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This manuscript focuses on new image segmentation model for noisy and intensity inhomogeneity images on the basis of natural logarithmic increasing density function. Local image information is necessary for inhomogeneous images, but it is ineffective for noisy images. As a result local information misguides the motion of active contour. However, the natural logarithmic function in new proposed model is capable to capture minute details of images. Moreover, it also reduces the noise in the images and helps to clarify the exact boundaries. Comparing with local Chan-Vese Model, our new proposed model gives better performance while treating noisy and intensity inhomogeneity images. Experiments on noisy and intensity inhomogeneity images show the robustness of our new proposed model.