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.