We present a new descriptor and feature matching solution for omnidirectional images. The descriptor builds on the log-polar planar descriptors, but adapts to the specific geometry and non-uniform sampling density of spherical images. We further propose a rotation-invariant matching method for the proposed descriptor that is particularly interesting for mobile devices. It permits to reduce the computational complexity in the detection phase by eliminating the orientation assignment and to shift it to the feature matching step. We then use a criteria based on the Kullback- Leibler divergence in order to improve the feature matching performance. Experimental results with spherical images show that the new descriptors offer promising performance and improve on SIFT descriptors computed on the sphere or on tangent planes.