Representation of local geometry in the visual system
Biological Cybernetics
Regular Article: Computing Fourier Transforms and Convolutions on the 2-Sphere
Advances in Applied Mathematics
Robot Vision
Gaussian Scale-Space Theory
Signal Processing for Computer Vision
Signal Processing for Computer Vision
Spherical Diffusion for 3D Surface Smoothing
IEEE Transactions on Pattern Analysis and Machine Intelligence
Processing Sparse Panoramic Images via Space Variant Operators
Journal of Mathematical Imaging and Vision
Wide-angle Visual Feature Matching for Outdoor Localization
International Journal of Robotics Research
On azimuthally symmetric 2-sphere convolution
Digital Signal Processing
Central catadioptric image processing with geodesic metric
Image and Vision Computing
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We present linear filters for image processing in the case that the image data is given on the sphere rather than on a plane. Such spherical images occur in various situations in computer vision and computer graphics. The class of filters we present is derived from the spherical Gaussian kernel defined as the Green's function of the spherical diffusion equation. The derived filters include Laplacian of Gaussian, directional Gaussian derivatives, and their Hilbert transform. All computations are directly performed on the sphere without ever switching to a planar domain. These filters allow spherical image processing on multiple scales. We present results on images obtained from an omnidirectional camera.