4,133 research outputs found
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
Combinatorial Continuous Maximal Flows
Maximum flow (and minimum cut) algorithms have had a strong impact on
computer vision. In particular, graph cuts algorithms provide a mechanism for
the discrete optimization of an energy functional which has been used in a
variety of applications such as image segmentation, stereo, image stitching and
texture synthesis. Algorithms based on the classical formulation of max-flow
defined on a graph are known to exhibit metrication artefacts in the solution.
Therefore, a recent trend has been to instead employ a spatially continuous
maximum flow (or the dual min-cut problem) in these same applications to
produce solutions with no metrication errors. However, known fast continuous
max-flow algorithms have no stopping criteria or have not been proved to
converge. In this work, we revisit the continuous max-flow problem and show
that the analogous discrete formulation is different from the classical
max-flow problem. We then apply an appropriate combinatorial optimization
technique to this combinatorial continuous max-flow CCMF problem to find a
null-divergence solution that exhibits no metrication artefacts and may be
solved exactly by a fast, efficient algorithm with provable convergence.
Finally, by exhibiting the dual problem of our CCMF formulation, we clarify the
fact, already proved by Nozawa in the continuous setting, that the max-flow and
the total variation problems are not always equivalent.Comment: 26 page
Multi-Atlas Segmentation using Partially Annotated Data: Methods and Annotation Strategies
Multi-atlas segmentation is a widely used tool in medical image analysis,
providing robust and accurate results by learning from annotated atlas
datasets. However, the availability of fully annotated atlas images for
training is limited due to the time required for the labelling task.
Segmentation methods requiring only a proportion of each atlas image to be
labelled could therefore reduce the workload on expert raters tasked with
annotating atlas images. To address this issue, we first re-examine the
labelling problem common in many existing approaches and formulate its solution
in terms of a Markov Random Field energy minimisation problem on a graph
connecting atlases and the target image. This provides a unifying framework for
multi-atlas segmentation. We then show how modifications in the graph
configuration of the proposed framework enable the use of partially annotated
atlas images and investigate different partial annotation strategies. The
proposed method was evaluated on two Magnetic Resonance Imaging (MRI) datasets
for hippocampal and cardiac segmentation. Experiments were performed aimed at
(1) recreating existing segmentation techniques with the proposed framework and
(2) demonstrating the potential of employing sparsely annotated atlas data for
multi-atlas segmentation
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