Microscope Image Processing

x  x

c

y  y

c

z  z

c

2

4

3

5

¼

cos u sin u cos f sin u sin f

sin u cos u cos f cos u sin f

0 sin f cos f

2

4

3

5

xx  xx

c

yy  yy

c

zz  zz

c

2

4

3

5

(14:37)

where (x

c

, y

c

, z

c

), (xx

c

, yy

c

, zz

c

) are the rotation centers in the input and output

images, and u and f are the rotation angles about the z- and x- axis, respectively.

Typically, such computations result in noninteger values for the coordinates

that need to be truncated or rounded. This may result in more than one voxel’s

being mapped to the same position, which leaves holes in the rotated image

(see Chapter 5). This can be avoided by using an inverse implementation, where,

for each voxel (xx, yy, zz) of the output image, the corresponding input voxel

(x, y, z) value is evaluated [58]. Both translation and rotation ...