Theory Of Fractal Multiwavelet And Texture Image Segmentation

The first two chapters in this paper summaried the theory of the fractal Multi_wavelet and the development of texture image segmentation respectively.A texture image segmentation based on fractal wavelet is the first work.It includes the several steps as follow:At first, Use variogram function to decide the size of feature window and modifying to a uniform window.Then texture feature extraction to image using the fractal wavelet and selecting sample_points in one of the texture region; Secondly , searching match_point in feature space according to the sample_point and connecting all kind of match_ point to form the connecting region separately.Finally overlaping each connecting region to obtain the coarse edge and skeleton it .The definition of variogram function for the local variable Z(x) is as follow:r(x,h)= (1/2)E[Z(x)-Z(x+h)]2-(1/2){E[Z(x)]-E[Z(x+h)]}2.For it can satisfy the suppose of charactistic,i.e, E[Z(x)] is a constant when Z(x) is considered as the texture image value, the variogram function can tranform to the form r(x,h)= (1/2)E[Z(x)-Z(x+h)]2.Searching the position of first smaller value in the horizontal and vertical variogram function and modifying them as the width and height of the feature window.Then the feature window is divided into a number of location and the average value of each location is calculatied as the parameter in the feature window .The feature description using the fractal wavelet. We use the following filter matirx,horizontal: vertical: .It equals to the spatial frequent filter model template.Generally, the window to calculate feature is the size region ,where the feature position (x,y) is the center position.In order to improve the precise edge, we did not choose the region where the center is the feature position (x,y) but the feature position acts as the left_top ,right_top,right_bottom and left_bottom positon of the region. It decomposes the feature window by using the fractal wavelet .The decomposition coefficients form the feature vector of the feature point (x,y).The sample_ point should be chosen in a feature space .We select a point in a kind of texture region in characteristic space randomly as the sample_point.In order to obtain more the match_point ,we select other point as the sample point,which locate at the left ,right,top and bottom of the sample_point selected randomly .Once chosen the sample point in the feature space,the match points are searched,which are the feature points like the sample point and the distance to the sample point is lower than a threshold. More match points will appear at the texture region where the sample point was seleted and fewer at other region.There are two way to connect the match points:the gridding connection and the smaller value filter template connection.The whole image region is partitioned into local gridding ,which is not overlapped ,and accumulate the match points at each grid.If the number of match points in a grid is bigger than a threshold,this grid is called the texture grid.Connect the texture grid to form the conncective texture region and clean the region which grid number is lower than value.It is gridding connection.Then another way is to move the smaller value filter template in the whole image region and connect into the texture region.The coarse edge is obtained by overlapping each connective texture region and skeleton it to form a precise edge.The experient result showed that the texture image segmentation based on fractal wavelet can achieve good texture edge and low error rate.