Active contour models (ACM) are efficient frameworks for image segmentation because they can provide smooth and closed contours to recover object boundaries with sub-pixel accuracy. Region-based ACM use regional statistical information as an additional constraint to stop the contours on the boundaries of the desired objects. One of the most popular region-based ACM is the C-V model

which has been successfully used in binary phase segmentation with the assumption that each image region is statistically homogeneous. However

typical region-based models do not work well on images with intensity inhomogeneity because these models rely on the uniformity of intensities. This paper presents a new level-set-based K-means active contour model that can segment images with intensity inhomogeneity. We derived this model from a linear level-set-based K-means model constructed by researching the properties of the Euler-Lagrange equation of the C-V model. Our background model is the C-V model

which consists of a fitting term and a regularization term. The fitting term corresponds to classical K-means. When parameters in a threshold are fixed

all pixels in an image have identical thresholds

and the evolution function has a quadratic form

normal K-means and the associated ACM will be unable to process images with intensity inhomogeneity.By researching the reasons for the aforementioned problems of the C-V model

a novel active contour based on a modified K-means is proposed in this paper. Compared with a K-means using fixed parameters

the new K-means contains a variable-weight coefficient matrix

which can be defined with different values for different pixels. Thus

the defined K-means can overcome the drawbacks of the C-V model. Moreover

we defined a local adaptive weighting (LAW) function thatcan identify the cluster threshold of each pixel according to its neighborhood statistical information. This threshold protects the model from the influence of intensity inhomogeneity and enables a successful segmentation ofinhomogeneity images. The LAW-based model can successfully detect objects on a noisy synthetic image with intensity inhomogeneity. Experimental results for medical images show that compared with the local binary fitting (LBF) model

local image fitting (LIF) model

and local correntropy-based K-means model

the proposed model can yield competitive results. Furthermore

when using the provided undesirable initial contours

the proposed model can still derive a correct segmentation of inhomogeneity images

whereas the LBF and LIF models are easily trapped into local minima. This result demonstrates that the proposed model is robust to contour initialization. Given the use of fixed-weight parameters

the typical C-V model may fail to detect meaningful objects from images with intensity inhomogeneity. This paper proposes a modified K-means-based active contour by employing a variable-weight coefficient matrix. Different choices of variable-weight coefficient matrix can be defined to process specific images. We also provide a LAW function for this framework to segment inhomogeneous images. Experiment results indicate that the proposed model can effectively process images with intensity inhomogeneity and is robust to the position of the initial curve.