In neuroimage analysis, the automatic identification of symmetry plane has various applications. Despite the considerable amount of research, this remains an open problem. Most of the existing work based on image intensity is either sensitive to strong noise or not applicable to different imaging modalities. This paper presents a novel approach for identifying symmetry plane in three-dimensional brain magnetic resonance (MR) images based on the concepts of fractal dimension and lacunarity analysis which characterizes the complexity and homogeneity of an object. Experimental results, evaluation, and comparison with two other state-of-the-art techniques show the accuracy and the robustness of our method.