Microscope Image Processing

16.3.2 Wavelet-Based Multiresolution

Autofocus Functions

A wavelet-transform-based method to compute autofocus functions at multiple

resolutions is described here [18]. If we denote the 2-D wavelet transform as

W

k

2

j

I(x, y) ¼ (I  c

k

2

j

)(x, y), j ¼ 0, 1, ..., J, k ¼ 1, 2, 3 (16:10)

where W

k

2

j

I(x, y) is the wavelet transform of an image I(x, y) at resolution j and

in subband k, c

k

2

j

is the corresponding wavelet, and J is the minimum resolution

(i.e., maximum decomposition) level to be computed, then the wavelet-based

autofocus function at resolution j is computed as the sum of the squared values

of the wavelet coefficients at resolution j; that is,

f ¼

X

k

X

x

X

y

W

k

2

j

I(x, y)



2

, while W

k

2

j

I(x, y)









$  (16:11)

Here  is a threshold value that can be determined ...