Augmented reality for laparoscopic liver resection is a visualisation mode that allows a surgeon to localise tumours and vessels embedded within the liver by projecting them on top of a laparoscopic image. Preoperative 3D models extracted from CT or MRI data are registered to the intraoperative laparoscopic images during this process. In terms of 3D-2D fusion, most of the algorithms make use of anatomical landmarks to guide registration. These landmarks include the liver's inferior ridge, the falciform ligament, and the occluding contours. They are usually marked by hand in both the laparoscopic image and the 3D model, which is time-consuming and may contain errors if done by a non-experienced user. Therefore, there is a need to automate this process so that augmented reality can be used effectively in the operating room. We present the Preoperative-to-Intraoperative Laparoscopic Fusion Challenge (P2ILF), held during the Medical Imaging and Computer Assisted Interventions (MICCAI 2022) conference, which investigates the possibilities of detecting these landmarks automatically and using them in registration. The challenge was divided into two tasks: 1) A 2D and 3D landmark detection task and 2) a 3D-2D registration task. The teams were provided with training data consisting of 167 laparoscopic images and 9 preoperative 3D models from 9 patients, with the corresponding 2D and 3D landmark annotations. A total of 6 teams from 4 countries participated, whose proposed methods were evaluated on 16 images and two preoperative 3D models from two patients. All the teams proposed deep learning-based methods for the 2D and 3D landmark segmentation tasks and differentiable rendering-based methods for the registration task. Based on the experimental outcomes, we propose three key hypotheses that determine current limitations and future directions for research in this domain.
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The Sum-of-Squares (SOS) approximation method is a technique used in optimization problems to derive lower bounds on the optimal value of an objective function. By representing the objective function as a sum of squares in a feature space, the SOS method transforms non-convex global optimization problems into solvable semidefinite programs. This note presents an overview of the SOS method. We start with its application in finite-dimensional feature spaces and, subsequently, we extend it to infinite-dimensional feature spaces using reproducing kernels (k-SOS). Additionally, we highlight the utilization of SOS for estimating some relevant quantities in information theory, including the log-partition function.
We consider linear bounded operators acting in Banach spaces with a basis, such operators can be represented by an infinite matrix. We prove that for an invertible operator there exists a sequence of invertible finite-dimensional operators so that the family of norms of their inverses is uniformly bounded. It leads to the fact that solutions of finite-dimensional equations converge to the solution of initial operator equation with infinite-dimensional matrix.
The sparsity-ranked lasso (SRL) has been developed for model selection and estimation in the presence of interactions and polynomials. The main tenet of the SRL is that an algorithm should be more skeptical of higher-order polynomials and interactions *a priori* compared to main effects, and hence the inclusion of these more complex terms should require a higher level of evidence. In time series, the same idea of ranked prior skepticism can be applied to the possibly seasonal autoregressive (AR) structure of the series during the model fitting process, becoming especially useful in settings with uncertain or multiple modes of seasonality. The SRL can naturally incorporate exogenous variables, with streamlined options for inference and/or feature selection. The fitting process is quick even for large series with a high-dimensional feature set. In this work, we discuss both the formulation of this procedure and the software we have developed for its implementation via the **fastTS** R package. We explore the performance of our SRL-based approach in a novel application involving the autoregressive modeling of hourly emergency room arrivals at the University of Iowa Hospitals and Clinics. We find that the SRL is considerably faster than its competitors, while producing more accurate predictions.
Multi-contrast (MC) Magnetic Resonance Imaging (MRI) reconstruction aims to incorporate a reference image of auxiliary modality to guide the reconstruction process of the target modality. Known MC reconstruction methods perform well with a fully sampled reference image, but usually exhibit inferior performance, compared to single-contrast (SC) methods, when the reference image is missing or of low quality. To address this issue, we propose DuDoUniNeXt, a unified dual-domain MRI reconstruction network that can accommodate to scenarios involving absent, low-quality, and high-quality reference images. DuDoUniNeXt adopts a hybrid backbone that combines CNN and ViT, enabling specific adjustment of image domain and k-space reconstruction. Specifically, an adaptive coarse-to-fine feature fusion module (AdaC2F) is devised to dynamically process the information from reference images of varying qualities. Besides, a partially shared shallow feature extractor (PaSS) is proposed, which uses shared and distinct parameters to handle consistent and discrepancy information among contrasts. Experimental results demonstrate that the proposed model surpasses state-of-the-art SC and MC models significantly. Ablation studies show the effectiveness of the proposed hybrid backbone, AdaC2F, PaSS, and the dual-domain unified learning scheme.
