2D color shapes description by quaternion Disc-Harmonic moments

Robustness to photometric transformations and invariance under geometric transformations are two crucial criteria that a shape descriptor must satisfy. In this direction, orthogonal moments have proved their performance since the image can be reconstructed from its descriptor. However, these conventional moments deal only with binary and gray-level images. Recently, the algebra of quaternions have been widely used in combination with these moments in order to describe color images. In this paper, we introduce the quaternion Disc- Harmonic moments (QDHMs) as an extension of the conventional Disc-Harmonic moments (DHMs) for describing 2D color shapes. The conventional DHMs were inspired by the spherical harmonics which use orthogonal basis functions and are known for their rotation-invariance property. Experiments on images extracted from the COIL-100 database were conducted in order to evaluate the performance of our descriptor. First, we have fixed some parameters that are the maximal order, the measure of similarity and the color space. Second, tests on photometric transformations robustness are provided. Finally, the discriminative power of the QDHMs based on recall-precision criterion is compared to the conventional disc-harmonic moments and the existing orthogonal quaternion-based moments.