In this work, we present a technique which suggests the use of symmetry to reduce the redundancy in images. A symmetry-based image segmentation and coding scheme is described. A segmentation technique is analyzed, and applied on natural images, performing their efficient partition. In order to find symmetries in regions of any shape, the concept of axes of symmetry is generalized to skeletons of symmetry, dividing the regions into two symmetric subparts by the introduction of the Medial Axis Transformation of the regions. Each subpart of the regions is then linearly predicted with respect to the skeletons. An efficient coding strategy specifying the shape and the luminance of the regions is described. Results on natural images show that the described technique outperforms the more classical second generation image coding methods in terms of visual quality.