medical images are popular in real world because they give intuitive expression . with the development of image processing , computer - aided diagnosis are more important with the ever increasing images . but medical images are often with intensity inhomogeneities ; so it is a hard work to segment in such images as angiogram and mr bladder images . the active contour model has been increasingly applied to image segmentation in the past decade , because it provides very good frameworks of variational image segmentations . chan - vese ( cv ) model   is the most popular active contour model for image segmentation based on the feature of mean gray value of different regions . the variance information can solve the question of different areas with same mean gray value and different variance . the map ( maximum a posterior ) is an efficient region descriptor for the segmentation task . zhu , paragios and deriche , and rousson and deriche   approximated the map of the given image by a mixture of gaussians . the features deduced by map method are very popular in images with different probability distributions . but they are a failure in image segmentation with intensity inhomogeneities , because there are no features that can be deduced for segmentation using the active contour model . the method is proposed for medical images with complex topological structure , strong contrast , and low noise characteristics . it makes full use of the image area information , builds an energy model , and uses variation gradient information to establish a global energy model to get the minimization value . they combine active contour model with diffusion filter for multiobject segmentation of the noisy image . a target adaptive scheme is designed for adjusting the model to solving a particular image processing task . all the methods mentioned above are region - based models aiming to identify each region of interest by using a certain region descriptor to guide the motion of the active contour . for images with intensity inhomogeneity , there is much important information such as image gradient and laplace that are ignored in active contour model . for medical images , intensity inhomogeneity is usually due to technical limitations or artifacts introduced by the object being imaged . so incorporate edge information alone is not enough , we also incorporate higher order diffusion term into the active contour model aiding segmentation . in this paper , we propose a new active contour model with gradient and higher - order information of the image . the model can also be deemed as active contour model coupling with high - order diffusion , diffusion , because the introduction of laplace information and the difference scheme becomes more difficult . to enhance the efficiency of the segmentation , the fast split bregman algorithm is designed for the segmentation implementation . , we will introduce the active contour and high - order diffusion related methods briefly . then the new active model with high - order diffusion method is proposed in section 3 . generalized perona - malik equation for image restoration   was the first paper that introduced and implemented high - order anisotropic diffusion partial differential equations ( pdes ) for image analysis . there are also many other high - order pdes that have been already applied to image processing [ 13 , 14 ] . incorporating laplace term , higher - order diffusion can use more information near the edges . in this paper , we select the total variation with higher - order diffusion because of the simplicity . the total variation model with higher - order diffusion is depicted as : 
 ( 1)e(u)=12(uf)2dx  dy+1|u|dx  dy+2|u|dx  dy , 
 where  is the image domain ,  u  is the denoised image , and f is the noisy image . the active contour model using mean gray value is depicted as : 
 ( 2)arg  min{||dx  dy  + (1|fu1|2+2|fu2|2(1))dx  dy } , 
 where  is the level set function and u 
 1 and u 
 2 are the mean gray value of different areas . bresson transformed the original active contour model to a convex minimization problem by relaxing   { 0,1 } to     and showed that the characteristic function is the global minimizer . this model is based on mean gray value and it has drawbacks with different usages . for medical images we incorporate the edges and laplace information into active contour model for dealing with intensity inhomogeneities . the new model has the abilities of both ( 1 ) and ( 2 ) . it is hard to segment medical images because the edges are always weak and the images are also noisy . we couple the higher - order diffusion model with active contour model for medical images segmentation . the new model that couples higher - order diffusion with active contour model is 
 ( 3)arg  min{||dx  dy+((1|fu1|2+1|u1|+1|u1|)+(2|fu2|2+2|u2|+2|u2|)(1))dx  dy } , 
 
 where  is the image domain ,  
 1 ,   
 1 ,   
 1 ,   
 2 ,   
 2 ,   
 2 are the positive parameters , f is the original image , u 
 1 and u 
 2 are the mean values in different image parts , and  is a standard level set function . we use the form of ( 3 ) mainly because the image features in different areas are not always the same . this is a natural extension of chen and vese   and vese and chen   model for piecewise constant or smooth model . we can get the solution using alternating iteration . because there are gradient and laplace information , straightforward solving of ( 3 ) by introducing forth - order term of difference scheme is a hard work . the split bregman method [ 17 , 18 ] is introduced for the easy implementation of the model . we introduce the auxiliary variables w1=(w11,w12)t ,  w 
 2 and bregman iteration parameters  b=(b1,b2)t , when the following energy function gets its minimization , w1u ,  w2u . equation ( 3 ) can be divided into the following three sub - problems of minimization : fix    and  u 
 2 , the energy function of ( 3 ) became the following form : 
 ( 4)(u1k+1,w1k+1,w2)=arg  minw1,u1{(1|w1|+1|w2|+1|fu1|2+12(w1u1b1k)2+12(w2w1)2)  dx  dy } , 
 
 where w1k+1=u1k+1 ,  b1k+1=b1k+u1k+1-w1k+1 ,  w2=w1 ,   
 1 , and   
 1  are the positive parameters . the energy function of u 
 1 is 
 ( 5)e(u1)=(1|fu1|2+12(w1u1b1k)2)  dx  dy . the discretion of u 
 1 is 
 ( 7)u1=1(21 + 41)(21f+1(u1,i , j+1k+u1,i , j1k  + u1,i+1,jk+u1,i1,jk  + (b1kw1k ) ) ) . the energy function of w1 is 
 ( 8)e(w1)=(1|w1|+12(w1u1b1k)2  + 12(w2w1)2)  dx  dy . using eular - lagrange equation , we can get 
 ( 9)w1k+1=uk+1+bk+1+11(w1w2)11w1k+1|w1k+1| . 
