Efficient simulations of tubulin-driven axonal growth

This work concerns efficient and reliable numerical simulations of the dynamic behaviour of a moving-boundary model for tubulin-driven axonal growth. The model is nonlinear and consists of a coupled set of a partial differential equation (PDE) and two ordinary differential equations. The PDE is defined on a computational domain with a moving boundary, which is part of the solution. Numerical simulations based on standard explicit time-stepping methods are too time consuming due to the small time steps required for numerical stability. On the other hand standard implicit schemes are too complex due to the nonlinear equations that needs to be solved in each step. Instead, we propose to use the Peaceman--Rachford splitting scheme combined with temporal and spatial scalings of the model. Simulations based on this scheme have shown to be efficient, accurate, and reliable which makes it possible to evaluate the model, e.g.\ its dependency on biological and physical model parameters. These evaluations show among other things that the initial axon growth is very fast, that the active transport is the dominant reason over diffusion for the growth velocity, and that the polymerization rate in the growth cone does not affect the final axon length.Comment: Authors' accepted version, (post refereeing). The final publication (in Journal of Computational Neuroscience) is available at Springer via http://dx.doi.org/10.1007/s10827-016-0604-

Affine Approximation for Direct Batch Recovery of Euclidean Motion From Sparse Data

We present a batch method for recovering Euclidian camera motion from sparse image data. The main purpose of the algorithm is to recover the motion parameters using as much of the available information and as few computational steps as possible. The algorithmthus places itself in the gap between factorisation schemes, which make use of all available information in the initial recovery step, and sequential approaches which are able to handle sparseness in the image data. Euclidian camera matrices are approximated via the affine camera model, thus making the recovery direct in the sense that no intermediate projective reconstruction is made. Using a little known closure constraint, the FA-closure, we are able to formulate the camera coefficients linearly in the entries of the affine fundamental matrices. The novelty of the presented work is twofold: Firstly the presented formulation allows for a particularly good conditioning of the estimation of the initial motion parameters but also for an unprecedented diversity in the choice of possible regularisation terms. Secondly, the new autocalibration scheme presented here is in practice guaranteed to yield a Least Squares Estimate of the calibration parameters. As a bi-product, the affine camera model is rehabilitated as a useful model for most cameras and scene configurations, e.g. wide angle lenses observing a scene at close range. Experiments on real and synthetic data demonstrate the ability to reconstruct scenes which are very problematic for previous structure from motion techniques due to local ambiguities and error accumulation

A novel joint points and silhouette-based method to estimate 3D human pose and shape

This paper presents a novel method for 3D human pose and shape estimation from images with sparse views, using joint points and silhouettes, based on a parametric model. Firstly, the parametric model is fitted to the joint points estimated by deep learning-based human pose estimation. Then, we extract the correspondence between the parametric model of pose fitting and silhouettes on 2D and 3D space. A novel energy function based on the correspondence is built and minimized to fit parametric model to the silhouettes. Our approach uses sufficient shape information because the energy function of silhouettes is built from both 2D and 3D space. This also means that our method only needs images from sparse views, which balances data used and the required prior information. Results on synthetic data and real data demonstrate the competitive performance of our approach on pose and shape estimation of the human body.Comment: Accepted to ICPR 2020 3DHU worksho

Bilinear Parameterization For Differentiable Rank-Regularization

Low rank approximation is a commonly occurring problem in many computer vision and machine learning applications. There are two common ways of optimizing the resulting models. Either the set of matrices with a given rank can be explicitly parametrized using a bilinear factorization, or low rank can be implicitly enforced using regularization terms penalizing non-zero singular values. While the former approach results in differentiable problems that can be efficiently optimized using local quadratic approximation, the latter is typically not differentiable (sometimes even discontinuous) and requires first order subgradient or splitting methods. It is well known that gradient based methods exhibit slow convergence for ill-conditioned problems. In this paper we show how many non-differentiable regularization methods can be reformulated into smooth objectives using bilinear parameterization. This allows us to use standard second order methods, such as Levenberg--Marquardt (LM) and Variable Projection (VarPro), to achieve accurate solutions for ill-conditioned cases. We show on several real and synthetic experiments that our second order formulation converges to substantially more accurate solutions than competing state-of-the-art methods.Comment: 17 page

Towards Grading Gleason Score using Generically Trained Deep convolutional Neural Networks

We developed an automatic algorithm with the purpose to assist pathologists to report Gleason score on malignant prostatic adenocarcinoma specimen. In order to detect and classify the cancerous tissue, a deep convolutional neural network that had been pre-trained on a large set of photographic images was used. A specific aim was to support intuitive interaction with the result, to let pathologists adjust and correct the output. Therefore, we have designed an algorithm that makes a spatial classification of the whole slide into the same growth patterns as pathologists do. The 22-layer network was cut at an earlier layer and the output from that layer was used to train both a random forest classifier and a support vector machines classifier. At a specific layer a small patch of the image was used to calculate a feature vector and an image is represented by a number of those vectors. We have classified both the individual patches and the entire images. The classification results were compared for different scales of the images and feature vectors from two different layers from the network. Testing was made on a dataset consisting of 213 images, all containing a single class, benign tissue or Gleason score 3-5. Using 10-fold cross validation the accuracy per patch was 81 %. For whole images, the accuracy was increased to 89 %

An improved method for detecting and delineating genomic regions with altered gene expression in cancer

A method is presented for identifying genomic regions with altered gene expression in gene expression maps

Trust Your IMU: Consequences of Ignoring the IMU Drift

In this paper, we argue that modern pre-integration methods for inertial measurement units (IMUs) are accurate enough to ignore the drift for short time intervals. This allows us to consider a simplified camera model, which in turn admits further intrinsic calibration. We develop the first-ever solver to jointly solve the relative pose problem with unknown and equal focal length and radial distortion profile while utilizing the IMU data. Furthermore, we show significant speed-up compared to state-of-the-art algorithms, with small or negligible loss in accuracy for partially calibrated setups. The proposed algorithms are tested on both synthetic and real data, where the latter is focused on navigation using unmanned aerial vehicles (UAVs). We evaluate the proposed solvers on different commercially available low-cost UAVs, and demonstrate that the novel assumption on IMU drift is feasible in real-life applications. The extended intrinsic auto-calibration enables us to use distorted input images, making tedious calibration processes obsolete, compared to current state-of-the-art methods

The high resolution X-ray spectrum of SNR 0506-68 using XMM-Newton

Aims: We study the supernova remnant 0506-68 in order to obtain detailed information about, among other things, the ionisation state and age of the ionised plasma. Methods: Using the Reflection Grating Spectrometer (RGS) onboard the XMM-Newton satellite we are able to take detailed spectra of the remnant. In addition, we use the MOS data to obtain spectral information at higher energies. Results: The spectrum shows signs of recombination and we derive the conditions for which the remnant and SNR in general are able to cool rapidly enough to become over-ionised. The elemental abundances found are mostly in agreement with the mean LMC abundances. Our models and calculations favour the lower age estimate mentioned in the literature of $\sim4000$ year.Comment: 8 pages, 9 figure