WP1 has proposed a general mathematical model, constructed a unified function for 2-, 3- and 4-sided patches, obtained an approximate analytical solution of the mathematical model, used the constructed 2-, 3-, and 4-sided PDE patches to develop the three new modelling techniques of PDE patch-based geometric modelling, PDE wireframe-based geometric modelling, and PDE primitive-based geometric modelling, investigated the applications of PDE-based geometric modelling techniques in character modelling , skin deformation, facial blendshapes, optimal conversion of PDE surface-represented train heads into the NURBS representation, multi-objective aerodynamic optimization of high-speed train heads, styling design of automobiles, and developed machine learning-based techniques to solve PDEs for surface creation. The research into WP1 has led to 28 scientific publications.
WP2 has proposed a convexified global variational model for depth estimation from stereo images, investigated a fast numerical algorithm based on the augmented Lagrangian method, examined a fast direct solver for this PDE based on the fast Fourier transform and an iterative solver using the conjugate gradient iteration, for the Poisson equation in a narrow band about the solution. It has also solved the problem of surface reconstruction from point clouds by constructing the unsigned distance function and an inner product function to propose a variational model for surface construction from point clouds, implemented two software programs respectively for the two variational models and an integrated software suite in MATLAB, documented the user guide for the software, and applied the variational models, algorithms, and computer programs in the services of IDF. It also investigated machine learning-based image processing. The research into WP2 has led to 22 scientific publications.
WP3 has analyzed the methods developed in WP1 and WP2, proposed a theoretical framework of PDE-based shape reconstruction, investigated the accurate closed form solution of the theoretical framework to exactly satisfy the constraints on four boundaries of a PDE surface patch, applied the closed form solution to develop new shape reconstruction techniques for static surface and object/scene reconstruction. It has also proposed a dynamic partial differential equation, investigated its analytical solution, and used the analytical solution to develop new time-dependent shape reconstruction techniques for dynamic surface and object/scene reconstruction. In addition, it has also developed new techniques integrating artificial intelligence methods for shape reconstruction, and applied them in real-world problems, such as in the fields of entertainment (automatic skeletal motion learning routines for computer animation, virtual reality, and video games), swarm robotics (including the physical assembly of real robotic units by hardware, as well as new software libraries for programming and simulation), and in medical fields (image segmentation of medical images, e.g. human brain MRI, digital images of melanoma and other skin lesions). As a result of this work, WP3 has published 88 scientific papers.
WP4 has organized the PDE-GIR consortium to successfully complete all planned PDE-GIR secondments and project research tasks, achieve knowledge transfer, ESRs’ trainings, partners’ collaborations, publish 138 papers, disseminate research output at international conferences, organize 5 PDE-GIR workshops and 3 special issues, and exploit the applications of the developed PDE-GIR techniques in industrial and academic sectors.
During the implementation, the PDE-GIR project has always complied with the “ethics requirements” set out in WP5.
