PDE-GIR · PDE-based geometric modelling, image processing, and shape reconstruction

PDE-based geometric modelling, image processing, and shape reconstruction

Geometric modelling, image processing, and shape reconstruction have huge applications in various sectors and greatly impact on EU’s economy, human health, security, entertainment and others. Existing problems such as big data and heavy manual operations in geometric modelling, incapacity in image processing in continuous domains, and lack of continuity and differentiability in shape reconstruction seriously affect quality, efficiency and capacity. Partial differential equation (PDE) based techniques provide effective solutions to these problems. However, current PDE-based techniques face the following problems. The existing research on PDE-based geometric modeling only develops analytical solutions of PDEs under boundary constraints of 2-sided patches. Such 2-sided patches are incapable in creating many 3D models with branch structures that can only be tackled by 3- and 4-sided patches. Since the analytical solutions for 3- and 4-sided PDE patches are difficult to obtain, numerical methods have to be applied. It causes three problems: big data increasing storage and network transmission cost, heavy computational burden leading to low efficiency, and discrete nodes inapplicable to curved boundaries and good continuity requirement at boundaries. Variational image-processing models, involving PDEs, energy optimization, regularization, level set functions, and numerical algorithms, offer high-quality processing capabilities for imaging. They have been widely applied in image denoising, image deblurring, image segmentation, image reconstruction, restoration of mixed noise types, and three-dimensional surface restoration. However, existing PDE-based image processing techniques suffer from expensive cost and local minimization. Shape reconstruction based on polygon, CSG and NURBS involves big data which cause many problems such as heavy geometry processing, high data storage cost, and slow transmission over computer networks. PDE-based shape reconstruction has not been developed. The PDE-GIR project aims to tackle these problems. Its objectives are: 1) developing 3- and 4-sided PDE patches and three PDE-based geometric modelling techniques, 2) developing variational models and fast algorithms for depth information from images and surface reconstruction from point clouds, 3) developing new static and dynamic shape reconstruction techniques from 3- and 4-sided PDE patches, variational models, and fast algorithms, and 4) organizing staff exchanges, research collaborations, knowledge transfer, dissemination and application exploitation of the new techniques.

Data: CORDIS, © European Union