 by wavelet soft threshold 
 ( 10)w1k+1=max(|u1k+1+b1k+11(w1w2)|11,0)u1k+1+b1k+(1/1)(w1w2)|u1k+1+b1k+(1/1)(w1w2)| . the energy function of w 
 2 is 
 ( 11)e(w2)=(1|w2|+12(w2w1)2)  dx  dy . using eular - lagrange equation , we can get 
 ( 12)w2k+1=w1k+111w2k+1|w2k+1| . 
 by wavelet soft threshold , 
 ( 13)w2k+1=max(|w1k+1|11,0)w2k+1|w2k+1| . 
 for solving u 
 2 the energy function can be rewritten as : 
 ( 15)arg  min{e()=||dx  dy+r(u1,u2)  dx  dy}. 
 for solving  , we also use the split bregman method by introducing v=. then the energy function of ( 14 ) is transformed as : 
 ( 16)(k+1,vk+1 )  = arg  mind,{|v|dx  dy  + r(u1,u2)  dx  dy  + 2(vdk)2dx  dy } , 
 where dk+1=dk+k+1-vk+1 ,  is the positive parameter . fixing v for solving  : 
 ( 17)r(u1,u2)(k+1+dkvk)=0 . 
 using gradient descent method , 
 ( 18)ddt=(k+1+dkvk)r(u1,u2 ) . after discretion , 
 ( 19)k+1  = ( 11 + 4dt)dt  ((i , j1k+i , j+1k+i1,jk+i+1,jk+dkvk )  r(u1,u2 ) ) . 
 to ensure that   , so in every step we use the following function : 
 ( 20)k+1=min(max(k+1,0),1 ) . fix  for solving v , we can get 
 ( 21)vk+1=max(|k+1+dk|1,0)k+1+dk|k+1+dk| . 
  in the end of calculation , we set 
 ( 22)(x)={0(x) 
 th 
 1(x)<th , 
 where th is the preset threshold . to verify the effect of our proposed method , we test our method on a variety of real images with intensity inhomogeneity . we compare our method with cv model   and mean shift algorithm   because they are highly cited and compared in image segmentation . the cv model which is used in our experiment for comparison is also global convex . for comparison with the mean shift algorithm , we used the software edison which is based on a fast implementation of the mean shift algorithm using a speed - up scheme described in [ 1921 ] . figure 1 shows the results for a real image of a t - shaped object with different lighting intensity . figure 4 is a test of mr image of blades with the comparison of cv model and mean shift method . all of them are selected because they are typical images with intensity inhomogeneity . the cv model and mean shift method can not get the proper results while our model can get the right results . the shadow of the object is the key element causing wrong segmentation of tradition methods . the vessel images in figures 2 and 3 fail to be segmented using traditional methods because of the intensity inhomogeneity . but using our model , the boundary of the object of interest ( the bladder ) is extracted very well . in these two images , parts of the vessel boundaries are quite weak ; our method can still segment them well . the result of mean shift algorithm for the first image is similar to that of our method , showing certain ability of the mean shift algorithm in handling intensity inhomogeneity . however , for the two - vessel image , a small portion of the vessel is missing . for segmenting the mr bladder image , the result is not so perfect for surrounding organs . we notice that the segmentation result of mean shift algorithm is somewhat sensitive to the choice of two major parameters : spatial bandwidth and range bandwidth . we have tweaked these two parameters and other minor parameters for the best segmentation results for these four images . in this paper , we present a new active contour model for medical image segmentation . it can segment images with intensity inhomogeneity and has desirable performance for images with weak object boundaries . experimental results have demonstrated the advantages of our method over several well - known methods for image segmentation .
active contour models are very popular in image segmentation . 
 different features such as mean gray and variance are selected for different purpose . but for image with intensity inhomogeneities , there are no features for segmentation using the active contour model . the images with intensity inhomogeneities often occurred in real world especially in medical images . to deal with the difficulties raised in image segmentation with intensity inhomogeneities , a new active contour model with higher - order diffusion method is proposed . with the addition of gradient and laplace information , the active contour model can converge to the edge of the image even with the intensity inhomogeneities . because of the introduction of laplace information , the difference scheme becomes more difficult . to enhance the efficiency of the segmentation , the fast split bregman algorithm is designed for the segmentation implementation . 
 the performance of our method is demonstrated through numerical experiments of some medical image segmentations with intensity inhomogeneities .