The investigator and his colleagues study the problem of extracting features of images and their properties via scales and local scales using the classical theory of function spaces and partial differential equations. They use the knowledge of scales and local scales in images to obtain an efficient method for image decompositions and multiscale representations, which are image dependent. Finally, they extend the theory of scales and local scales to higher dimensional data (graphs and manifolds), and to find efficient computational methods and algorithms to solve these problems.
Reducing a complex data to simpler representations that can be more easily analyzed is an important task in mathematics and information science. The study of scales and local scales provides a tool for doing this task. In particular, it provides a tool for organizing and clustering the internal multiscale structures of the data. Applications include medical imaging, hyperspectral imaging, satellite imaging, material science, terrain data analysis, and dimension reduction in higher dimensional data.
