Locally monotonic models for image and video processing

Definitions of locally monotonic images are introduced. The model definitions are complemented with algorithms that compute locally monotonic versions of a given image or video frame input. The property of local monotonicity provides a useful vehicle for image smoothing and denoising. Local monotonicity is also useful for scale space generation, wherein the degree of local monotonicity is the scale parameter. Currently, the property of local monotonicity is well defined for the 1-D case, but is not well defined for images or video. In this paper, models for multidimensional local monotonicity that extend the 1-D definition are rendered. Regression-based and diffusion-based processing methods are prescribed that yield meaningful locally monotonic images. The definitions and associated algorithms are applicable to image enhancement and a variety of multiscale tasks such as image segmentation and video coding.