Microscope Image Processing

14.10 Filtering

Image filtering operation s are typic ally used eith er to reduce nois e by smooth -

ing or to emphasize edges. Analogous to their 2-D counterparts (Chapter 6),

3-D filters can be defined as operat ors that map one 3-D image into anot her

3-D image as bx, y, zðÞ¼fax, y, zðÞðÞ,wherebx, y, zðÞis the output (filtered)

image that results from processing the input image ax, y, zðÞ.Eachvoxelinthe

output image is computed as a function of one or sev eral voxels loc ated i n it s

neighborhood in the input image. Depending on the nature of the filter

function f, the opera tion c an be classified as li near or nonlinear. Dig ital con-

volution filters are linear, since the output voxel values are linear combinations

of the input image voxels, but other ...