Assessment of the resolution properties of nonlinear imaging systems is a useful but challenging task. While the
modulation transfer function (MTF) fully describes contrast resolution as a function of spatial frequency for linear
systems, an equivalent metric does not exist for systems with significant nonlinearity. Therefore, this preliminary
investigation attempts to classify and quantify the amount of scaling and distortion imposed on a given image signal as
the result of a nonlinear process (nonlinear image processing algorithm).
As a proof-of-concept, a median filter is assessed in terms of its principle frequency response (PFR) and distortion
response (DR) functions. These metrics are derived in frequency space using a sinusoidal basis function, and it is shown
that, for a narrow-band sinusoidal input signal, the scaling and distortion properties of the nonlinear filter are described
exactly by PFR and DR, respectively. The use of matched sinusoidal basis and input functions accurately reveals the
frequency response to long linear structures of different scale. However, when more complex (multi-band) input signals
are considered, PFR and DR fail to adequately characterize the frequency response due to nonlinear interaction effects
between different frequency components during processing.
Overall, the results reveal the context-dependent nature of nonlinear image processing algorithm performance, and they
emphasize the importance of the basis function choice in algorithm assessment. In the future, more complex forms of
nonlinear systems analysis may be necessary to fully characterize the frequency response properties of nonlinear
algorithms in a context-dependent manner.