This paper presents a method to improve disparity maps computed from light field images using structure tensor methods, which tend to expand the borders of the occluding objects, enlarging their silhouette. The proposed method relies on the fact that such regions of the silhouette are defined by a mismatch between the disparity map edges, computed by the structure tensor, and those of the corresponding epipolar plane images (EPI) representing the light field. The proposed silhouette improvement method determines a correspondence between EPI edges and the disparity map edges, identifying the erroneous silhouette regions. The disparity map is corrected by using neighbouring values computed with high structure tensor reliability. The achieved results show that the disparity map is improved both around object edges and overall, reducing the MSE by 47.9% in comparison with other methods also based on the structure tensor.