Existing methods for layer-based backward compatible high dynamic range (HDR) image and video coding mostly focus on the rate-distortion optimization of base layer while neglecting the encoding of the residue signal in the enhancement layer. Although some recent studies handle residue coding by designing function based fixed global mapping curves for 8-bit conversion and exploiting standard codecs on the resulting 8-bit images, they do not take the local characteristics of residue blocks into account. Inspired by the local anisotropic characteristics of the residue signal and directional methods for motion compensated low dynamic range (LDR) video coding, in this paper we first investigate whether HDR image coding residue exhibits also local anisotropic characteristics. Specifically, we verify directional structures in residue blocks by means of auto-covariance analysis for different bitrates, spatial activities and dynamic ranges as the main variables in HDR image coding. Then, we compare the rate distortion performances of directional coding methods with the baseline residue coding methods in the literature along with different combinations of 8-bit conversion methods. The experiments indicate that content dependent 8-bit conversions and directional coding significantly outperforms the existing function based 8-bit conversions and typical coding for residue coding.