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But in concrete algorithm implementation, randomly selected thresholds even when they are in the reasonable scope just cannot guarantee any kind of optimality. So we formulate threshold selection as an optimization problem with two variables (Thresh1 and Thresh2) and tend to use an appropriate method to find the optimal solution. To formulate Imatinib cost a proper objective function f, let us introduce Dice Similarity Coefficient (DSC) first, which is usually used to evaluate segmentation effect quantitatively. In the next section, we will use it for quantitative comparison of the proposed method and two other segmentation schemes. It is defined as DSCA,B=2?A��BA+B, (2) where A is the area of the target region of ground truth image acted by the manually segmented images in this paper; B is the area of the target region of the result of an automatically segmented image. DSC varies between 0 and 1. The higher it is, the better segmentation accuracy it indicates. According to this fact, the objective function f we formulate is DSC=fThresh1,Thresh2. (3) In this way, the optimization problem here can be described as follows: make DSC be as large as possible by selecting appropriate Thresh1 and Thresh2. Since approximate ranges of Thresh1 and Thresh2 can be determined, what we should do next is to find the optimal value from all the possible choices. The golden section search method is a technique for finding the extremum (minimum or maximum) of a strictly unimodal function by successively narrowing the range of values inside which the extremum is known to exist. The technique derives its name from the fact that the algorithm maintains Oxymatrine the function values for triples of points whose distances form a golden ratio known as 0.618. It has been proved that compared to bisection method this value can enable us to obtain an optimal reduction factor for the search interval and minimal number of function calls when searching for the maximum point. Assume f(x) is a unimodal function in search region [a, b]; the maximum point is x and the assumed algorithm precision is epsilon. Let x1,??x2 be two points in region [a, b] and a Ivacaftor purchase 8). Figure 8 Flowchart of golden section search method. Step 1 . �� Let [a, b] be initial search interval and let algorithm precision be epsilon. Step 2 . �� Let x1 = a + 0.382?(b ? a), let x2 = a + 0.618?(b ? a), and compute f(x1), f(x2). Step 3 . �� If f(x1) > f(x2), b : = x2, jump to Step 4; if f(x1)