Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1202.94019
Calder, J.; Mansouri, A.; Yezzi, A.
Image sharpening via Sobolev gradient flows. (English)
[J] SIAM J. Imaging Sci. 3, No. 4, 981-1014, electronic only (2010). ISSN 1936-4954/e

Summary: Motivated by some recent work in active contour applications, we study the use of Sobolev gradients for PDE-based image diffusion and sharpening. We begin by studying, for the case of isotropic diffusion, the gradient descent/ascent equation obtained by modifying the usual metric on the space of images, which is the $L^2$ metric, to a Sobolev metric. We present existence and uniqueness results for the Sobolev isotropic diffusion, derive a number of maximum principles, and show that the differential equations are stable and well-posed both in the forward and backward directions. This allows us to apply the Sobolev flow in the backward direction for sharpening. Favorable comparisons to the well-known shock filter for sharpening are demonstrated. Finally, we continue to exploit this same well-posed behavior both forward and backward in order to formulate new constrained gradient flows on higher order energy functionals which preserve the first order energy of the original image for interesting combined smoothing and sharpening effects.

MSC 2000:: *94A08 Image processing
35A01
35A02
35A35 Theoretical approximation to solutions of PDE

Keywords: image diffusion; partial differential equations; gradient descent; gradient ascent; Sobolev spaces; image sharpening

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]