Summary: In Proceedings, European Conference on Computer Vision, May 2002.
Volterra Filtering of Noisy Images of Curves
Robotics Institute, Carnegie Mellon University, Pittsburgh, PA 15213, USA
Abstract. How should one filter very noisy images of curves? While
blurring with a Gaussian reduces noise, it also reduces contour contrast.
Both non-homogeneous and anisotropic diffusion smooth images while
preserving contours, but these methods assume a single local orientation
and therefore they can merge or distort nearby or crossing contours. To
avoid these difficulties, we view curve enhancement as a statistical esti-
mation problem in the three-dimensional (x, y, )-space of positions and
directions, where our prior is a probabilistic model of an ideal edge/line
map known as the curve indicator random field (cirf). Technically, this
random field is a superposition of local times of Markov processes that
model the individual curves; intuitively, it is an idealized artist's sketch,
where the value of the field is the amount of ink deposited by the artist's
pen. After reviewing the cirf framework and our earlier formulas for the
cirf cumulants, we compute the minimum mean squared error (mmse)
estimate of the cirf embedded in large amounts of Gaussian white noise.
The derivation involves a perturbation expansion in an infinite noise