% formatted on 970304 by morris
\documentstyle{article}
\setcounter{page}{51}
\textheight 9.5in
\textwidth 5.75in
\voffset -1in
\hoffset -0.55in
%\documentstyle{llncs}
\begin{document}
\title{Adaptive Image Smoothing Respecting Feature Directions}
\author{Sifen Zhong \\
Department of Civil Engineering and Operations Research\\
Princeton University \\
Princeton, NJ 08544, USA}
\date{}
\maketitle
A goal of adaptive image smoothing is to remove image noise and any 
irregular components while preserving image features such as edges, 
lines and textures. One of its principles is to apply minimal smoothing
in the direction across the image features and maximal smoothing in the
direction along the image features.  This principle is the motivation of
the Anisotropic Diffusion scheme and other ``PDE approaches to image
processing''. \\

We show however that, because the image feature directions are miscalculated
in the early PDE approaches, the anisotropic principle is actually violated.
The method used in the PDE approaches for extracting image feature directions,
the gradient method, is too local to capture the actual image feature 
directions, and yield disastrous results on these image features.\\

Accurate extraction of the feature directions is essential to adaptive 
smoothing and other image processing tasks.  We have developed two new methods,
the Hessian method and the Gabor method, to achieve higher accuracy.  The
Hessian method represents an attempt at using higher order differentiation, 
and the Gabor method represents an attempt at using local spectrum.  Both
higher order differentiation and local spectrum are effective for capturing
oscillations.  The Hessian method is more computationally efficient, and the
Gabor method is more general.  Experimental results on natural images show
that adaptive smoothing using our new methods can preserve image features
which are damaged by PDE approaches.\\

\end{document}