Temporal network data is often encoded as time-stamped interaction events between senders and receivers, such as co-authoring scientific articles or communication via email. A number of relational event frameworks have been proposed to address specific issues raised by complex temporal dependencies. These models attempt to quantify how individual behaviour, endogenous and exogenous factors, as well as interactions with other individuals modify the network dynamics over time. It is often of interest to determine whether changes in the network can be attributed to endogenous mechanisms reflecting natural relational tendencies, such as reciprocity or triadic effects. The propensity to form or receive ties can also, at least partially, be related to actor attributes. Nodal heterogeneity in the network is often modelled by including actor-specific or dyadic covariates. However, comprehensively capturing all personality traits is difficult in practice, if not impossible. A failure to account for heterogeneity may confound the substantive effect of key variables of interest. This work shows that failing to account for node level sender and receiver effects can induce ghost triadic effects. We propose a random-effect extension of the relational event model to deal with these problems. We show that it is often effective over more traditional approaches, such as in-degree and out-degree statistics. These results that the violation of the hierarchy principle due to insufficient information about nodal heterogeneity can be resolved by including random effects in the relational event model as a standard.
We propose a new concept of lifts of reversible diffusion processes and show that various well-known non-reversible Markov processes arising in applications are lifts in this sense of simple reversible diffusions. Furthermore, we introduce a concept of non-asymptotic relaxation times and show that these can at most be reduced by a square root through lifting, generalising a related result in discrete time. Finally, we demonstrate how the recently developed approach to quantitative hypocoercivity based on space-time Poincar\'e inequalities can be rephrased and simplified in the language of lifts and how it can be applied to find optimal lifts.
This paper presents a novel stochastic optimisation methodology to perform empirical Bayesian inference in semi-blind image deconvolution problems. Given a blurred image and a parametric class of possible operators, the proposed optimisation approach automatically calibrates the parameters of the blur model by maximum marginal likelihood estimation, followed by (non-blind) image deconvolution by maximum-a-posteriori estimation conditionally to the estimated model parameters. In addition to the blur model, the proposed approach also automatically calibrates the noise variance as well as any regularisation parameters. The marginal likelihood of the blur, noise variance, and regularisation parameters is generally computationally intractable, as it requires calculating several integrals over the entire solution space. Our approach addresses this difficulty by using a stochastic approximation proximal gradient optimisation scheme, which iteratively solves such integrals by using a Moreau-Yosida regularised unadjusted Langevin Markov chain Monte Carlo algorithm. This optimisation strategy can be easily and efficiently applied to any model that is log-concave, and by using the same gradient and proximal operators that are required to compute the maximum-a-posteriori solution by convex optimisation. We provide convergence guarantees for the proposed optimisation scheme under realistic and easily verifiable conditions and subsequently demonstrate the effectiveness of the approach with a series of deconvolution experiments and comparisons with alternative strategies from the state of the art.
Robust Markov Decision Processes (RMDPs) are a widely used framework for sequential decision-making under parameter uncertainty. RMDPs have been extensively studied when the objective is to maximize the discounted return, but little is known for average optimality (optimizing the long-run average of the rewards obtained over time) and Blackwell optimality (remaining discount optimal for all discount factors sufficiently close to 1). In this paper, we prove several foundational results for RMDPs beyond the discounted return. We show that average optimal policies can be chosen stationary and deterministic for sa-rectangular RMDPs but, perhaps surprisingly, that history-dependent (Markovian) policies strictly outperform stationary policies for average optimality in s-rectangular RMDPs. We also study Blackwell optimality for sa-rectangular RMDPs, where we show that {\em approximate} Blackwell optimal policies always exist, although Blackwell optimal policies may not exist. We also provide a sufficient condition for their existence, which encompasses virtually any examples from the literature. We then discuss the connection between average and Blackwell optimality, and we describe several algorithms to compute the optimal average return. Interestingly, our approach leverages the connections between RMDPs and stochastic games.
We present a new methodology for decomposing flows with multiple transports that further extends the shifted proper orthogonal decomposition (sPOD). The sPOD tries to approximate transport-dominated flows by a sum of co-moving data fields. The proposed methods stem from sPOD but optimize the co-moving fields directly and penalize their nuclear norm to promote low rank of the individual data in the decomposition. Furthermore, we add a robustness term to the decomposition that can deal with interpolation error and data noises. Leveraging tools from convex optimization, we derive three proximal algorithms to solve the decomposition problem. We report a numerical comparison with existing methods against synthetic data benchmarks and then show the separation ability of our methods on 1D and 2D incompressible and reactive flows. The resulting methodology is the basis of a new analysis paradigm that results in the same interpretability as the POD for the individual co-moving fields.
We often rely on censuses of triangulations to guide our intuition in $3$-manifold topology. However, this can lead to misplaced faith in conjectures if the smallest counterexamples are too large to appear in our census. Since the number of triangulations increases super-exponentially with size, there is no way to expand a census beyond relatively small triangulations; the current census only goes up to $10$ tetrahedra. Here, we show that it is feasible to search for large and hard-to-find counterexamples by using heuristics to selectively (rather than exhaustively) enumerate triangulations. We use this idea to find counterexamples to three conjectures which ask, for certain $3$-manifolds, whether one-vertex triangulations always have a "distinctive" edge that would allow us to recognise the $3$-manifold.
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