IDSS: deformation invariant signatures for molecular shape comparison

<p>Abstract</p> <p>Background</p> <p>Many molecules of interest are flexible and undergo significant shape deformation as part of their function, but most existing methods of molecular shape comparison (MSC) treat them as rigid bodies, which may lead to incorrect measure of the shape similarity of flexible molecules.</p> <p>Results</p> <p>To address the issue we introduce a new shape descriptor, called Inner Distance Shape Signature (IDSS), for describing the 3D shapes of flexible molecules. The inner distance is defined as the length of the shortest path between landmark points within the molecular shape, and it reflects well the molecular structure and deformation without explicit decomposition. Our IDSS is stored as a histogram which is a probability distribution of inner distances between all sample point pairs on the molecular surface. We show that IDSS is insensitive to shape deformation of flexible molecules and more effective at capturing molecular structures than traditional shape descriptors. Our approach reduces the 3D shape comparison problem of flexible molecules to the comparison of IDSS histograms.</p> <p>Conclusion</p> <p>The proposed algorithm is robust and does not require any prior knowledge of the flexible regions. We demonstrate the effectiveness of IDSS within a molecular search engine application for a benchmark containing abundant conformational changes of molecules. Such comparisons in several thousands per second can be carried out. The presented IDSS method can be considered as an alternative and complementary tool for the existing methods for rigid MSC. The binary executable program for Windows platform and database are available from <url>https://engineering.purdue.edu/PRECISE/IDSS</url>.</p

Shape conforming volumetric interpolation with interior distances

Source based heterogeneous modelling is a powerful way of defining gradient materials within a volume. The current solutions do not take into account the topology of the object and can provide counter intuitive results for complex objects. This paper presents a method to interpolate material properties and attributes based on the accessibility of the points with respect to the material features defined by the user. Our method requires the nonoverlapping source features with constant material to interpolate gradient materials, by using Voronoi diagrams on interior distances. It leads to intuitive material properties across the shape regardless of its topology or complexity. We show how the shape conforming field is defined inside the volume and can be extended outside the volume to create a valid operator for a heterogeneous modelling system dealing with scalar fields. The presented method is computationally efficient and has several applications, such as material property interpolation and shape aware procedural micro structures

3DMolNavi: A Web-Based Retrieval and Navigation Tool for Flexible Molecular Shape Comparison.

Background Many molecules of interest are flexible and undergo significant shape deformation as part of their function, but most existing methods of molecular shape comparison treat them as rigid shapes, which may lead to incorrect measure of the shape similarity of flexible molecules. Currently, there still is a limited effort in retrieval and navigation for flexible molecular shape comparison, which would improve data retrieval by helping users locate the desirable molecule in a convenient way. Results To address this issue, we develop a web-based retrieval and navigation tool, named 3DMolNavi, for flexible molecular shape comparison. This tool is based on the histogram of Inner Distance Shape Signature (IDSS) for fast retrieving molecules that are similar to a query molecule, and uses dimensionality reduction to navigate the retrieved results in 2D and 3D spaces. We tested 3DMolNavi in the Database of Macromolecular Movements (MolMovDB) and CATH. Compared to other shape descriptors, it achieves good performance and retrieval results for different classes of flexible molecules. Conclusions The advantages of 3DMolNavi, over other existing softwares, are to integrate retrieval for flexible molecular shape comparison and enhance navigation for user’s interaction. 3DMolNavi can be accessed via https://engineering.purdue.edu/PRECISE/3dmolnavi/index.html webcite

Using diffusion distances for flexible molecular shape comparison

<p>Abstract</p> <p>Background</p> <p>Many molecules are flexible and undergo significant shape deformation as part of their function, and yet most existing molecular shape comparison (MSC) methods treat them as rigid bodies, which may lead to incorrect shape recognition.</p> <p>Results</p> <p>In this paper, we present a new shape descriptor, named Diffusion Distance Shape Descriptor (DDSD), for comparing 3D shapes of flexible molecules. The diffusion distance in our work is considered as an average length of paths connecting two landmark points on the molecular shape in a sense of inner distances. The diffusion distance is robust to flexible shape deformation, in particular to topological changes, and it reflects well the molecular structure and deformation without explicit decomposition. Our DDSD is stored as a histogram which is a probability distribution of diffusion distances between all sample point pairs on the molecular surface. Finally, the problem of flexible MSC is reduced to comparison of DDSD histograms.</p> <p>Conclusions</p> <p>We illustrate that DDSD is insensitive to shape deformation of flexible molecules and more effective at capturing molecular structures than traditional shape descriptors. The presented algorithm is robust and does not require any prior knowledge of the flexible regions.</p

3D object reconstruction using computer vision : reconstruction and characterization applications for external human anatomical structures

Tese de doutoramento. Engenharia Informática. Faculdade de Engenharia. Universidade do Porto. 201

