Spherical Diffusion for Scale-Invariant Keypoint Detection in Wide-Angle Images

Two variants of the SIFT algorithm are presented which operate on calibrated central projection wide-angle images characterised as having extreme radial distortion. Both define the scale-space kernel, termed the spherical Gaussian, as the solution of the heat diffusion equation on the unit sphere. Scale-space images are obtained as the convolution of the image mapped to the sphere with the spherical Gaussian which is shift invariant to pure rotation and the radial distortion in the original image. The first method termed sSIFT implements convolution in the spherical Fourier domain, and the second termed pSIFT approximates this process more efficiently in the spatial domain using stereographic projection. Results using real fisheye and equiangular catadioptric image sequences show improvements in the overall matching performance (recall vs 1-precision) of these methods versus SIFT, which treats the image as planar perspective.