arXiv subjects

Fabian Rathke

Publications and source records attributed to Fabian Rathke.

2 recordsLinked to original sources

arXiv2019

Fast Multivariate Log-Concave Density Estimation

A novel computational approach to log-concave density estimation is proposed. Previous approaches utilize the piecewise-affine parametrization of the density induced by the given sample set. The number of parameters as well as non-smooth subgradient-based convex optimization for determining the maximum likelihood density estimate cause long runtimes for dimensions $d \geq 2$ and large sample sets. The presented approach is based on mildly non-convex smooth approximations of the objective function and \textit{sparse}, adaptive piecewise-affine density parametrization. Established memory-efficient numerical optimization techniques enable to process larger data sets for dimensions $d \geq 2$. While there is no guarantee that the algorithm returns the maximum likelihood estimate for every problem instance, we provide comprehensive numerical evidence that it does yield near-optimal results after significantly shorter runtimes. For example, 10000 samples in $\mathbb{R}^2$ are processed in two seconds, rather than in $\approx 14$ hours required by the previous approach to terminate. For higher dimensions, density estimation becomes tractable as well: Processing $10000$ samples in $\mathbb{R}^6$ requires 35 minutes. The software is publicly available as CRAN R package fmlogcondens.

stat.CO↗

arXiv2014

Probabilistic Intra-Retinal Layer Segmentation in 3-D OCT Images Using Global Shape Regularization

With the introduction of spectral-domain optical coherence tomography (OCT), resulting in a significant increase in acquisition speed, the fast and accurate segmentation of 3-D OCT scans has become evermore important. This paper presents a novel probabilistic approach, that models the appearance of retinal layers as well as the global shape variations of layer boundaries. Given an OCT scan, the full posterior distribution over segmentations is approximately inferred using a variational method enabling efficient probabilistic inference in terms of computationally tractable model components: Segmenting a full 3-D volume takes around a minute. Accurate segmentations demonstrate the benefit of using global shape regularization: We segmented 35 fovea-centered 3-D volumes with an average unsigned error of 2.46 $\pm$ 0.22 μm as well as 80 normal and 66 glaucomatous 2-D circular scans with errors of 2.92 $\pm$ 0.53 μm and 4.09 $\pm$ 0.98 μm respectively. Furthermore, we utilized the inferred posterior distribution to rate the quality of the segmentation, point out potentially erroneous regions and discriminate normal from pathological scans. No pre- or postprocessing was required and we used the same set of parameters for all data sets, underlining the robustness and out-of-the-box nature of our approach.

cs.CV↗