Otsikko

1
Robust Curve Reconstruction with k-Order a-Shapes
Dmitry Krasnoshchekov (Institute for Dynamics of
the Geospheres) Valentin Polishchuk
(Helsinki Institute for Information Technology)
Noisy sample of seismic coda
What is the shape of the underlying curve?
Edelsbrunner, Kirkpatrick,Seidel83 a-shape
roll radius-a ball over the points keep the
ball empty
New notion
k-order a-shape roll radius-a ball over the
points keep k points inside the ball
Inner shape k controls how deep to dig into
the points
k 0
Outer shape
Sensitive to outliers
k 3
k 5
Implementation Arto Vihavainen (Computer
Science, University of Helsinki) Java applet
available at http//www.cs.helsinki.fi/group/comp
geom/kapplet/
Ignores k outliers
Apply to the data
Use noise to train the ball choose a and k
Drag radius-a ballskeeping k points inside
a std(noise)
k mean of points inside dragged balls
of points inside balls
drag
a, k
the balls shave off the noise
Final result
Time
k-hull
a-k-hull
Ongoing work Link between shape
modeling and statistics Generalizing
statistical depth a-k-hull,
a-k-depth contour, etc.
oversmoothing
clusters discovered
k 2
k 2
(a 8)
a lt 8
Institute for Dynamics of the Geospheres belongs
to Russian Academy of Sciences.