A novel region based Active Contour Model (ACM) for image segmentation is presented using image local information for intensity inhomogeneity images. A transcendental (trigonometric) energy functional based on Local Fitted Image (LFI) energy is suggested to extract the image local information. The difference between the original and fitting image is introduced as an angular constraint of the trigonometric function. This new approach has the ability to handle images with severe intensity inhomogeneity, multiple intensity classes and regions with non-homogeneous pixel intensities. To regularize and maintain the level set function, Gaussian filtering procedure is adopted that not only maintains the level set consistency but also eliminates re-initialization procedure to avoid computational complexity. Furthermore, the proposed model holds boundary regularization property and achieves sub-pixel accuracy. Experimental results on several real and synthetic images demonstrate that the proposed model has higher performance and better accuracy in comparison to the state-of-the-art models.