In this chapter we demonstrated two different approaches to analysing 3D textures. One is just the 3D orientation histogram of the texture computed by counting gradient vectors in various orientation bins. The other is an extension to 3D of Chetverikov's method [3] of cooccurrence matrices of arbitrary displacement and calculation of the inertia as proposed by [5]. This method effectively projects all gradients on all directions and adds their square magnitudes. It is more robust to noise than the gradient method, but less sensitive to microtexture analysis and certainly much more time-consuming. Time is a very important factor when dealing with 3D data, so for most of our experiments with real data we adopted the gradient method, as it was also more appropriate for the analysis of the microtextures that are present in medical images. The robustness of the INV method, on the other hand, makes it more appropriate for the global description of macrotextures.

This chapter presented the potential that 3D texture measures have for diagnosing a pathology, quantifying its severity, and quantifying its change with time. Extensive studies are needed to determine the clinical value of 3D texture quantification, and some studies are currently in progress. For example, Segovia-Martinez et al. [26] recently reported a trend in anisotropy measures F2 and F3 related to the severity of the condition in Alzheimer's patients, using CT data from 24 cases. This chapter is about demonstrating the potential of such an analysis in (1) diagnosing a pathology, (2) quantifying the severity of the pathology, (3) quantifying the change with time of a certain pathological condition.

The anisotropy measures presented in this chapter are only illustrative examples. Many other metrics, inspired from two dimensions, can be used depending on image modality, type of pathology, and the task at hand.

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