[Colloquium] Reminder: Talk at TTI-C Today 12:00pm -Miguel Carreira-Perpinan

[Katherine Cumming]

TOYOTA TECHNOLOGICAL INSTITUTE TALK 

Speaker: Miguel Carreira-Perpinan ,  CSEE, OGI, Oregon Health & Science
University

Speaker's homepage: http://www.cse.ogi.edu/~miguel/
Time:  12:00pm 
Date:  July 5, 2006
Place:   TTI-C Conference Room
(Refreshments provided) 
Title: Gaussian Mean-Shift Algorithms
Abstract: 
 
I will describe theoretical and practical results of mean-shift, an
algorithm for finding the modes of a kernel density estimate (eg a Gaussian
mixture). This algorithm, based on ideas by Fukunaga & Hostetler (1975), has
attracted considerable attention in recent years in computer vision
applications such as image segmentation and tracking. In the first part of
the talk I'll show that mean-shift is an EM algorithm for the Gaussian
kernel and a generalised EM algorithm for other kernels. Gaussian mean-shift
(GMS) converges from any starting point and its convergence rate is linear
in general (superlinear or sublinear in particular cases), thus very slow. I
will also show that the GMS convergence domains (which determine the
clusters) can be fractal. I will then give several acceleration strategies
based on spatial discretisation, sparse EM, and Newton's method, which can
speed up GMS by two orders of magnitude with minimal alteration to the
clustering. In the second part of the talk I'll focus on the original (and
still neglected) version of Gaussian mean-shift that Fukunaga & Hostetler
really proposed, Gaussian blurring mean-shift (GBMS). In GBMS the data set
iteratively shrinks under the application of GMS steps. I'll show how to
stop the iteration to achieve good clusterings; prove that its convergence
rate for Gaussian clusters is cubic; give a relation with spectral
clustering; and give an accelerated (but otherwise equivalent) version of
GBMS. The resulting GBMS algorithm is much faster than GMS while achieving
results of similar quality.  All algorithms will be illustrated with image
segmentation results. 
If you have questions, or would like to meet the speaker, please contact
Katherine at 4-1994 or kcumming at tti-c.org. For information on future TTI-C
talks or events, please go to the TTI-C Events
<http://ttic.uchicago.edu/events/events_dyn.php>  page. 
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