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TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20320314T030000 RDATE:20321107T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20330313T030000 RDATE:20331106T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20340312T030000 RDATE:20341105T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20350311T030000 RDATE:20351104T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20360309T030000 RDATE:20361102T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20370308T030000 RDATE:20371101T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT END:VTIMEZONE BEGIN:VEVENT UID:7eb2c98a8358a27245483c41d8e278c1 CATEGORIES:Human and computer vision series:Spring 2008 CREATED:20151203T141541 SUMMARY:Learning on Riemannian Manifolds for Interpretation of Visual Environments LOCATION:Rutgers University\, Computer Science & ECE Department\, DESCRIPTION:
Classical machine learning techniques provide effective methods for anal
yzing data when
the parameters of the underlying process lie in a Eucli
dean space. However, various
parameter spaces commonly occurring in com
puter vision problems violate this
assumption. We derive novel learning
methods for parameter spaces having Riemannian
manifold structure and
apply to three important computer vision problems: motion
estimation, o
bject detection, and tracking.
We start with a modified version of t
he mean shift algorithm which can find the modes of
a distribution havi
ng matrix Lie group structure. We demonstrate the superior
performance
of the proposed algorithm on multiple 3D motion estimation problem where the points are sampled rigid motion matrices from noisy point corresponde
nces. The
algorithm successfully finds the number of motions in the sce
ne and the corresponding
motion parameters in the presence of large amo
unt of outliers.
Next we present a new algorithm to detect humans in
still images utilizing covariance
matrices as object descriptors. The
space of d-dimensional nonsingular covariance
matrices can be represent
ed as a connected Riemannian manifold. A novel classification
algorithm
is derived by incorporating the a priori information about the geometry of
the
space. The algorithm was tested on INRIA human database where supe
rior detection
rates are observed over the previous approaches.
Finally we describe a novel learning based tracking model combined with obj
ect
detection. The motion model is learned on the Lie algebra of the tr
ansformation group
and the formulation minimizes a first order approxim
ation to the sum of squared geodesic
error. The motion estimator is the
n integrated to an existing pose dependent object
detector and a pose i
nvariant object detection algorithm is developed. The proposed
model ca
n accurately detect objects in various poses and the size of the search spa
ce is
only a fraction compared to the existing object detection methods
.
�
Related Works:� http://www.caip.rutgers.edu/riul/research.htm l
�
CONTACT:Oncel Tuzel X-EXTRAINFO:Oncel Tuzel (http://www.caip.rutgers.edu/~otuzel/) DTSTAMP:20240329T073307 DTSTART;TZID=America/New_York:20080211T130000 DTEND;TZID=America/New_York:20080211T140000 SEQUENCE:0 TRANSP:OPAQUE END:VEVENT END:VCALENDAR