Joint Image Reconstruction and Segmentation Using the Potts Model

We propose a new algorithmic approach to the non-smooth and non-convex Potts problem (also called piecewise-constant Mumford-Shah problem) for inverse imaging problems. We derive a suitable splitting into specific subproblems that can all be solved efficiently. Our method does not require a priori knowledge on the gray levels nor on the number of segments of the reconstruction. Further, it avoids anisotropic artifacts such as geometric staircasing. We demonstrate the suitability of our method for joint image reconstruction and segmentation. We focus on Radon data, where we in particular consider limited data situations. For instance, our method is able to recover all segments of the Shepp-Logan phantom from $7$ angular views only. We illustrate the practical applicability on a real PET dataset. As further applications, we consider spherical Radon data as well as blurred data

A convolutional autoencoder approach for mining features in cellular electron cryo-tomograms and weakly supervised coarse segmentation

Cellular electron cryo-tomography enables the 3D visualization of cellular organization in the near-native state and at submolecular resolution. However, the contents of cellular tomograms are often complex, making it difficult to automatically isolate different in situ cellular components. In this paper, we propose a convolutional autoencoder-based unsupervised approach to provide a coarse grouping of 3D small subvolumes extracted from tomograms. We demonstrate that the autoencoder can be used for efficient and coarse characterization of features of macromolecular complexes and surfaces, such as membranes. In addition, the autoencoder can be used to detect non-cellular features related to sample preparation and data collection, such as carbon edges from the grid and tomogram boundaries. The autoencoder is also able to detect patterns that may indicate spatial interactions between cellular components. Furthermore, we demonstrate that our autoencoder can be used for weakly supervised semantic segmentation of cellular components, requiring a very small amount of manual annotation.Comment: Accepted by Journal of Structural Biolog

A parametric level-set method for partially discrete tomography

This paper introduces a parametric level-set method for tomographic reconstruction of partially discrete images. Such images consist of a continuously varying background and an anomaly with a constant (known) grey-value. We represent the geometry of the anomaly using a level-set function, which we represent using radial basis functions. We pose the reconstruction problem as a bi-level optimization problem in terms of the background and coefficients for the level-set function. To constrain the background reconstruction we impose smoothness through Tikhonov regularization. The bi-level optimization problem is solved in an alternating fashion; in each iteration we first reconstruct the background and consequently update the level-set function. We test our method on numerical phantoms and show that we can successfully reconstruct the geometry of the anomaly, even from limited data. On these phantoms, our method outperforms Total Variation reconstruction, DART and P-DART.Comment: Paper submitted to 20th International Conference on Discrete Geometry for Computer Imager

A phase field method for tomographic reconstruction from limited data.

Classical tomographic reconstruction methods fail for problems in which there is extreme temporal and spatial sparsity in the measured data. Reconstruction of coronal mass ejections (CMEs), a space weather phenomenon with potential negative effects on the Earth, is one such problem. However, the topological complexity of CMEs renders recent limited data reconstruction methods inapplicable. We propose an energy function, based on a phase field level set framework, for the joint segmentation and tomographic reconstruction of CMEs from measurements acquired by coronagraphs, a type of solar telescope. Our phase field model deals easily with complex topologies, and is more robust than classical methods when the data are very sparse. We use a fast variational algorithm that combines the finite element method with a trust region variant of Newton’s method to minimize the energy. We compare the results obtained with our model to classical regularized tomography for synthetic CME-like images

A phase field method for tomographic reconstruction from limited data

Classical tomographic reconstruction methods fail for problems in which there is extreme temporal and spatial sparsity in the measured data. Reconstruction of coronal mass ejections (CMEs), a space weather phenomenon with potential negative effects on the Earth, is one such problem. However, the topological complexity of CMEs renders recent limited data reconstruction methods inapplicable. We propose an energy function, based on a phase field level set framework, for the joint segmentation and tomographic reconstruction of CMEs from measurements acquired by coronagraphs, a type of solar telescope. Our phase field model deals easily with complex topologies, and is more robust than classical methods when the data are very sparse. We use a fast variational algorithm that combines the finite element method with a trust region variant of Newton’s method to minimize the energy. We compare the results obtained with our model to classical regularized tomography for synthetic CME-like images

A virtual world of paleontology

Computer-aided visualization and analysis of fossils has revolutionized the study of extinct organisms. Novel techniques allow fossils to be characterized in three dimensions and in unprecedented detail. This has enabled paleontologists to gain important insights into their anatomy, development, and preservation. New protocols allow more objective reconstructions of fossil organisms, including soft tissues, from incomplete remains. The resulting digital reconstructions can be used in functional analyses, rigorously testing long-standing hypotheses regarding the paleobiology of extinct organisms. These approaches are transforming our understanding of long-studied fossil groups, and of the narratives of organismal and ecological evolution that have been built upon them