Continuous Multiclass Labeling Approaches and Algorithms

We study convex relaxations of the image labeling problem on a continuous domain with regularizers based on metric interaction potentials. The generic framework ensures existence of minimizers and covers a wide range of relaxations of the originally combinatorial problem. We focus on two specific relaxations that differ in flexibility and simplicity -- one can be used to tightly relax any metric interaction potential, while the other one only covers Euclidean metrics but requires less computational effort. For solving the nonsmooth discretized problem, we propose a globally convergent Douglas-Rachford scheme, and show that a sequence of dual iterates can be recovered in order to provide a posteriori optimality bounds. In a quantitative comparison to two other first-order methods, the approach shows competitive performance on synthetical and real-world images. By combining the method with an improved binarization technique for nonstandard potentials, we were able to routinely recover discrete solutions within 1%--5% of the global optimum for the combinatorial image labeling problem

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 {\mu}m as well as 80 normal and 66 glaucomatous 2-D circular scans with errors of 2.92 $\pm$ 0.53 {\mu}m and 4.09 $\pm$ 0.98 {\mu}m 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.Comment: Accepted for publication in Medical Image Analysis (MIA), Elsevie