Topological descriptors for 3D surface analysis

We investigate topological descriptors for 3D surface analysis, i.e. the classification of surfaces according to their geometric fine structure. On a dataset of high-resolution 3D surface reconstructions we compute persistence diagrams for a 2D cubical filtration. In the next step we investigate different topological descriptors and measure their ability to discriminate structurally different 3D surface patches. We evaluate their sensitivity to different parameters and compare the performance of the resulting topological descriptors to alternative (non-topological) descriptors. We present a comprehensive evaluation that shows that topological descriptors are (i) robust, (ii) yield state-of-the-art performance for the task of 3D surface analysis and (iii) improve classification performance when combined with non-topological descriptors.Comment: 12 pages, 3 figures, CTIC 201

Quantitative toxicity prediction using topology based multi-task deep neural networks

The understanding of toxicity is of paramount importance to human health and environmental protection. Quantitative toxicity analysis has become a new standard in the field. This work introduces element specific persistent homology (ESPH), an algebraic topology approach, for quantitative toxicity prediction. ESPH retains crucial chemical information during the topological abstraction of geometric complexity and provides a representation of small molecules that cannot be obtained by any other method. To investigate the representability and predictive power of ESPH for small molecules, ancillary descriptors have also been developed based on physical models. Topological and physical descriptors are paired with advanced machine learning algorithms, such as deep neural network (DNN), random forest (RF) and gradient boosting decision tree (GBDT), to facilitate their applications to quantitative toxicity predictions. A topology based multi-task strategy is proposed to take the advantage of the availability of large data sets while dealing with small data sets. Four benchmark toxicity data sets that involve quantitative measurements are used to validate the proposed approaches. Extensive numerical studies indicate that the proposed topological learning methods are able to outperform the state-of-the-art methods in the literature for quantitative toxicity analysis. Our online server for computing element-specific topological descriptors (ESTDs) is available at http://weilab.math.msu.edu/TopTox/Comment: arXiv admin note: substantial text overlap with arXiv:1703.1095

Structuprint: a scalable and extensible tool for two-dimensional representation of protein surfaces

© 2016 Kontopoulos et al.Background: The term molecular cartography encompasses a family of computational methods for two-dimensional transformation of protein structures and analysis of their physicochemical properties. The underlying algorithms comprise multiple manual steps, whereas the few existing implementations typically restrict the user to a very limited set of molecular descriptors. Results: We present Structuprint, a free standalone software that fully automates the rendering of protein surface maps, given - at the very least - a directory with a PDB file and an amino acid property. The tool comes with a default database of 328 descriptors, which can be extended or substituted by user-provided ones. The core algorithm comprises the generation of a mould of the protein surface, which is subsequently converted to a sphere and mapped to two dimensions, using the Miller cylindrical projection. Structuprint is partly optimized for multicore computers, making the rendering of animations of entire molecular dynamics simulations feasible. Conclusions: Structuprint is an efficient application, implementing a molecular cartography algorithm for protein surfaces. According to the results of a benchmark, its memory requirements and execution time are reasonable, allowing it to run even on low-end personal computers. We believe that it will be of use - primarily but not exclusively - to structural biologists and computational biochemists

Spherical harmonics coeffcients for ligand-based virtual screening of cyclooxygenase inhibitors

Background: Molecular descriptors are essential for many applications in computational chemistry, such as ligand-based similarity searching. Spherical harmonics have previously been suggested as comprehensive descriptors of molecular structure and properties. We investigate a spherical harmonics descriptor for shape-based virtual screening. Methodology/Principal Findings: We introduce and validate a partially rotation-invariant three-dimensional molecular shape descriptor based on the norm of spherical harmonics expansion coefficients. Using this molecular representation, we parameterize molecular surfaces, i.e., isosurfaces of spatial molecular property distributions. We validate the shape descriptor in a comprehensive retrospective virtual screening experiment. In a prospective study, we virtually screen a large compound library for cyclooxygenase inhibitors, using a self-organizing map as a pre-filter and the shape descriptor for candidate prioritization. Conclusions/Significance: 12 compounds were tested in vitro for direct enzyme inhibition and in a whole blood assay. Active compounds containing a triazole scaffold were identified as direct cyclooxygenase-1 inhibitors. This outcome corroborates the usefulness of spherical harmonics for representation of molecular shape in virtual screening of large compound collections. The combination of pharmacophore and shape-based filtering of screening candidates proved to be a straightforward approach to finding novel bioactive chemotypes with minimal experimental effort

