Session Slot: 2:00- 3:50 Tuesday
Estimated Audience Size:
AudioVisual Request: Two Overheads
Session Title: Special Invited Papers
Theme Session: No
Applied Session: Yes
Session Organizer: Lindsay, Bruce Penn State University
Address: 422 Thomas Building, Department of Statistics, University Park, PA 16802
Phone: (814) 865-1220
Fax: (814) 863-7114
Session Timing: 110 minutes total (Sorry about format):
Opening Remarks by Chair - 5 First Speaker -45 minutes Second Speaker - 45 Floor Discusion - 10 minutes
Session Chair: Li, Bing The Pennsylvania State University
Address: Department of Statistics The Pennsylvania State University 326 Joab Thomas Building University Park, PA 16802, USA
Phone: (814) 865 1952
Fax: (814) 863 7114
1. Shapes, Directions and Images
Mardia, Kanti V., University of Leeds
Address: Department of Statistics University of Leeds Leeds, LS2 9JT, England
Phone: 0113 233 5100
Fax: 0113 233 5102
Abstract: In general, the methods of multivariate analysis break down for data in non-Euclidean spaces. Directions and shapes are two prime examples. A shape is described by the information in a set of landmarks which is invariant under the transformations of location, rotation and scaling, and shape analysis concentrates on methods which respect these invariances and preserve geometrical properties of object. We deal with statistical methodolgy to measure, describe and compare the shapes of objects; of particular importance is the need to visualize shape variability. Considerations are similar to the well established topic of directional data analysis but somewhat more complex.
This talk coincides with the 80th anniversary of the famous classic book "Growth and Form" of D'Arcy Thompson which raised basic biological questions about shape analysis. We describe the latest developments in shape space, Procrustes methods, tangent approximations, shape distributions, symmetry in shape, image warping and averaging, and object recognition. Practical examples will be given from various fields including medical imaging, face analysis and biology.
2. Statistical Analysis of Shape for Pattern Differentiation and Recognition
Rao, C. R., Pennsylvania State University
Address: 326 Joab Thomas Building, University Park, PA 16802
Abstract: The shape of an object, data set or image can be defined as the total of all information that is invariant under translations, rotations, and isotropic rescaling. Thus two objects are said to have the same shape if one object can be exactly fitted into the other by the above transformations.
The last decade has seen a considerable growth in interest in the statistical theory of shape. There are different groups of research workers headed by Bookstein, Kendall and Mardia who advocate different methods of shape analysis. An attempt will be made to prove a unified treatment by defining shape measurements which are independent of scale, translation and rotation, and developing methods of statistical inference based on them. If an object is characterized by certain landmarks, then Euclidean distances between landmarks as suggested by Lele, or the angles of triangles obtained by suitable triangulation of landmarks consitute shape measurements on which parametric or nonparametric statistical methods could be applied. If landmarks are not available, geometrical properties like curvature of the boundary of objects provide shape measurements for which appropriate statistical methods could be developed.
A number of examples with live data will be presented illustrating the use of shape measurements in pattern recognition and tests of hypotheses on shape differences.
List of speakers who are nonmembers: None