The laplacian operator applied to the coordinates of a manifold provides the mean curvature vector. Manipulating the metric of the manifold or interpreting its coordinates in various ways provide useful tools for shape and image processing and representation. We will review some of these tools focusing on scale invariant geometry, curvature flow with respect to an embedding of the image manifold in a high dimensional space, and object segmentation by active contours defined via the shape laplacian operator. Such generalizations of the curvature vector and its numerical approximation as part of an image flow or triangulated shape representation, demonstrate the omnipresence of this operator and its usefulness in imaging sciences.
Keywords: Image denoising, scale invariant, active contours, segmentation
@article{ACIRM_2013__3_1_131_0,
author = {Yonathan Aflalo and Anastasia Dubrovina and Ron Kimmel and Aaron Wetzler},
title = {Curvature in image and shape processing},
journal = {Actes des rencontres du CIRM},
pages = {131--139},
publisher = {CIRM},
volume = {3},
number = {1},
year = {2013},
doi = {10.5802/acirm.62},
zbl = {06938610},
language = {en},
url = {https://acirm.centre-mersenne.org/articles/10.5802/acirm.62/}
}
TY - JOUR AU - Yonathan Aflalo AU - Anastasia Dubrovina AU - Ron Kimmel AU - Aaron Wetzler TI - Curvature in image and shape processing JO - Actes des rencontres du CIRM PY - 2013 SP - 131 EP - 139 VL - 3 IS - 1 PB - CIRM UR - https://acirm.centre-mersenne.org/articles/10.5802/acirm.62/ DO - 10.5802/acirm.62 LA - en ID - ACIRM_2013__3_1_131_0 ER -
%0 Journal Article %A Yonathan Aflalo %A Anastasia Dubrovina %A Ron Kimmel %A Aaron Wetzler %T Curvature in image and shape processing %J Actes des rencontres du CIRM %D 2013 %P 131-139 %V 3 %N 1 %I CIRM %U https://acirm.centre-mersenne.org/articles/10.5802/acirm.62/ %R 10.5802/acirm.62 %G en %F ACIRM_2013__3_1_131_0
Yonathan Aflalo; Anastasia Dubrovina; Ron Kimmel; Aaron Wetzler. Curvature in image and shape processing. Actes des rencontres du CIRM, Volume 3 (2013) no. 1, pp. 131-139. doi : 10.5802/acirm.62. https://acirm.centre-mersenne.org/articles/10.5802/acirm.62/
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