  In this paper, we propose an active contour model with a local variance force
(LVF) term that can be applied to multi-phase image segmentation problems. With
the LVF, the proposed model is very effective in the segmentation of images
with noise. To solve this model efficiently, we represent the regularization
term by characteristic functions and then design a minimization algorithm based
on a modification of the iterative convolution-thresholding method (ICTM),
namely ICTM-LVF. This minimization algorithm enjoys the energy-decaying
property under some conditions and has highly efficient performance in the
segmentation. To overcome the initialization issue of active contour models, we
generalize the inhomogeneous graph Laplacian initialization method (IGLIM) to
the multi-phase case and then apply it to give the initial contour of the
ICTM-LVF solver. Numerical experiments are conducted on synthetic images and
real images to demonstrate the capability of our initialization method, and the
effectiveness of the local variance force for noise robustness in the
multi-phase image segmentation.

Computer Vision and Pattern Recognition;Numerical Analysis;Numerical Analysis