Rotation Invariant Classification of 3D Surface Textures using Photometric Stereo and Surface Magnitude Spectra

Many image-rotation invariant texture classification approaches have been presented. However, image rotation is not necessarily the same as surface rotation. This paper proposes a novel scheme that is surface-rotation invariant. It uses magnitude spectra of the partial derivatives of the surface obtained using photometric stereo. Unfortunately the partial derivative operator is directional. It is therefore not suited for direct use as a rotation invariant feature. We present a simple frequency domain method of removing the directional artefacts. Polarograms (polar functions of spectra) are extracted from resulting spectra. Classification is performed by comparing training and classification polarograms over a range of rotations (1° steps over the range 0° to 180°). Thus the system both classifies the test texture and estimates its orientation relative to the relevant training texture. A proof for the removal of directional artefacts from partial derivative spectra is provided. Results obtained using the classification scheme on synthetic and real textures are presented.