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.

Numerous scale-invariant feature matching algorithms using scale-space analysis have been proposed for use with perspective cameras, where scale-space is defined as convolution with a Gaussian. The contribution of this work is a method suitable for use with wide angle cameras. Given an input image, we map it to the unit sphere and obtain scale-space images by convolution with the solution of the spherical diffusion equation on the sphere which we implement in the spherical Fourier domain. Using such an approach, the scale-space response of a point in space is independent of its position on the image plane for a camera subject to pure rotation. Scale-invariant features are then found as local extrema in scale-space. Given this set of scale-invariant features, we then generate feature descriptors by considering a circular support region defined on the sphere whose size is selected relative to the feature scale. We compare our method to a naive implementation of SIFT where the image is treated as perspective, where our results show an improvement in matching performance.