Visual reconstruction
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
A globally and quadratically convergent affine scaling method for linear ℓ1 problems
Mathematical Programming: Series A and B
Variational methods in image segmentation
Variational methods in image segmentation
Use of the Hough transformation to detect lines and curves in pictures
Communications of the ACM
Graph theory: An algorithmic approach (Computer science and applied mathematics)
Graph theory: An algorithmic approach (Computer science and applied mathematics)
A computational algorithm for minimizing total variation in image restoration
IEEE Transactions on Image Processing
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Total variation minimization (in the 1-norm) has edge preserving and enhancing properties which make it suitable for image segmentation. We present Image Simplification, a new formulation and algorithm for image segmentation. We illustrate the edge enhancing properties of 1-norm total variation minimization in a discrete setting by giving exact solutions to the problem for piecewise constant functions in the presence of noise. In this case, edges can be exactly recovered if the noise is sufficiently small. After optimization, segmentation is completed using edge detection. We find that our image segmentation approach yields good results when applied to the segmentation of pulmonary nodules.