  Most image smoothing filters in the literature assume a piecewise constant
model of smoothed output images. However, the piecewise constant model
assumption can cause artifacts such as gradient reversals in applications such
as image detail enhancement, HDR tone mapping, etc. In these applications, a
piecewise linear model assumption is more preferred. In this paper, we propose
a simple yet very effective framework to smooth images of piecewise linear
model assumption using classical filters with the piecewise constant model
assumption. Our method is capable of handling with gradient reversal artifacts
caused by the piecewise constant model assumption. In addition, our method can
further help accelerated methods, which need to quantize image intensity values
into different bins, to achieve similar results that need a large number of
bins using a much smaller number of bins. This can greatly reduce the
computational cost. We apply our method to various classical filters with the
piecewise constant model assumption. Experimental results of several
applications show the effectiveness of the proposed method.
