Segmentation of images is a critical pre-processing step in image processing. The objective of segmentation is to divide an image into two homogeneous segments based on similar features. Recently, energy-based segmentation methods, such as the level set algorithm, have exhibited remarkable performance in segmenting various types of image data. However, such methods fail to produce satisfactory results on textured images, leading to inaccurate foreground and background segmentation. To address this issue, the proposed method utilizes a feature space based on image local energy, which is independent of image intensity. This feature space provides a more robust representation of texture in the image. By taking advantage of a unique feature space, images can be represented with a sum of Legendre polynomials. The reproduced image is injected into the L2S algorithm. The level set function is optimized from the average difference of Legendre polynomial coefficients to provide the best representation of the image. Consequently, the proposed method results in better segmentation accuracy, with an average increase of 19.33 compared to existing state-of-the-art methods.