Yiying Tong | Michigan State University (original) (raw)
Papers by Yiying Tong
Recent years have witnessed a trend that advanced mathematical tools, such as algebraic topology,... more Recent years have witnessed a trend that advanced mathematical tools, such as algebraic topology, differential geometry, graph theory, and partial differential equations, have been developed for describing biological macromolecules. These tools have considerably strengthened our ability to understand the molecular mechanism of macromolecular function, dynamics and transport from their structures. However, currently, there is no unified mathematical theory to analyze, describe and characterize biological macromolecular geometry, topology, flexibility and natural mode at a variety of scales. We introduce the de Rham-Hodge theory, a landmark of 20th Century's mathematics, as a unified paradigm for analyzing biological macromolecular geometry and algebraic topology, for predicting macromolecular flexibility, and for modeling macromolecular natural modes at a variety of scales. In this paradigm, macromolecular geometric characteristic and topological invariants are revealed by de Rha...
Multiscale modeling is of paramount importance to the understanding of biomolecular structure, fu... more Multiscale modeling is of paramount importance to the understanding of biomolecular structure, function, dynamics and transport. Geometric modeling provides structural representations of molecular data from the Protein Data Bank (PDB) and the Electron Microscopy Data Bank (EMDB). Commonly used geometric models, such as molecular surface (MS), van der Waals surface, and
We propose a compact data structure for volumetric meshes of arbitrary topology and bounded valen... more We propose a compact data structure for volumetric meshes of arbitrary topology and bounded valence that offers cell-face, face-edge, and edge-vertex incidence queries in constant time. Our structure is simple to implement, easy to use, and allows for arbitrary, user-defined 3-cells such as prisms and hexahedra, while remaining very efficient in memory usage compared to previous work. Its time complexity for commonly-used incidence and adjacency queries such as vertex and dart one-rings is analyzed.
ACM Transactions on Graphics
Bulletin of mathematical biology, 2020
Biological macromolecules have intricate structures that underpin their biological functions. Und... more Biological macromolecules have intricate structures that underpin their biological functions. Understanding their structure-function relationships remains a challenge due to their structural complexity and functional variability. Although de Rham-Hodge theory, a landmark of twentieth-century mathematics, has had a tremendous impact on mathematics and physics, it has not been devised for macromolecular modeling and analysis. In this work, we introduce de Rham-Hodge theory as a unified paradigm for analyzing the geometry, topology, flexibility, and Hodge mode analysis of biological macromolecules. Geometric characteristics and topological invariants are obtained either from the Helmholtz-Hodge decomposition of the scalar, vector, and/or tensor fields of a macromolecule or from the spectral analysis of various Laplace-de Rham operators defined on the molecular manifolds. We propose Laplace-de Rham spectral-based models for predicting macromolecular flexibility. We further construct a L...
My main research goal is to develop robust, predictive, and multi-purpose computation tools by le... more My main research goal is to develop robust, predictive, and multi-purpose computation tools by leveraging differential geometric concepts and foundations. In particular, I wish to contribute a number of practical applications in computer graphics and related areas, such as medical imaging, biometrics, medical simulation, and visualization, by focusing on the geometrical foundations common to computational science and graphics.
The eukaryotic cytoskeleton plays essential roles in cell signaling, trafficking, and motion. Rec... more The eukaryotic cytoskeleton plays essential roles in cell signaling, trafficking, and motion. Recent work towards defining the temporal and spatial dynamics of cytoskeletal organization, including as a function of cell status, has utilized quantitative analysis of cytoskeletal fluorescence images as a standard approach to define cytoskeletal function. However, due to the uneven spatial distribution of the cytoskeleton, including varied shape and unstable binding efficiency to staining markers, these approaches may not segment cytoskeletal fractions accurately. Additionally, quantitative approaches currently suffer from human bias as well as information loss caused by z-axis projection of raw images. To overcome these obstacles, we developed Implicit Laplacian of Enhanced Edge (ILEE), a cytoskeletal component segmentation algorithm, which uses an 2D/3D-compatible, unguided local thresholding approach, therefore providing less biased and stable results. Empowered by ILEE, we construct...
