Lehrveranstaltungsinhalt aus - Institute for Computer Graphics and ...

1.2. THE IMAGE AS A RASTER DATA SET 39
1.2 The Image as a Raster Data Set
A digital image is an array of pixels. It was already mentioned that in principle the images are
continuous functions f(x, y). A very simple “image model” states that f(x, y) is the product of
two separate functions. One function is the illumination I and the other function describes the
properties of the object that is being illuminated, namely the reflection R. The reflection function
may vary between 0 and 1 whereas the illumination function may vary between 0 and ∞.
We now need to discretize this continuous function in order to end up with a digital image.
We might create 800 by 1000 pixels, a very typical arrangement of pixels for the digital sensing
environment. So we sample our continuous function f(x, y) into an N × M matrix with N rows
and M columns. Typically our image dimension are 2 n . So our number of rows may be 64, 128,
512, 1024 etc. We not only discretize or sample the image (x, y)-locations. We also have to take
the gray value at each location and discretize it. We do that also at 2 b , with b typically being
small and producing 2, 4, 8, 12, 16 bits per pixels.
Definition 1 Amount of data in an image
Definition 3: ”The amount of data of an image”
To calculate the amount of data of an image you have to have given the geometric and radiometric
resolution of the image.
Let’s say we have an image with N columns and M rows (geometric resolution) and with the
radiometric resolution of R bits per pixel.
The amount of data b of the image is then calculated using the formula:
b = N ∗ M ∗ R
A very simple question is shown in Slide 1.20. If we create an image of an object and we need to
understand from the image a certain detail in the object, say a spec of dirt on a piece of wood of
60 cm by 60 cm, and if that dirt can be as small as 0.08 mm 2 , what’s the size of the image to be
sure that we recognize all the dirt spots?
The resolution of an image is a widely discussed issue. When we talk about a geometric resolution
of an image than we typically associate with this the size of the pixel on the object and the number
of pixels in an image. When we talk about radiometric resolution than we describe here the number
of bits we have per pixel. Let us take the example of geometric resolution. We have in Slide 1.22
and Slide 1.23 a sequence of images of a rose that begins with a resolution of a 1000 by 1000 pixels.
We go down from there to ultimately 64 by 64 or even 32 by 32 pixels. Clearly at 32 by 32 pixels
we cannot recognize the rose any more.
Lets take a look at the radiometric resolution. We have in Slide 1.24 a black and white image of
that a rose at 8 bits per pixel. We reduce the number of bits and in the extreme case we have
one bit only, resulting in a binary image (either black or white). In the end we may have a hard
time interpreting what we are looking at, unless we know already what to expect. As we will see
later, image processing a 8-bits in black & white images is very common. A radiometric resolution
at more bits per black & white pixel is needed for example in radiology. In medicine it is not
uncommon to use 16 bits per pixel. With 8 bits we obviously get 256 gray values, if we have 12
bits we have 4096 gray values.
The color representation is more complex, we will talk about that extensively. In that case we
do not have one 8-bit number per color pixel, but we typically have three numbers, one each for
red/green/blue, thus 24 bits in total per each color pixel.