5) μm for scene flow estimation caused by simulated relative movement between the OCT probe and bone. The scene flow estimation for 4D OCT enables its use for markerless tracking of mastoid bone structures for image guidance in general, and automated laser ablation control. © 2019 SPIE

A Scale-Separated Dynamic Mode Decomposition From Observations of the Ionospheric Electron Density Profile

We present a method for modeling a time series of ionospheric electron density profiles using modal decompositions. Our method is based on the Dynamic Mode Decomposition (DMD), which provides a means of determining spatiotemporal modes from measurements alone. DMD-derived models can be easily updated as new data is recorded and do not require any physics to inform the dynamics. However, in the case of ionospheric profiles, we find a wide range of oscillations, including some far above the diurnal frequency. Therefore, we propose nontrivial extensions to DMD using multiresolution analysis (MRA) via wavelet decompositions. We call this method the Scale-Separated Dynamic Mode Decomposition (SSDMD) since the MRA isolates fluctuations at different scales within the time series into separated components. We show that this method provides a stable reconstruction of the mean plasma density and can be used to predict the state of the vertical profile at future time steps. We demonstrate the SSDMD method on data sets covering periods of high and low solar activity.Comment: 26 pages, 16 figure

Non-parametric belief propagation for mobile mapping sensor fusion

© 2016 Wuhan University. Published by Informa UK Limited, trading as Taylor & Francis Group. Many different forms of sensor fusion have been proposed each with its own niche. We propose a method of fusing multiple different sensor types. Our approach is built on the discrete belief propagation to fuse photogrammetry with GPS to generate three-dimensional (3D) point clouds. We propose using a non-parametric belief propagation similar to Sudderth et al’s work to fuse different sensors. This technique allows continuous variables to be used, is trivially parallel making it suitable for modern many-core processors, and easily accommodates varying types and combinations of sensors. By defining the relationships between common sensors, a graph containing sensor readings can be automatically generated from sensor data without knowing a priori the availability or reliability of the sensors. This allows the use of unreliable sensors which firstly, may start and stop providing data at any time and secondly, the integration of new sensor types simply by defining their relationship with existing sensors. These features allow a flexible framework to be developed which is suitable for many tasks. Using an abstract algorithm, we can instead focus on the relationships between sensors. Where possible we use the existing relationships between sensors rather than developing new ones. These relationships are used in a belief propagation algorithm to calculate the marginal probabilities of the network. In this paper, we present the initial results from this technique and the intended course for future work

Kernel Sequential Monte Carlo

We propose kernel sequential Monte Carlo (KSMC), a framework for sampling from static target densities. KSMC is a family of sequential Monte Carlo algorithms that are based on building emulator models of the current particle system in a reproducing kernel Hilbert space. We here focus on modelling nonlinear covariance structure and gradients of the target. The emulator’s geometry is adaptively updated and subsequently used to inform local proposals. Unlike in adaptive Markov chain Monte Carlo, continuous adaptation does not compromise convergence of the sampler. KSMC combines the strengths of sequental Monte Carlo and kernel methods: superior performance for multimodal targets and the ability to estimate model evidence as compared to Markov chain Monte Carlo, and the emulator’s ability to represent targets that exhibit high degrees of nonlinearity. As KSMC does not require access to target gradients, it is particularly applicable on targets whose gradients are unknown or prohibitively expensive. We describe necessary tuning details and demonstrate the benefits of the the proposed methodology on a series of challenging synthetic and real-world examples