Discrete & Continuous Dynamical Systems - B
Foundations of Data Science
Computer Graphics Forum
Based on a new spectral vector field analysis on triangle meshes, we construct a compact represen... more Based on a new spectral vector field analysis on triangle meshes, we construct a compact representation for near conformal mesh surface correspondences. Generalizing the functional map representation, our representation uses the map between the low‐frequency tangent vector fields induced by the correspondence. While our representation is as efficient, it is also capable of handling a more generic class of correspondence inference. We also formulate the vector field preservation constraints and regularization terms for correspondence inference, with function preservation treated as a special case. A number of important vector field–related constraints can be implicitly enforced in our representation, including the commutativity of the mapping with the usual gradient, curl, divergence operators or angle preservation under near conformal correspondence. For function transfer between shapes, the preservation of function values on landmarks can be strictly enforced through our gradient domain representation, enabling transfer across different topologies. With the vector field map representation, a novel class of constraints can be specified for the alignment of designed or computed vector field pairs. We demonstrate the advantages of the vector field map representation in tests on conformal datasets and near‐isometric datasets.
ACM Transactions on Graphics
SIAM Journal on Applied Algebra and Geometry
IEEE transactions on visualization and computer graphics, 2017
Decorating the surfaces of 3D printed objects with color textures is still not readily available ... more Decorating the surfaces of 3D printed objects with color textures is still not readily available in most consumer-level or even high-end 3D printers. Existing techniques such as hydrographics color transfer suffer from the issues of air pockets in concave regions and discoloration in overly stretched regions. We propose a novel thermoforming-based coloring technique to alleviate these problems as well as to simplify the overall procedure. Thermoforming is a widely used technique in industry for plastic thin shell product manufacturing by pressing heated plastic sheets onto molds using atmospheric pressure. We attach on the transparent plastic sheet a precomputed color pattern decal prior to heating, and adhere it to 3D printed models treated as the molds in thermoforming. The 3D models are thus decorated with the desired color texture, as well as a thin, polished protective cover. The precomputation involves a physical simulation of the thermoforming process to compute the correct c...
ACM Transactions on Graphics
We propose a real-time approach for indoor scene reconstruction. It is capable of producing a rea... more We propose a real-time approach for indoor scene reconstruction. It is capable of producing a ready-to-use 3D geometric model even while the user is still scanning the environment with a consumer depth camera. Our approach features explicit representations of planar regions and nonplanar objects extracted from the noisy feed of the depth camera, via an online structure analysis on the dynamic, incomplete data. The structural information is incorporated into the volumetric representation of the scene, resulting in a seamless integration with KinectFusion's global data structure and an efficient implementation of the whole reconstruction process. Moreover, heuristics based on rectilinear shapes in typical indoor scenes effectively eliminate camera tracking drift and further improve reconstruction accuracy. The instantaneous feedback enabled by our on-the-fly structure analysis, including repeated object recognition, allows the user to selectively scan the scene and produce high-fi...
The variation caused by aging has not received adequate attention compared with pose, lighting, a... more The variation caused by aging has not received adequate attention compared with pose, lighting, and expression variations. Aging is a complex process that affects both the 3D shape of the face and its texture (e.g., wrinkles). While the facial age modeling has been widely studied in computer graphics community, only a few studies have been reported in computer vision literature on age-invariant face recognition. We propose an automatic aging simulation technique that can assist any existing face recognition engine for aging-invariant face recognition. We learn the aging patterns of shape and the corresponding texture in 3D domain by adapting a 3D morphable model to the 2D aging database (public domain FG-NET). At recognition time, each probe and all gallery images are modified to compensate for the age-induced variation using an intermediate 3D model deformation and a texture modification, prior to matching. The proposed approach is evaluated on a set of age-separated probe and gall...
