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Also, ?1 can be chosen to be any of the diffusivity functions from the traditional nonhomogeneous isotropic diffusion equation, which depends on the first order derivative of the intensity in this direction, as ?1(uv1?) = uv1?e?(uv1?/k)2 and ?2(uv2?) = �� �� uv2?, with 0 Protease Inhibitor Library solubility dmso from the original image u0 (at t = 0) and of the result of the diffusion process at convergence. The anisotropic diffusion equation becomes ?u?t=��i=12div?iuvi?��vi?+��u?u0. (10) In order to evaluate the denoising effects of the directional anisotropic diffusion (DAD), we have added a Gaussian white noise to each of the images in Figure 4. Once the diffusion method is applied to these noisy images, its effectiveness in reducing the noise is got by calculating the peak signal to noise ratio (PSNR) relative to the original image as follows: PSNR=10��log?10d2MSE, (11) where d = 255 and MSE is Unoprostone the mean-squared error which is written as MSE=1NM��i=1N��j=1MIoriginali,j?Idenoisedi,j2, (12) where Ioriginal refers to the original image without noise and Idenoised is the image after the denoising process. Figure 4 Original images (a) and the corresponding images with additive Gaussian noise (b); denoised images: best result with GF (c), best result with MF (d), best result with PM filter (e), and best result with directional anisotropic diffusion filter (f). The higher the PSNR is, the better the effect of the denoising is. Note that this measure does not necessarily imply that an image with a higher PSNR is also more visually gratifying. However, based on our experiments using the three test images with an additive white Gaussian noise, we can draw some observations. First, all the techniques www.selleckchem.com/products/bgj398-nvp-bgj398.html we have tried have several parameters that must be selected carefully to obtain the best results. Since we have a ��clean�� original image, as well as one with noise, we can use the increment in the PSNR value to guide our choice of the parameters. These parameters and the obtained results are indicated in Tables ?Tables1,1, ?,2,2, and ?and3,3, where we can observe that for the images corrupted with an additive Gaussian noise, the DAD method performs better than the PM method. It gains a higher PSNR (40.4337, 20.9045, and 33.3515) and a smaller MSE (5.8845, 527.9932, and 30.0557) than the aforementioned three methods. Table 1 Parameters and results of different filters for vessel image. Table 2 Parameters and results of different filters for phantom image. Table 3 Parameters and results of different filters for Lena image.