  The performance of image segmentation highly relies on the original inputting
image. When the image is contaminated by some noises or blurs, we can not
obtain the efficient segmentation result by using direct segmentation methods.
In order to efficiently segment the contaminated image, this paper proposes a
two step method based on the hybrid total variation model with a box constraint
and the K-means clustering method. In the first step, the hybrid model is based
on the weighted convex combination between the total variation functional and
the high-order total variation as the regularization term to obtain the
original clustering data. In order to deal with non-smooth regularization term,
we solve this model by employing the alternating split Bregman method. Then, in
the second step, the segmentation can be obtained by thresholding this
clustering data into different phases, where the thresholds can be given by
using the K-means clustering method. Numerical comparisons show that our
proposed model can provide more efficient segmentation results dealing with the
noise image and blurring image.
