Automated Vector Extraction from Airborne Laser Scan Data. This project considers the problem of automatically extracting and vectorising the outlines of objects from Airborne Laser Scanning (ALS) data. The industry partner, AAM GeoScan, is a leading user of ALS systems in Australia, and has a need to develop automated solutions to this problem. ALS data is typically a dense cloud of 3D point data which represents the local terrain, as well as any trees, buildings or vehicles which may be in t ....Automated Vector Extraction from Airborne Laser Scan Data. This project considers the problem of automatically extracting and vectorising the outlines of objects from Airborne Laser Scanning (ALS) data. The industry partner, AAM GeoScan, is a leading user of ALS systems in Australia, and has a need to develop automated solutions to this problem. ALS data is typically a dense cloud of 3D point data which represents the local terrain, as well as any trees, buildings or vehicles which may be in the field of view. Spatial data is a very important resource, widely used in many types of urban and rural planning operations. Planning software packages require vectorised descriptions of building outlines and other spatial data, however this is not presently available from raw ALS data. The project will investigate this problem and develop new and effective means for producing it automatically from raw ALS data. Expected outcomes include a successful research masters studentship, the development of novel solutions to the problem which are directly applicable to the industry partner's core business, peer reviewed publications, and an strengthened link between the universities and the industry partner.Read moreRead less
Geometric partial differential systems and their applications. This proposal addresses questions central to the understanding of nonlinear partial differential systems from classical, quantum field theory and liquid crystals. Applications to physical problems such as the Yang-Mills flow, Faddeev's model and liquid crystal systems are of great interest and importance in the broader scientific community. The project will yield internationally significant results in theoretical mathematics, with ....Geometric partial differential systems and their applications. This proposal addresses questions central to the understanding of nonlinear partial differential systems from classical, quantum field theory and liquid crystals. Applications to physical problems such as the Yang-Mills flow, Faddeev's model and liquid crystal systems are of great interest and importance in the broader scientific community. The project will yield internationally significant results in theoretical mathematics, with applications in physics and and other sciences. Specialist training will be provided for Australia's next generation of mathematicians. This project will enable Australian researchers to stay at the forefront of research in this area, strengthening links with a number of world-leading mathematicians.Read moreRead less
Geometric variational problems and nonlinear partial differential systems. We will investigate several important problems on non-linear partial differential systems, bridging analysis, differential geometry and mathematical physics. Harmonic maps are the prototype of maps minimizing the Dirichlet energy. The liquid crystal configuration generalizes the harmonic map with values into two dimensional spheres. The Yang-Mills equations originated from particle physics. We will make fundamental contri ....Geometric variational problems and nonlinear partial differential systems. We will investigate several important problems on non-linear partial differential systems, bridging analysis, differential geometry and mathematical physics. Harmonic maps are the prototype of maps minimizing the Dirichlet energy. The liquid crystal configuration generalizes the harmonic map with values into two dimensional spheres. The Yang-Mills equations originated from particle physics. We will make fundamental contributions to these topics: Regularity problem and energy minimality of weakly harmonic maps, Weak solutions of the liquid crystal equilibrium system, Yang-Mills heat flow and singular Yang-Mills connections.
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