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. Author manuscript; available in PMC: 2017 Aug 1.
Published in final edited form as: Magn Reson Med. 2015 Oct 19;76(2):663–678. doi: 10.1002/mrm.25888

Figure 6.

Figure 6

The behavior of the error incurred when approximating the smooth surface of an ideal ellipsoid using polyhedra with increasing number of faces. The gold standard is an ideal ellipsoid with a known closed form FT. a) The log of the l2-norm of the gold standard volume versus the number of faces in the triangular mesh. Arrows indicate error corresponding to meshes in Figure 2 and subfigures b and c show image space and k-space details respectively for these meshes. b top row) The z=0 slice of reconstructed 3D volume and image space error. c) The intensity profiles corresponding to the dotted lines on the slices. b bottom row) The magnitude of the image space error for the z=0 slice. d top row) The log of the absolute value of the k-space error corresponding to the kz=0 plane. d bottom row) The log of the absolute value of the k-space error normalized by the absolute value of the gold standard.