| Edges are important features in images. They mark the boundaries of objects, and they are used by the human perceptual system. Unfortunately, traditional image processing methods for removing noise from images or for deblurring images often have trouble with edges. Smoothing methods can eliminate noise, but they also smooth out edges; some restoration techniques remove blur, but introduce artifacts at edges.; Total variation minimization has edge preserving and enhancing properties, which makes it useful for image processing. We illustrate the edge enhancing properties of total variation minimization in a discrete setting by giving exact solutions for piecewise constant images in the presence of noise. We present a conjugate gradient method for fast solution of total variation problems.; Total variation minimization does an excellent job of restoring images that have been blurred and corrupted by noise. We make no assumptions about the statistics of the noise, nor do we require that the blur operator be spatially invariant.; We present Image Simplification, a new formulation and algorithm for image segmentation. Total variation minimization is applied to an image, followed by edge detection to complete the segmentation. We find that our image segmentation approach yields good results when applied to the segmentation of pulmonary nodules. |
