Scale-Invariant Features on the Sphere

This paper considers an application of scale-invariant feature detection using scale-space analysis suitable for use with wide field of view cameras. Rather than obtain scale- space images via convolution with the Gaussian function on the image plane, we map the image to the sphere and obtain scale-space images as the solution to the heat (diffusion) equation on the sphere which is implemented in the frequency domain using spherical harmonics. The percentage correlation of scale-invariant features that may be matched between any two wide-angle images subject to change in camera pose is then compared using each of these methods. We also present a means by which the required sampling bandwidth may be determined and propose a suitable anti-aliasing filter which may be used when this bandwidth exceeds the maximum permissible due to computational requirements. The results show improved performance using scale-space images obtained as the solution of the diffusion equation on the sphere, with additional improvements observed using the anti-aliasing filter.