The de Rham-Hodge theory is a landmark of the 20^th Century's mathematics and has had a great... more The de Rham-Hodge theory is a landmark of the 20^th Century's mathematics and has had a great impact on mathematics, physics, computer science, and engineering. This work introduces an evolutionary de Rham-Hodge method to provide a unified paradigm for the multiscale geometric and topological analysis of evolving manifolds constructed from a filtration, which induces a family of evolutionary de Rham complexes. While the present method can be easily applied to close manifolds, the emphasis is given to more challenging compact manifolds with 2-manifold boundaries, which require appropriate analysis and treatment of boundary conditions on differential forms to maintain proper topological properties. Three sets of unique evolutionary Hodge Laplacian operators are proposed to generate three sets of topology-preserving singular spectra, for which the multiplicities of zero eigenvalues correspond to exactly the persistent Betti numbers of dimensions 0, 1, and 2. Additionally, three set...
IEEE transactions on pattern analysis and machine intelligence, Jan 7, 2016
Given a photo collection of "unconstrained" face images of one individual captured unde... more Given a photo collection of "unconstrained" face images of one individual captured under a variety of unknown pose, expression, and illumination conditions, this paper presents a method for reconstructing a 3D face surface model of the individual along with albedo information. Unlike prior work on face reconstruction that requires large photo collections, we formulate an approach to adapt to photo collections with a high diversity in both the number of images and the image quality. To achieve this, we incorporate prior knowledge about face shape by fitting a 3D morphable model to form a personalized template, following by using a novel photometric stereo formulation to complete the fine details, under a coarse-to-fine scheme. Our scheme incorporates a structural similarity-based local selection step to help identify a common expression for reconstruction while discarding occluded portions of faces. The evaluation of reconstruction performance is through a novel quality mea...
Computer Graphics Forum, 2008
ACM Transactions on Graphics
Communications in Information and Systems
Recent years have witnessed a trend that advanced mathematical tools, such as algebraic topology,... more Recent years have witnessed a trend that advanced mathematical tools, such as algebraic topology, differential geometry, graph theory, and partial differential equations, have been developed for describing biological macromolecules. These tools have considerably strengthened our ability to understand the molecular mechanism of macromolecular function, dynamics and transport from their structures. However, currently, there is no unified mathematical theory to analyze, describe and characterize biological macromolecular geometry, topology, flexibility and natural mode at a variety of scales. We introduce the de Rham-Hodge theory, a landmark of 20th Century's mathematics, as a unified paradigm for analyzing biological macromolecular geometry and algebraic topology, for predicting macromolecular flexibility, and for modeling macromolecular natural modes at a variety of scales. In this paradigm, macromolecular geometric characteristic and topological invariants are revealed by de Rha...
Multiscale modeling is of paramount importance to the understanding of biomolecular structure, fu... more Multiscale modeling is of paramount importance to the understanding of biomolecular structure, function, dynamics and transport. Geometric modeling provides structural representations of molecular data from the Protein Data Bank (PDB) and the Electron Microscopy Data Bank (EMDB). Commonly used geometric models, such as molecular surface (MS), van der Waals surface, and
We propose a compact data structure for volumetric meshes of arbitrary topology and bounded valen... more We propose a compact data structure for volumetric meshes of arbitrary topology and bounded valence that offers cell-face, face-edge, and edge-vertex incidence queries in constant time. Our structure is simple to implement, easy to use, and allows for arbitrary, user-defined 3-cells such as prisms and hexahedra, while remaining very efficient in memory usage compared to previous work. Its time complexity for commonly-used incidence and adjacency queries such as vertex and dart one-rings is analyzed.
