In recent years there has been proliferation of sensors that create 3D data, particularly in medicine. These sensors either operate in the plane, creating multiple slices that can be treated as volume data if they are dense enough, or operate in 3D space directly, such as new PET techniques that reconstruct volume data by considering out-of-plane coincident events. Generally volume data are analyzed and viewed as a set of 2D images. Often this is due to the fact that only sparse slices are available. However, even when sufficient volume data are availably analysis and visualization of volume data are typically guided by the limited abilities of human perception, which is not suited well to process volume data. As a result, a large part of the information content of the data may be ignored.
Computerized analysis offers the exciting option of escaping from the anthropocentric description of images, and go beyond the limitations of the human visual and cognitive system. This chapter is a very small step in that direction. We
Based on "Texture Anisotrophy in 3D Images," by V.A. Kovalev, M. Petrou, and Y.S. Bondar which appeared in IEEE Transactions on Image Processing. vol. 8, pp. 346-360. © 1999 IEEE.
present some techniques appropriate for the texture analysis of volume data in the context of medical applications. The microstructural features that can be calculated this way offer a totally new perspective to the clinician, and the exciting possibility of identifying new descriptions and new indicators that may prove valuable in the diagnosis and prognosis of various conditions.
Although the field of 2D texture analysis has been very extensively studied, there has been very little work done in the area of characterization and estimation of 3D textures, with a few notable exceptions. Waksman and Rosenfeld [28,29] specifically dealt with the problem of characterizing 3D textures consisting of opaque planar texels uniformly distributed in volume ("snowflakes"). Their main concern was the evaluation of visibility through such a medium for various texel orientation models. In general, extension of 2D methods to three dimensions has largely been confined to the development of 3D edge detectors [21,30]. However, the use of edge detector filters for the estimation of gradients for texture analysis in 3D is hindered by the fact that most edge detection methods assume that they are dealing with isolated edges and they cannot cope with the interference caused by the presence of multiple edges. Liou and Singh  developed gradient estimation operators that are more appropriate for high-
Copyright © 2000 by Academic Press.
resolution medical images. In a similar way, when the density of lines is very high, as is the case of angiograms and mammograms, the optimal linear filters of  suffer from interference and fail. Much simpler linear filters have been proved more effective in these cases .
In this chapter, we first discuss ways in which one can construct and visualize the orientation histogram of volume data. Then we concentrate on the calculation of features from the orientation histogram, and in particular features that encapsulate the anisotropy of the texture. Finally, we present some examples of applying these techniques to medical data.
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