10 citations · 18 across the 14 of their papers we have counts for
14 papers
Accelerating Returns and the Qualitative Engine for Science
Guojun Liao
Ray Kurzweil described a thesis of accelerating returns, which is the most influential narratives in discussions of technological progress. Its central claim is that advances in mu…
A Three-Layer Framework for AI in Scientific Discovery
Guojun Liao
Current discussions of AI in scientific discovery are often dominated by two visible capabilities: search over existing knowledge and execution through optimization, simulation, an…
VPREG: An Optimal Control Formulation for Diffeomorphic Image Registration Based on the Variational Principle Grid Generation Method
Zicong Zhou, Baihan Zhao, Andreas Mang +1
This paper introduces VPreg, a novel diffeomorphic image registration method. This work provides several improvements to our past work on mesh generation and diffeomorphic image re…
Recent insights on the Uniqueness Problem of Diffeomorphisms determined by Prescribed Jacobian Determinant and Curl
Zicong Zhou, Guojun Liao
Variational Principle (VP) forms diffeomorphisms with prescribed Jacobian determinant (JD) and curl. Examples demonstrate that, (i) JD alone can not uniquely determine a diffeomorp…
Construction of Diffeomorphisms with Prescribed Jacobian Determinant and Curl
Zicong Zhou, Guojun Liao
The variational principle (VP) is designed to generate non-folding grids (diffeomorphisms) with prescribed Jacobian determinant (JD) and curl. Its solution pool of the original VP…
Deformable Registration Using Average Geometric Transformations for Brain MR Images
Yongpei Zhu, Zicong Zhou, Guojun Liao +1
Accurate registration of medical images is vital for doctor's diagnosis and quantitative analysis. In this paper, we propose a new deformable medical image registration method base…
Multi-Block Grid deformation Method in 3D
Guojun G Liao, Jie Liu
Multi-block grids provide the computational efficiency of structured grids and the flexibility for complex geometry. Thus, Multi-block structured grids are widely used for field si…
The Method of Multimodal MRI Brain Image Segmentation Based on Differential Geometric Features
Yongpei Zhu, Zicong Zhou, Guojun Liao +2
Accurate segmentation of brain tissue in magnetic resonance images (MRI) is a diffcult task due to different types of brain abnormalities. Using information and features from multi…
Computational Technologies for Brain Morphometry
Zicong Zhou, Ben Hildebrandt, Xi Chen +1
In this paper, we described a set of computational technologies for image analysis with applications in Brain Morphometry. The proposed technologies are based on a new Variational…
Uniqueness of Transformation based on Jacobian Determinant and curl-Vector
Zicong Zhou, Xi Chen, Xian Xin Cai +1
Numerical examples demonstrated that a prescribed positive Jacobian determinant alone can not uniquely determine a diffeomorphism. It is conjectured that the uniqueness of a transf…
A Novel Deformation Method for Higher Order Mesh Generation
Zicong Zhou, Xi Chen, Guojun Liao
The development of higher order finite elements methods has become an active research area. The deformation method for mesh generation has achieved a prescribed positive Jacobian d…
New method of averaging diffeomorphisms based on Jacobian determinant and curl vector
Xi Chen, Guojun Liao
Averaging diffeomorphisms is a challenging problem, and it has great applications in areas like medical image atlases. The simple Euclidean average can neither guarantee the averag…
New Variational Method of Grid Generation with Prescribed Jacobian Determinant and Prescribed Curl
Xi Chen, Guojun Liao
Adaptive grid generation is an active research topic for numer- ical solution of differential equations. In this paper, we propose a variational method which generates transformati…
A New Method for Triangular Mesh Generation
Guojun G Liao, Xi Chen, Xianxin Cai +2
Computational mathematics plays an increasingly important role in computational fluid dynamics (CFD). The aeronautics and aerospace re- search community is working on next generati…