Laplace–Beltrami eigenvalues and topological features of eigenfunctions for statistical shape analysis

This paper proposes the use of the surface based Laplace-Beltrami and the volumetric Laplace eigenvalues and -functions as shape descriptors for the comparison and analysis of shapes. These spectral measures are isometry invariant and therefore allow for shape comparisons with minimal shape pre-processing. In particular, no registration, mapping, or remeshing is necessary. The discriminatory power of the 2D surface and 3D solid methods is demonstrated on a population of female caudate nuclei (a subcortical gray matter structure of the brain, involved in memory function, emotion processing, and learning) of normal control subjects and of subjects with schizotypal personality disorder. The behavior and properties of the Laplace-Beltrami eigenvalues and -functions are discussed extensively for both the Dirichlet and Neumann boundary condition showing advantages of the Neumann vs. the Dirichlet spectra in 3D. Furthermore, topological analyses employing the Morse-Smale complex (on the surfaces) and the Reeb graph (in the solids) are performed on selected eigenfunctions, yielding shape descriptors, that are capable of localizing geometric properties and detecting shape differences by indirectly registering topological features such as critical points, level sets and integral lines of the gradient field across subjects. The use of these topological features of the Laplace-Beltrami eigenfunctions in 2D and 3D for statistical shape analysis is novel

Laplace–Beltrami eigenvalues and topological features of eigenfunctions for statistical shape analysis

This paper proposes the use of the surface based Laplace-Beltrami and the volumetric Laplace eigenvalues and -functions as shape descriptors for the comparison and analysis of shapes. These spectral measures are isometry invariant and therefore allow for shape comparisons with minimal shape pre-processing. In particular, no registration, mapping, or remeshing is necessary. The discriminatory power of the 2D surface and 3D solid methods is demonstrated on a population of female caudate nuclei (a subcortical gray matter structure of the brain, involved in memory function, emotion processing, and learning) of normal control subjects and of subjects with schizotypal personality disorder. The behavior and properties of the Laplace-Beltrami eigenvalues and -functions are discussed extensively for both the Dirichlet and Neumann boundary condition showing advantages of the Neumann vs. the Dirichlet spectra in 3D. Furthermore, topological analyses employing the Morse-Smale complex (on the surfaces) and the Reeb graph (in the solids) are performed on selected eigenfunctions, yielding shape descriptors, that are capable of localizing geometric properties and detecting shape differences by indirectly registering topological features such as critical points, level sets and integral lines of the gradient field across subjects. The use of these topological features of the Laplace-Beltrami eigenfunctions in 2D and 3D for statistical shape analysis is novel

Streaming Algorithm for Euler Characteristic Curves of Multidimensional Images

We present an efficient algorithm to compute Euler characteristic curves of gray scale images of arbitrary dimension. In various applications the Euler characteristic curve is used as a descriptor of an image. Our algorithm is the first streaming algorithm for Euler characteristic curves. The usage of streaming removes the necessity to store the entire image in RAM. Experiments show that our implementation handles terabyte scale images on commodity hardware. Due to lock-free parallelism, it scales well with the number of processor cores. Our software---CHUNKYEuler---is available as open source on Bitbucket. Additionally, we put the concept of the Euler characteristic curve in the wider context of computational topology. In particular, we explain the connection with persistence diagrams

Keyframe-based monocular SLAM: design, survey, and future directions

Extensive research in the field of monocular SLAM for the past fifteen years has yielded workable systems that found their way into various applications in robotics and augmented reality. Although filter-based monocular SLAM systems were common at some time, the more efficient keyframe-based solutions are becoming the de facto methodology for building a monocular SLAM system. The objective of this paper is threefold: first, the paper serves as a guideline for people seeking to design their own monocular SLAM according to specific environmental constraints. Second, it presents a survey that covers the various keyframe-based monocular SLAM systems in the literature, detailing the components of their implementation, and critically assessing the specific strategies made in each proposed solution. Third, the paper provides insight into the direction of future research in this field, to address the major limitations still facing monocular SLAM; namely, in the issues of illumination changes, initialization, highly dynamic motion, poorly textured scenes, repetitive textures, map maintenance, and failure recovery