Preliminary investigation of the frequency response and distortion properties of nonlinear image processing algorithms

Abstract

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.