Rotation Covariant Image Processing for Biomedical Applications

Figure 1

A spherical harmonic decomposition of images can be seen as some kind of frequency decomposition. A band limited expansion of a volumetric images is illustrated. We see that lower frequency components (right-hand side) are roughly representing the important characteristics of the objects. However, higher frequency components are necessary to represent the details. For the expansion here, we use a Fourier-like basis for representing the images in radial direction. Here, ℓ represents the order of the spherical harmonics and 𝑘 the number of radial frequency components taken into account. The image shows an isosurface rendering together with the centered 𝑋,𝑌, and 𝑍-slice. The interested reader is referred to [2].