Tensor Modeling and Visualization of Three-dimensional Geospatial Datasets

Prof. Jaya

" 1. We identify scientific and engineering, with a focus on geospatial and earth observation, datasets with inherent complexity, e.g. LiDAR point clouds with position coordinates but of large size as well as large variability owing to outside environment; and ocean observation dataset with multiple variables (e.g. temperature, salinity, chlorophyll, etc.)

2. We generate second-order positive semi-definite tensor fields to analyze the aforementioned complex datasets.

• For LiDAR point clouds, we find local geometric descriptors which we have proved is a positive semidefinite second-order tensor field.
• For ocean dataset, we compute covariance tensor as well as structure tensors (using differentials), which again are known to be positive semi-definite second order tensor field.

3. We further use the tensor fields for further data processing.

• For LiDAR point clouds, we use these tensor fields for comparing between two different fields used as local geometric descriptors, and thus improving the local geometric descriptor for the purpose of geometric reconstruction. We select one of these local geometric descriptors, for the data processing workflow for geometric reconstruction. We have focused on simple gabled roof, with two surface panels. We have used the technique of finding salient line feature extraction from the roofs to reconstruct the building roofs. We extract the roof boundaries, this way, and then validate them using ground truth based on roof geometry ground truth.
• For ocean observation data, we use the structure tensor field for visualization. We study the topological graph generated in the structure tensor field.
• For ocean observation data, we use the covariance tensor field. We study the projection of the covariance tensor field onto the spatial coordinate vector space. "