ACM Transactions on Graphics
Bulletin of mathematical biology, 2020
Biological macromolecules have intricate structures that underpin their biological functions. Und... more Biological macromolecules have intricate structures that underpin their biological functions. Understanding their structure-function relationships remains a challenge due to their structural complexity and functional variability. Although de Rham-Hodge theory, a landmark of twentieth-century mathematics, has had a tremendous impact on mathematics and physics, it has not been devised for macromolecular modeling and analysis. In this work, we introduce de Rham-Hodge theory as a unified paradigm for analyzing the geometry, topology, flexibility, and Hodge mode analysis of biological macromolecules. Geometric characteristics and topological invariants are obtained either from the Helmholtz-Hodge decomposition of the scalar, vector, and/or tensor fields of a macromolecule or from the spectral analysis of various Laplace-de Rham operators defined on the molecular manifolds. We propose Laplace-de Rham spectral-based models for predicting macromolecular flexibility. We further construct a L...
My main research goal is to develop robust, predictive, and multi-purpose computation tools by le... more My main research goal is to develop robust, predictive, and multi-purpose computation tools by leveraging differential geometric concepts and foundations. In particular, I wish to contribute a number of practical applications in computer graphics and related areas, such as medical imaging, biometrics, medical simulation, and visualization, by focusing on the geometrical foundations common to computational science and graphics.
The eukaryotic cytoskeleton plays essential roles in cell signaling, trafficking, and motion. Rec... more The eukaryotic cytoskeleton plays essential roles in cell signaling, trafficking, and motion. Recent work towards defining the temporal and spatial dynamics of cytoskeletal organization, including as a function of cell status, has utilized quantitative analysis of cytoskeletal fluorescence images as a standard approach to define cytoskeletal function. However, due to the uneven spatial distribution of the cytoskeleton, including varied shape and unstable binding efficiency to staining markers, these approaches may not segment cytoskeletal fractions accurately. Additionally, quantitative approaches currently suffer from human bias as well as information loss caused by z-axis projection of raw images. To overcome these obstacles, we developed Implicit Laplacian of Enhanced Edge (ILEE), a cytoskeletal component segmentation algorithm, which uses an 2D/3D-compatible, unguided local thresholding approach, therefore providing less biased and stable results. Empowered by ILEE, we construct...
Discrete & Continuous Dynamical Systems - B
Foundations of Data Science
Computer Graphics Forum
Based on a new spectral vector field analysis on triangle meshes, we construct a compact represen... more Based on a new spectral vector field analysis on triangle meshes, we construct a compact representation for near conformal mesh surface correspondences. Generalizing the functional map representation, our representation uses the map between the low‐frequency tangent vector fields induced by the correspondence. While our representation is as efficient, it is also capable of handling a more generic class of correspondence inference. We also formulate the vector field preservation constraints and regularization terms for correspondence inference, with function preservation treated as a special case. A number of important vector field–related constraints can be implicitly enforced in our representation, including the commutativity of the mapping with the usual gradient, curl, divergence operators or angle preservation under near conformal correspondence. For function transfer between shapes, the preservation of function values on landmarks can be strictly enforced through our gradient domain representation, enabling transfer across different topologies. With the vector field map representation, a novel class of constraints can be specified for the alignment of designed or computed vector field pairs. We demonstrate the advantages of the vector field map representation in tests on conformal datasets and near‐isometric datasets.
ACM Transactions on Graphics
SIAM Journal on Applied Algebra and Geometry
IEEE transactions on visualization and computer graphics, 2017
Decorating the surfaces of 3D printed objects with color textures is still not readily available ... more Decorating the surfaces of 3D printed objects with color textures is still not readily available in most consumer-level or even high-end 3D printers. Existing techniques such as hydrographics color transfer suffer from the issues of air pockets in concave regions and discoloration in overly stretched regions. We propose a novel thermoforming-based coloring technique to alleviate these problems as well as to simplify the overall procedure. Thermoforming is a widely used technique in industry for plastic thin shell product manufacturing by pressing heated plastic sheets onto molds using atmospheric pressure. We attach on the transparent plastic sheet a precomputed color pattern decal prior to heating, and adhere it to 3D printed models treated as the molds in thermoforming. The 3D models are thus decorated with the desired color texture, as well as a thin, polished protective cover. The precomputation involves a physical simulation of the thermoforming process to compute the correct c...
