Preliminaries
  1. This is the Examples file, under the "Help" pull-down menu, in the MR3D package.
  2. MR3D supports image formats FITS and Analyze (HDR/IMG), and also allows conversion to/from AVI video.
  3. Data sets provided are PET and an astronomical 3D volume survey set of galaxy positions, in files names counts*.

  4. A PET image is shown expanded in scale. It can be cycled through.

  5. The wavelet transform options. We recommend only the B3 spline à trous algorithm at present.

  6. The files produced can be read in. The different resolution scales are named: pet_1, pet_2, pet_3, pet_4.
  7. Resolution scale 2:

  8. The "Difference" operation (see "Operations" pull-down menu) works in this way. With an already displayed image volume, carrying out a "Difference" between image volumes first gives a prompt to specify the other image volume to be subtracted. Then the result of the subtraction is displayed.

Example: Segmentation of a Brain Image
  1. Consider T1.fits, an aggregated representative brain, derived from MRI data. It is of dimensions 91 x 109 x 91.
  2. Use "Marginal Range" in the "Segmentation" pull-down menu to decide, from the plot produced, that the BIC criterion suggests that a 6 cluster solution is best.
  3. Then use "Marginal" with 6 clusters requested, again in the "Segmentation" pull-down menu. Save the output as T1_segm_marg6.fits
  4. Next investigate segmentation in wavelet space. First carry out a wavelet transform. The B3 spline a trous wavelet transform is used with 4 levels (i.e. 3 wavelet resolution scales). The output produced is in files 
    T1_1.fits
T1_2.fits
T1_3.fits
T1_4.fits
  5. Use the wavelet resolution scales as input to "K-Means", in the "Segmentation" pull-down menu. Specify 6 clusters. Save the output as T1_segm_kmean6.fits
  6. Now we will assess T1_segm_marg6 versus T1_segm_kmean6. If we use BIC, giving the T1 image and first one and then the second of these segmented images, we find essentially the same BIC value. (The BIC values differ in about the 12th decimal place.) Note though that the model used by BIC is the same as that used for the marginal segmentation; but it is not the same as that used for k-means. Therefore it is not fair to use BIC to assess across models, as opposed to its use within a family of the same model.
  7. Using Renyi quadratic entropy, in the "Segmentation" pull-down menu, we find 4.4671 for the marginal result, and 1.7559 for the k-means result.