Glyph Representation
For second order tensors there exist a large number of yet simple, yet powerful glyphs to represent symmetric part of second order tensor data. All of these can be applied to diffusion tensor data which is symmetric and strictly positive (or if defined the other way around) strictly negative definite, i.e. all eigenvalues have the same sign. |
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Octahedron glyph: easy to paint and not so much geometry, but still a 3D glyph containing all information available. |
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box glyph: just another way of looking at it. |
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Haber tensor glyph: it has it's home in mechanical engineering. There may be additional data mapped to the circle plates but I haven't implemented this as it's not really useful for medical images. |
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Kindlmann's superquadrics (sharp edges): edge sharpness can be modified to be between sharp, cylindric glyphs... |
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Kindlmann's superquadrics (softer edges) |
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Kindlmann's superquadrics (again softer edges) ... something like ellipsoids or even be ellipsoids in the extreme case of sharpness parameter to be set to zero. |
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Second order surface glyphs: Glyph representation of the surface function used by Frank on the same second order tensor dataset. |
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Fourth order glyphs glyphs painted in a fourth order data set created using the HARDI method (ref. Frank) on a similar slice of the brain. As the main direction is sensitive to noise, the color often swaps between principal and second direction, but the local change is always smooth. |
The color coding in the last two examples may be misleading, as it is done by the maximum value on the surface, only, as an anisotropy computation is not easy obvious in higher order representations. This leads to "noisy" color changes in areas of low fractional anisotropy. The fourth order image has a smooth change of the glyphs. The color change is not smooth as it changes from the principal to the second direction and back especially in areas where noise is present.
The area close to the corpus collosum in the left part of the left images without any glyphs is because of a low signal to noise ratio at these positions in the raw scanner data. All glyphs are scaled by a factor that the largest eigenvalue is 1.0 to prevent cluttering in areas of high diffusion but low fractional anisotropy. In areas of low diffusion and high noise, this may lead to misleading results.