ACM Transactions on Graphics
We propose a real-time approach for indoor scene reconstruction. It is capable of producing a rea... more We propose a real-time approach for indoor scene reconstruction. It is capable of producing a ready-to-use 3D geometric model even while the user is still scanning the environment with a consumer depth camera. Our approach features explicit representations of planar regions and nonplanar objects extracted from the noisy feed of the depth camera, via an online structure analysis on the dynamic, incomplete data. The structural information is incorporated into the volumetric representation of the scene, resulting in a seamless integration with KinectFusion's global data structure and an efficient implementation of the whole reconstruction process. Moreover, heuristics based on rectilinear shapes in typical indoor scenes effectively eliminate camera tracking drift and further improve reconstruction accuracy. The instantaneous feedback enabled by our on-the-fly structure analysis, including repeated object recognition, allows the user to selectively scan the scene and produce high-fi...
The variation caused by aging has not received adequate attention compared with pose, lighting, a... more The variation caused by aging has not received adequate attention compared with pose, lighting, and expression variations. Aging is a complex process that affects both the 3D shape of the face and its texture (e.g., wrinkles). While the facial age modeling has been widely studied in computer graphics community, only a few studies have been reported in computer vision literature on age-invariant face recognition. We propose an automatic aging simulation technique that can assist any existing face recognition engine for aging-invariant face recognition. We learn the aging patterns of shape and the corresponding texture in 3D domain by adapting a 3D morphable model to the 2D aging database (public domain FG-NET). At recognition time, each probe and all gallery images are modified to compensate for the age-induced variation using an intermediate 3D model deformation and a texture modification, prior to matching. The proposed approach is evaluated on a set of age-separated probe and gall...
The de Rham-Hodge theory is a landmark of the 20^th Century's mathematics and has had a great... more The de Rham-Hodge theory is a landmark of the 20^th Century's mathematics and has had a great impact on mathematics, physics, computer science, and engineering. This work introduces an evolutionary de Rham-Hodge method to provide a unified paradigm for the multiscale geometric and topological analysis of evolving manifolds constructed from a filtration, which induces a family of evolutionary de Rham complexes. While the present method can be easily applied to close manifolds, the emphasis is given to more challenging compact manifolds with 2-manifold boundaries, which require appropriate analysis and treatment of boundary conditions on differential forms to maintain proper topological properties. Three sets of unique evolutionary Hodge Laplacian operators are proposed to generate three sets of topology-preserving singular spectra, for which the multiplicities of zero eigenvalues correspond to exactly the persistent Betti numbers of dimensions 0, 1, and 2. Additionally, three set...
IEEE transactions on pattern analysis and machine intelligence, Jan 7, 2016
Given a photo collection of "unconstrained" face images of one individual captured unde... more Given a photo collection of "unconstrained" face images of one individual captured under a variety of unknown pose, expression, and illumination conditions, this paper presents a method for reconstructing a 3D face surface model of the individual along with albedo information. Unlike prior work on face reconstruction that requires large photo collections, we formulate an approach to adapt to photo collections with a high diversity in both the number of images and the image quality. To achieve this, we incorporate prior knowledge about face shape by fitting a 3D morphable model to form a personalized template, following by using a novel photometric stereo formulation to complete the fine details, under a coarse-to-fine scheme. Our scheme incorporates a structural similarity-based local selection step to help identify a common expression for reconstruction while discarding occluded portions of faces. The evaluation of reconstruction performance is through a novel quality mea...
Computer Graphics Forum, 2008
ACM Transactions on Graphics
Communications in Information and Systems