by
Ofer Levi, Ben-Gurion University of Negev, Israel
→
Europe/Berlin
Bldg. 25b, Rm. 456
Bldg. 25b, Rm. 456
Description
Three-dimensional volumetric data are becoming increasingly available in a
wide range of scientific and technical disciplines. With the right tools, we
can expect such data to yield valuable insights about many important systems
in our three-dimensional world. This work presents new multi-scale geometric
tools for both analysis and synthesis of 3D data which may be scattered or
observed in voxel arrays, which are typically very noisy, and which may
contain one-dimensional structures such as line segments and filaments or
two-dimensional structures such as plane patches and smooth manifolds. These
tools mainly rely on two kinds of transforms: The 3D Beamlet Transform
offering the collection of line integrals along a strategic multi-scale set
of line segments (Beamlets) running through the image at different
orientations, positions, and lengths, and the 3D Planelet Transform offering
the collection of plane integrals over a strategic multi-scale set of plane
patches (Planelets). Fast advanced fft based algorithms for line and plan
integration make it possible to analyze even moderately large 3D digital
images.
Several basic applications for these tools will be presented, for example,
in finding faint structures buried in noisy data as well as segmentation of
3D smooth objects with extremely low SNR.
