# 2. Digital development of CCD images

1) Hyperbolic conversion
2) Edge emphasis

#### 1) Hyperbolic conversion

X: the original image data
Y: the converted data
i x j : Array of CCD pixcels

X=[Xij]=

 X11,X12,X13,------------X1j X21,------------------------ X31,------------------------ ----------------------------- ---------------------------Xij

Y=[Yij]

The one step process to the photo-quality, what is called, "digital development process DDP" in Japan, is written as:

 Yij = k [ Xij / ({Xij} + a ) ] + b ....(equation-1)

k : A constant to control the maximum value of Yij,

which is not important. (k=1)

'a' & 'b' : Artificial pedestals,

which are the important parameters.

{Xij} : the unsharpened (blured) data of the original image [Xij].

(a) Case without edge emphasis

 Fig-3 When {Xij} = [Xij], i.e. no low pass filter was used, the equation results just a hyperbolic conversion of gamma curve. The relation between Xij and Yij is shown in Fig-3. The curve at X>>b becomes a hyperbolic curve. You can see that the curve is very similar to the S-shape gamma curve of conventional film.

 Fig-3 The meanings of the key parameters 'a' and 'b' are clear in the figure.   1) When b < Xij < a, the gamma is linear. 2) When a

 Fig-3 3) The minimum value of Yij is b. This is similar to the base level of chemical film, which is never zero. The base pedestal results in the low contrast in the low level region, which will improve the visual S/N ratio in background level. This fact plays a very important role to attain the 'photo quality' by films. But, this has been overlooked in CCD processing. (Do not set at b=0!)

 Fig-3 4) The gamma value is unity (=1.0) at b < Xij < a in this example. If you replace Xij by Xij to the G power (xij^G), the gamma value will became G, while we assume G=1.0 througthout this report for simple discussion. The curve of the Log-conversion, which is available in most image processing softwares, is also shown. Note that there is no linear region in this Log curve.

I believe that the linear region of gamma curve should be important to achieve the 'photo quality', because any photographic films have this linear region. Therefore the 'photo quality' will not be attained by the simple log conversion.

The Hyperbolic conversion will be

the simplest and easiest pass to 'photo quality'.

(b) Case with edge emphasis