Ricci flow for image processing

Author

Sonn, Ezri ; Saucan, Emil ; Appelboim, Eli ; Zeevi, Yehoshua Y.

Author_Institution

Ollendorff Center for Vision & Image Sci., Technion - Israel Inst. of Technol., Haifa, Israel

fYear

2014

fDate

3-5 Dec. 2014

Firstpage

1

Lastpage

5

Abstract

A new discrete model of the Ricci flow for images is presented, using a purely combinatorial method for calculating the Ricci curvature, based on R. Forman´s work on generalized Laplacians for cell complexes. We describe the discrete Ricci curvature operator, and the implementation of the Ricci flow, and then proceed to show the results of applying the flow to both synthetic and real images. Finally, we implement the discrete Ricci flow in some applications of image processing and vision, such as high dynamic range (HDR) imaging, forward-and-backward (FAB) Ricci flow, and change detection in aerial images.

Keywords

combinatorial mathematics; computational geometry; computer graphics; image processing; FAB Ricci flow; HDR imaging; aerial image change detection; cell complexes; combinatorial method; discrete Ricci curvature operator; discrete Ricci flow; forward-and-backward flow; generalized Laplacians; high dynamic range; image processing; Image edge detection; Image reconstruction; Manifolds; Measurement; Numerical models; Surface treatment;

fLanguage

English

Publisher

ieee

Conference_Titel

Electrical & Electronics Engineers in Israel (IEEEI), 2014 IEEE 28th Convention of

Conference_Location

Eilat

Print_ISBN

978-1-4799-5987-7

Type

conf

DOI

10.1109/EEEI.2014.7005808

Filename

7005808