Page 309 - Fundamentals of Light Microscopy and Electronic Imaging

292 DIGITAL IMAGE PROCESSING

that the light source has been refocused or changed, after which a new master flat-
field frame should be prepared.
•A dark frame contains the bias offset signal plus the electronic and thermal noise
components that are present in the image. Bias counts are from the positive voltage
applied to the CCD as required for proper digitization; electronic noises include the
components contributing to the readout noise of the camera; thermal noise is due to
the kinetic vibration of silicon atoms in the chip. At full and one-quarter saturation
of a scientific-grade CCD camera, the bias count and noises may contribute roughly
5% and 20% of the apparent pixel amplitudes, respectively, and must be subtracted
from the flat-field frame and the raw frame to restore photometrically accurate pixel
values. Dark frames are prepared using the same exposure time as the raw image,
but without opening the shutter. Since dark frames have low signals, a master dark
frame should be prepared by averaging 9–16 dark frames together.

The equation for flat-field correction is
−
(Raw Dark)
Corr. Image = M
−
(Flat Dark)
where M is the mean pixel value in the raw image. The multiplication by M simply
keeps the intensity of the corrected image similar to that of the original raw image. In
applying the correction, the order in which the operations are performed is important.
The dark frame must be subtracted from the raw and flat frames first, followed by the
division of the dark-subtracted raw frame by the dark-subtracted flat frame. The correc-
tion is performed in floating point data type to preserve numeric accuracy. To be seen
optimally, the brightness and contrast of the corrected image might need to be adjusted.
The visual effect of flat-field correction looks similar to that obtained by background
subtraction, but performing the correction by division is more accurate. This is because
light amplitudes in an image result from a multiplicative process (luminous flux
exposure time). Once corrected, the relative amplitudes of objects in the image will be
photometrically accurate. Surprisingly, the corrected image lacks the optical defects that
were present in the raw image. An example of a flat-field corrected image is shown in
Figure 15-5. Practice in performing this correction is included as an exercise at the end
of this chapter.

IMAGE PROCESSING WITH FILTERS

Filtering is used to sharpen or blur an image by convolution, an operation that uses the
weighted intensity of neighboring pixels in the original image to compute new pixel val-
ues in a new filtered image. A matrix or kernel of numbers (the convolution matrix) is
multiplied against each pixel covered by the kernel, the products are summed, and the
resulting pixel value is placed in a new image. Only original pixel values are used to
compute the new pixel values in the processed image. The kernel or mask can have dif-
ferent sizes and cover a variable number of pixels such as 3 3, 4 4, and so forth.
Note that the sum of the numbers in the kernel always adds up to 1. As a result, the mag-
nitude of the new computed pixel value is similar to the group of pixels covered by the
kernel in the original image. After a pixel value has been computed, the kernel moves to
the next pixel in the original image, and the process is repeated until all of the pixels