Improved Description of Smoothly Varying Regions
It was shown previously that large errors between the original image and its
approximation occur in the vicinity of edges and in the regions which have
smoothly varying intensity. Because of visual masking, substantial errors
can be tolerated around the edges before they reach the threshold of
perception. In contrast, errors in the approximation corresponding to the
smoothly varying intensity (or flat) regions are readily perceptible.
In order to reduce the error in the approximation corresponding to the
smoothly varying regions, we would like to have a more accurate description
of these regions. The interiors of such regions, which previously were
approximated by the mean values, will now be approximated in the
least square sense by linear polynomial intensity functions.
The improved description of the smoothly varying regions involves
partitioning the image approximation into square windows, labeling those
windows which lay completely within the smoothly varying regions, and
approximating each labeled window with a linear polynomial intensity
function in the least square sense. Each labeled window is described by
a set of coefficients B0,B1,B2 (describing a linear polynomial). The average
of the window coefficients which lay inside a region is used to approximate
the intensity function of that region. Hence, each smoothly varying region
requires three coefficients for its description.