TY - JOUR
T1 - Diffusions and confusions in signal and image processing
AU - Sochen, N.
AU - Kimmel, R.
AU - Bruckstein, A. M.
PY - 2001/5
Y1 - 2001/5
N2 - In this paper we link, through simple examples, between three basic approaches for signal and image denoising and segmentation: (1) PDE axiomatics, (2) energy minimization and (3) adaptive filtering. We show the relation between PDE's that are derived from a master energy functional, i.e. the Polyakov harmonic action, and non-linear filters of robust statistics. This relation gives a simple and intuitive way of understanding geometric differential filters like the Beltrami flow. The relation between PDE's and filters is mediated through the short time kernel.
AB - In this paper we link, through simple examples, between three basic approaches for signal and image denoising and segmentation: (1) PDE axiomatics, (2) energy minimization and (3) adaptive filtering. We show the relation between PDE's that are derived from a master energy functional, i.e. the Polyakov harmonic action, and non-linear filters of robust statistics. This relation gives a simple and intuitive way of understanding geometric differential filters like the Beltrami flow. The relation between PDE's and filters is mediated through the short time kernel.
KW - Anisotropic diffusion
KW - Geometric filtering
KW - Selective smoothing
UR - http://www.scopus.com/inward/record.url?scp=0035328924&partnerID=8YFLogxK
U2 - 10.1023/A:1011277827470
DO - 10.1023/A:1011277827470
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:0035328924
SN - 0924-9907
VL - 14
SP - 195
EP - 209
JO - Journal of Mathematical Imaging and Vision
JF - Journal of Mathematical Imaging and Vision
IS - 3
ER -