ABHYANKAR 82nd BIRTHDAY CONFERENCE 

SPEAKER: Karthik Ramani (Purdue, ME)
         Donald W.Feddersen Professor of Mechanical Engineering
         School of Electrical and Computer Engineering (by Courtesy)

TITLE: Geometry inspired research in shape understanding 

ABSTRACT: The rapid growth of computational capabilities, low cost storage, 
and new means of creating data such as CAD/CAM programs, digital cameras, laser
scanners, computerized tomography, microscopy, 3D depth sensors and others
is continuing to result in a vast explosion of visual data. Much of this
digital data now is transforming to 3D. However, 3D shape data understanding
has not been explored as much needing approaches that lend themselves to
unstructured data spaces. Our initial work in geometric shape understanding
was developed in order to empower engineers and scientists to transform
their way of dealing with data in areas including design and manufacturing
and protein network analysis, and has had impact in several scientific areas
including geometric modeling and computer vision.

New distances for shape operations developed in our research will be
described that include a 2.5 D spherical harmonics, diffusion distances and
heat mapping, inner distance, temperature distribution descriptor, and
bi-harmonic kernel density function. These descriptors and kernels have been
used for several shape based operations including shape searching,
clustering of proteins, sketching constraint solving, and perceptive
segmentation of shapes. Our more recent work in natural user interfaces for
shape creation merges several perspectives from geometric modeling, to
machine learning and human computer interaction.

In summary, the common thread in all this research and resulting new
applications is geometric shape understanding using algorithmic approaches
driven by geometry.