A PDE technique for generating locally monotonic images

Local monotonicity provides a meaningful descriptor of smoothness for digital signals. Locally monotonic (LOMO) signals are scaleable by feature size, include both step and ramp edges, and are devoid of outliers due to noise. This paper contributes a partial differential equation (PDE) method for producing locally monotonic (LOMO) signals. Three different approaches for extending the LOMO diffusion technique to images are explored. Results demonstrate that the 2-D LOMO diffusion procedure affords effective image enhancement and denoising. In contrast to other anisotropic diffusion schemes, LOMO diffusion converges to a non-trivial signal, does not require ad hoc thresholds, and does not utilize additional filtering to remove impulses.