Application to Medical Image Characterization

Two series ofexperiments with real images are presented. In the first series, the objective is to characterize the texture of some MR-t2 brain images for the purpose of finding features that characterize the presence of pathologies with nonlocal manifestation, i.e., pathologies that result in the change of the textural appearance of the brain rather than the development of a tumor. In the second series of experiments, the change in the anisotropy descriptor of the brain images of some patients is studied with the help of images from the same subjects obtained with some time difference from each other. In total, seven MR-t2 and 2MR-t1 images are used for the first series of experiments and 14 for the second.

Figure 9 shows the coronal plane of a typical MR image. The horizontal lines mark the volume of interest, i.e., the range of slices used in the first experiment. The number of axial slices used are 35 for each image involved in this experiment, which is contacted with MR-t2 images.

FIGURE 9 Coronal plane of a 3D MR image with the horizontal lines indicating the part of the brain used for the first series of experiments.

Characterizing the texture anisotropy of a structure requires first the isolation of the structure of interest. Even after the brain component has been isolated in an MRI image, it is not desirable to try to characterize the anisotropy of the brain as a whole. Such an approach would be dominated by the anisotropy of the surface of the brain, which contains many folds that result in the creation of "shadows" with large gradient values. We are really interested in characterizing the texture of the brain volume rather than the roughness of its surface. For this purpose, in the first set of experiments, we use only the interior part of the brain, excluding the gray matter that concentrates on its surface. Brain segmentation is addressed in several chapters of the Segmentation Section in this Handbook. Here we simply use gray level thresholding and morphological postprocessing to remove "holes." The component we use corresponds to the dark interior part of the segments shown at the top of Fig. 10. On the left is the image of a normal brain, while on the right the image has been taken from a patient with advanced Alzheimer's disease. In Figs. 10c and 10d we show the orientation histograms constructed from the whole brain component of each image, using the gradient method. Next to each histogram, its projection on the z = 0 plane is shown. In Figs. 10e and 10f we show the results obtained when the method is applied to the interior component of the brain only. In Figs. 10g and 10h the indicatrices computed by the INV method are presented for the whole brain, and in Figs. 10i and 10j for the interior component only.

By comparing Figs. 10c and 10 g, we see that the elongation of the two indicatrices are in orthogonal directions. This indicates that the texture we are analyzing has a few strong edges in the vertical direction, whereas most of the gradients are oriented in the plane z = 0. This results in the observed difference in the two indicatrices because INV projects the various gradients on the chosen directions and sums up their square magnitudes. On the other hand, the GD method just counts vectors and ignores their magnitude (except the weakest 5%, which are ignored, because their orientation cannot really be calculated reliably). It is also interesting to note that when only the dark part of the image is retained, the two INV indicatrices (Figs. 10i and 10j) become very round, almost spherical. This confirms the observation from the simulated data that this method is not very appropriate for describing microtextures.

Figure 11 is similar to Fig. 10, except that it shows results concerning MR-t1 images. The difference between the two images is made more explicit here: The projection on the z = 0 plane of the orientation histogram of the normal brain on the left is much more anisotropic than the same projection of the orientation histogram of the Alzheimer's brain on the right.

In Fig. 12 we plot as bar charts the values of features F1 and F2 calculated from results like those shown in Fig. 10, for seven different MR-t2 images, two from healthy subjects and five from various pathological cases. Although the clinical interpretation of these results is not addressed here we note that the GD method shows a trend of increased anisotropy in the

F2=(SJS6

FIGURE 10 Experiments with MR-t2 images. All indicatrices and orientation histograms are shown as 3D structures and in projection on the z = 0 plane. (a) An MR-t2 image of a healthy brain. (b) An MR-t2 image of the brain of an Alzheimer's sufferer. (c, d) The corresponding orientation histograms constructed from the full brain component, with the GD method. (e, f) The corresponding orientation histograms constructed from the thresholded darkest component (the interior of the brain) with the GD method. (g, h) The corresponding indicatrices constructed from the full brain component, with the INV method. (i, j) The corresponding indicatrices constructed from the thresholded darkest component (the interior of the brain) with the INV method.

FIGURE 11 Experiments with MR-tl images, (a) An MR-tl image of a healthy brain, (b) An MR-tl image of the brain of an Alzheimer's sufferer, (c, d) The corresponding orientation histograms constructed from the full brain component, with the GD method, (e, f) Projections of the orientation histograms on the z = 0 plane,

FIGURE 11 Experiments with MR-tl images, (a) An MR-tl image of a healthy brain, (b) An MR-tl image of the brain of an Alzheimer's sufferer, (c, d) The corresponding orientation histograms constructed from the full brain component, with the GD method, (e, f) Projections of the orientation histograms on the z = 0 plane,

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