1. The Digital Image

2. Video course of digital image processing

3. The Digital Image
Majority of images don’t originate in the digital form, mostly in the form of optical light energy
Before we can process an image digitally it must be in digital form
Optical images: human sight, video camera, photograph, also X-ray, infrared, radar, and acoustic images.

4. Creating a Digital Image

5. Creating a Digital Image
A ”natural” image is composed of varying array of shades and colors
In photograph shades from ligth to dark and colors from reds through yellows to blues
Continuous-tone image, compiled from various shades and colors blended with no disruptions

6. A digital image is composed of discrete points of gray tone, or brightness, not continuosly varying tones
To convert a image as digital, the orginal image must be divided into individual points of brightness, with a specific digital data value
Sampling and Quantization = image digitization

7. An Image is sampled into a rectangular array of pixels
Each pixel has coordinates
corresponding to its location
within the image
x = pixel number, y = line number
The digital image actually exists as a large array of numbers (bits)
In gray-scale 0 to 255
0 =
255 =
Quality is directly related to the amount of pixels and lines, along with the range of brightness values = image resolution

8. Spatial Resolution
Term spatial refers to the concept of space – in this case, two-dimensional image space
The term Spatial Resolution is used to describe how many pixels comprise a digital image
The more pixels, the greater its spatial resolution

9. Spatial frequency 1
Every image contains details, some fine and some coarse
The details are made up of brightness transitions that cycle from dark to light and back to dark
The rate at which brightness cycle is the spatial frequency

10. Spatial frequency 2
In the cloudy sky area, the image details vary smoothly, not like the area with the tree, thus consists low rates of brightness change, or low spatial frequency.
The area with the trees has minute details where the brightness vary rapidly, so the minute tree details constitute a high rate of brightness change, or high spatial frequency

11. Sampling Theorem
”This theorem tells us mathematically that in order to represent fully the spatial details of an orginal continuous-tone image, we must sample the image at a rate at least twice as fast as the highest spatial frequency contained in it.”
To capture an image’s finest dark-to-light-to-dark detail, sampling should be at least two samples upon the detail.
Whatever the sampling rate used, the highest spatial frequency that can be contained in the resulting digital image will not exceed one-half the sampling rate
This frequency is referred to as the Nyquist rate.
If the rate is less than twice, Spatial Aliasing will occur.
We must determine the necessary sampling rate so that our degital image adequately resolve all the spatial details of the original continuous-tone image. This is done by using the classical sampling theorem.

12. Sampling Theorem

13. Sampling Theorem continued.
In real-life systems, the sampling rate of a particular image acquisition system is generally fixed
The camera is selected to meet the minimum spatial-resolution requirements of the application.

14. Images with different spatial resolutions
640 pixels x 480 lines
320 pixels x 240 lines
160 pixels x 120 lines
80 pixels x 60 lines
40 pixels x 30 lines
20 pixels x 15 lines

15. Spatial Aliasing
Spatial aliasing appears in a digital image when the details in an image are sampled at a rate less than twice their spatial frequency.
Not only are high-frequency details missed, but they are also corrupted to appear as new frequencies
When a detail within an image has a frequency greater than twice the sampling rate, the detail is called undersampled.

16. Spatial Aliasing

17. Spatial Aliasing
The high-frequency detail ends up being translated to a lower frequency because some of its brightness transitions are missed in the sampling process.

19. Group discussion
In which situations you have encountered spatial or temporal aliasing of images?
(temporal sampling means sampling in time domain, e.g. video frames)

20. Moiré patterns

22. Brightness Resolution
Brighness resolution tells us how accurately the digital pixel’s brightness represents the intensity of the orginal image
Dependent upon how many bits are used in the quantizer (3bits = 8 different colors, 111 =2^3=8)
The range of the gray scale is also referred to as dynamic range

23. Gray scales with different amounts of bits
3-bit gray scale
4-bit gray scale
5-bit gray scale
6-bit gray scale
7-bit gray scale
8-bit gray scale

24. Qualities of the Digital Image

25. Brightness Histograms
Brightness histogram shows the different gray levels of pixels within a digital image
horizontal axis = ”brightness” from 0 to 255
vertical axis = ”number of pixels”
with histogram it is easy to define whether an image is basically dark or light and high or low contrast

26. Contrast and Dynamic Range Indications
Contrast is a term that is often used to describe the brightness attributes of an image
Low contrast appears as tightly grouped mound of pixel brightness in the gray scale
High contrast appears as a bimodal histogram – two peaks exists at the outer brightness regions
The dynamic range is represented by how many gray levels in the gray scale are occupied

27. Low contrast and low dynamic range
High contrast and high dynamic range
Well-balanced contrast and low dynamic range

28. Color Histograms
Histograms for color images are threefold version of the regular, gray-level brightness histogram
Three histograms are computed and displayed, one for each color component
Can represent any color space (RGB, HSB, ...)
Each histogram can help us determine the brightness distributions, contrast, and dynamic ranges of the individual color components.