DeepDeform: Learning Non-rigid RGB-D Reconstruction with Semi-supervised Data

Applying data-driven approaches to non-rigid 3D reconstruction has been difficult, which we believe can be attributed to the lack of a large-scale training corpus. One recent approach proposes self-supervision based on non-rigid reconstruction. Unfortunately, this method fails for important cases such as highly non-rigid deformations. We first address this problem of lack of data by introducing a novel semi-supervised strategy to obtain dense inter-frame correspondences from a sparse set of annotations. This way, we obtain a large dataset of 400 scenes, over 390,000 RGB-D frames, and 2,537 densely aligned frame pairs; in addition, we provide a test set along with several metrics for evaluation. Based on this corpus, we introduce a data-driven non-rigid feature matching approach, which we integrate into an optimization-based reconstruction pipeline. Here, we propose a new neural network that operates on RGB-D frames, while maintaining robustness under large non-rigid deformations and producing accurate predictions. Our approach significantly outperforms both existing non-rigid reconstruction methods that do not use learned data terms, as well as learning-based approaches that only use self-supervision

Using biomechanical constraints to improve video-based motion capture

In motion capture applications whose aim is to recover human body postures from various input, the high dimensionality of the problem makes it desirable to reduce the size of the search-space by eliminating a priori impossible configurations. This can be carried out by constraining the posture recovery process in various ways. Most recent work in this area has focused on applying camera viewpoint-related constraints to eliminate erroneous solutions. When camera calibration parameters are available, they provide an extremely efficient tool for disambiguating not only posture estimation, but also 3D reconstruction and data segmentation. Increased robustness is indeed to be gained from enforcing such constraints, which we prove in the context of an optical motion capture framework. Our contribution in this respect resides in having applied such constraints consistently to each main step involved in a motion capture process, namely marker reconstruction and segmentation, followed by posture recovery. These steps are made inter-dependent, where each one constrains the other. A more application-independent approach is to encode constraints directly within the human body model, such as limits on the rotational joints. This being an almost unexplored research subject, our efforts were mainly directed at determining a new method for measuring, representing and applying such joint limits. To the present day, the few existing range of motion boundary representations present severe drawbacks that call for an alternative formulation. The joint limits paradigm we propose not only overcomes these drawbacks, but also allows to capture intra- and inter-joint rotation dependencies, these being essential to realistic joint motion representation. The range of motion boundary is defined by an implicit surface, its analytical expression enabling us to readily establish whether a given joint rotation is valid or not. Furthermore, its continuous and differentiable nature provides us with a means of elegantly incorporating such a constraint within an optimisation process for posture recovery. Applying constrained optimisation to our body model and stereo data extracted from video sequence, we demonstrate the clearly resulting decrease in posture estimation errors. As a bonus, we have integrated our joint limits representation in character animation packages to show how motion can be naturally constrained in this manner

Hybrid Function Representation for Heterogeneous Objects

Heterogeneous object modelling is an emerging area where geometric shapes are considered in concert with their internal physically-based attributes. This paper describes a novel theoretical and practical framework for modelling volumetric heterogeneous objects on the basis of a novel unifying functionally-based hybrid representation called HFRep. This new representation allows for obtaining a continuous smooth distance field in Euclidean space and preserves the advantages of the conventional representations based on scalar fields of different kinds without their drawbacks. We systematically describe the mathematical and algorithmic basics of HFRep. The steps of the basic algorithm are presented in detail for both geometry and attributes. To solve some problematic issues, we have suggested several practical solutions, including a new algorithm for solving the eikonal equation on hierarchical grids. Finally, we show the practicality of the approach by modelling several representative heterogeneous objects, including those of a time-variant nature

Doctor of Philosophy

dissertationShape analysis is a well-established tool for processing surfaces. It is often a first step in performing tasks such as segmentation, symmetry detection, and finding correspondences between shapes. Shape analysis is traditionally employed on well-sampled surfaces where the geometry and topology is precisely known. When the form of the surface is that of a point cloud containing nonuniform sampling, noise, and incomplete measurements, traditional shape analysis methods perform poorly. Although one may first perform reconstruction on such a point cloud prior to performing shape analysis, if the geometry and topology is far from the true surface, then this can have an adverse impact on the subsequent analysis. Furthermore, for triangulated surfaces containing noise, thin sheets, and poorly shaped triangles, existing shape analysis methods can be highly unstable. This thesis explores methods of shape analysis applied directly to such defect-laden shapes. We first study the problem of surface reconstruction, in order to obtain a better understanding of the types of point clouds for which reconstruction methods contain difficulties. To this end, we have devised a benchmark for surface reconstruction, establishing a standard for measuring error in reconstruction. We then develop a new method for consistently orienting normals of such challenging point clouds by using a collection of harmonic functions, intrinsically defined on the point cloud. Next, we develop a new shape analysis tool which is tolerant to imperfections, by constructing distances directly on the point cloud defined as the likelihood of two points belonging to a mutually common medial ball, and apply this for segmentation and reconstruction. We extend this distance measure to define a diffusion process on the point cloud, tolerant to missing data, which is used for the purposes of matching incomplete shapes undergoing a nonrigid deformation. Lastly, we have developed an intrinsic method for multiresolution remeshing of a poor-quality triangulated surface via spectral bisection