Guojun G. Liao

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A mathematical problem arising from data set alignment is studied. For two given real-valued functions defined on two (2D or 3D) domains, separately, find a transformation between the two domains that optimizes a similarity functional between the functions. Our approach is based on optimal control with PDE (partial differential equation) constraints.(More)
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 averaged transformation is a diffeomorphism, nor get reasonable result when there is a local rotation. The goal of this paper is to propose a new approach to averaging diffeomorphisms(More)
where d is the distance between the center of masses of the two symmetrical halves of the CSAs. Critical to the use of this theorem is the determination of the exact center of mass of each CSA (6, 7). The authors did not specify how the center of mass was determined nor the accuracy, precision, and variation of this measurement in the bovine lens. There are(More)
Computational mathematics plays an increasingly important role in computational fluid dynamics (CFD). The aeronautics and aerospace research community is working on next generation of CFD capacity that is accurate, automatic, and fast. A key component of the next generation of CFD is a greatly enhanced capacity for mesh generation and adaptivity of the mesh(More)
In this paper, an interesting regions resizing method based on div-curl model is proposed, in which the image dimension is intact. Specifically, the Div-curl mesh model is induced to deform the mesh just by controlling curl and Jacobian determinant and can avoid the mesh folding problem. In order to alleviate mesh bending, the curl constraint equation is(More)
Several new techniques based on the deformation method are reported. These include techniques for domains with moving boundaries, boundary fitted triangulation with prescribed boundary nodes, adaptation of multi-block meshes and curvilinear triangular meshes. c © 2015 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of organizing(More)
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