Spatial Domain Filter Design
                Torsten Moeller
                Ohio State University
ABSTRACT

In the past  years the    importance  of 3D volumetric datasets    has
increased steadily.   Through higher resolution acquisition devices we
are confronted  with larger data  sets  then ever before.  In order to
accurately manipulate and display these data sets on a computer screen
in real time, it is essential to reconstruct the underlying continuous
function and its  derivatives.  Choosing appropriate interpolation and
derivative filters   is  essential    in  obtaining  highly   accurate
renderings quickly.  Choosing filters by their accuracy and smoothness
behavior  is important  not only  for volume   rendering but  for many
applications. Most current filter design techniques, that are based on
frequency domain methods, do not provide such local controls. 

The  result  of  my   research  proposes  a new   methodology for  the
evaluation   and  design   of   reconstruction  filters   for  general
applications. This new method is stands in contrast to current methods
operating in  the frequency domain in  that it allows specification of
purely spatial domain parameters  including accuracy and smoothness of
reconstructed functions.  Nevertheless,  the  proposed design criteria
can also be translated  to equivalent frequency domain criteria, which
allow for an  assessment of global  features of the reconstruction  as
well. The theoretical contribution of our work is  an extension of the
fundamental  theory of signal  reconstruction  and interpolation.  Its
practical value is the establishment of  a tool box that practitioners
can use to easily and reliably design new interpolation and derivative
filters, adapted  to their  own   application needs.  In   the  design
process, users specify  very intuitive criteria,  such as accuracy and
smoothness, and   are  not constrained to  indirect   frequency domain
specifications.  We describe our method  and demonstrate its use using
examples from volume rendering and pattern matching. 

In the next  few years we would like  to explore the applicability  of
our methods in  different applications.   Smoothness and accuracy  are
sometimes  not the only   requirements  of a function  reconstruction.
E.g. in Computational Science monotony-preserving reconstruction plays
an important role.   Integrating other such  features into  the design
process is our goal. 


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