 
Summary: II. 1d elastic models curve
detection
II.1 Introduction
ffl Many imaging problems involve detecting the closed boundary of an object:
tumor in xray or MRI, heart ventricle in ultrasound.
ffl Difficult to obtain through standard bottom up edge detection and contour
tracing. See e.g. edge map of left heart ventricle in figure II.1.
ffl Introduce global constraints: `ideal' contour closed and continuous.
ffl Place a closed contour on image surface and let it deform continuously to adjust
to the shape of the contour of the desired object.
ffl Prior knowledge on shape represented in initial contour, and constraints on
deformations.
ffl Grenander (1970), Grenander et al. (1991), Kass et al. (1987).
II.2 Variational formulation
Most of the literature on these models in not formulated from a statistical point of
view. Moreover the corresponding statistical assumptions are rather questionable.
We therefore start with a nonstatistical formulation.
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II. 1D ELASTIC MODELS CURVE DETECTION 11
