Digital image processing with interpolation techniques

1. Digital Image processing

2. Introduction
“One picture is worth more than ten
thousand words”
Anonymous

3. Contents
– What is a digital image?
– What is digital image processing?
– Key stages in digital image processing.
– Art examples of digital image processing.
– Image Interpolation.
– Techniques of image interpolation.
– Summary

4. What is a Digital Image?
A digital image is a representation of a twodimensional image as a finite set of digital
values, called picture elements or pixels.

5. What is a Digital Image?
Common image formats include:
– 1 sample per point (B&W or Grayscale)
– 3 samples per point (Red, Green, and Blue)
– 4 samples per point (Red, Green, Blue, and “Alpha”,
a.k.a. Opacity)

6. What is Digital Image Processing?
Digital image processing focuses on two
major tasks
– Improvement of pictorial information for
human interpretation
– Processing of image data for storage,
transmission and representation for
autonomous machine perception

7. Key Stages in Digital Image Processing
Image
Restoration
Image
Enhancement
Segmentation
Image
Acquisition
Object
Recognition
Problem Domain
Representation
& Description
Colour Image
Processing
Image
Compression

8. Key Stages in Digital Image Processing:
Image Restoration
Image
Restoration
Image
Enhancement
Segmentation
Image
Acquisition
Object
Recognition
Problem Domain
Representation
& Description
Colour Image
Processing
Image
Compression

9. Key Stages in Digital Image Processing:
Segmentation
Image
Restoration
Image
Enhancement
Segmentation
Image
Acquisition
Object
Recognition
Problem Domain
Representation
& Description
Colour Image
Processing
Image
Compression

10. Key Stages in Digital Image Processing:
Object Recognition
Image
Restoration
Image
Enhancement
Segmentation
Image
Acquisition
Object
Recognition
Problem Domain
Representation
& Description
Colour Image
Processing
Image
Compression

11. Key Stages in Digital Image Processing:
Representation & Description
Image
Restoration
Image
Enhancement
Segmentation
Image
Acquisition
Object
Recognition
Problem Domain
Representation
& Description
Colour Image
Processing
Image
Compression

12. Key Stages in Digital Image Processing:
Image Compression
Image
Restoration
Image
Enhancement
Segmentation
Image
Acquisition
Object
Recognition
Problem Domain
Representation
& Description
Colour Image
Processing
Image
Compression

13. Key Stages in Digital Image Processing:
Colour Image Processing
Image
Restoration
Image
Enhancement
Segmentation
Image
Acquisition
Object
Recognition
Problem Domain
Representation
& Description
Colour Image
Processing
Image
Compression

14. Key Stages in Digital Image Processing:
Image Acquisition
Image
Restoration
Morphological
Processing
Image
Enhancement
Segmentation
Image
Acquisition
Object
Recognition
Problem Domain
Representation
& Description
Colour Image
Processing
Image
Compression

15. Key Stages in Digital Image Processing:
Image Enhancement
Image
Restoration
Morphological
Processing
Image
Enhancement
Segmentation
Image
Acquisition
Object
Recognition
Problem Domain
Representation
& Description
Colour Image
Processing
Image
Compression

16. Examples: Image Enhancement
One of the most common uses of DIP
techniques: improve quality, remove noise
etc

17. Examples: Artistic Effects
Artistic effects are
used to make
images more
visually appealing,
to add special
effects and to make
composite images

18. Examples: Medicine
Take slice from MRI scan of canine heart,
and find boundaries between types of tissue
– Image with gray levels representing tissue
density
– Use a suitable filter to highlight edges
Original MRI Image of a Dog Heart
Edge Detection Image

19. Examples: Industrial Inspection
•Human operators are
expensive, slow and
unreliable.
•Make machines do the
job instead.
•Industrial vision
systems .

20. Examples: Law Enforcement
Image processing
techniques are used
extensively by law
enforcers
– Number plate
recognition for speed
cameras/automated
toll systems
– Fingerprint recognition
– Enhancement of
CCTV images

21. Examples: HCI
Try to make human
computer interfaces more
natural
– Face recognition
– Gesture recognition
Does anyone remember the
user interface from “Minority
Report”?
These tasks can be
extremely difficult

22. Image interpolation
• What is image interpolation?
– An image f(x,y) tells us the intensity values at the
integral lattice locations, i.e., when x and y are
both integers
– Image interpolation refers to the “guess” of
intensity values at missing locations, i.e., x and y
can be arbitrary
– Note that it is just a guess (Note that all sensors
have finite sampling distance)
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24. Engineering Motivations
• Why do we need image interpolation?
– We want BIG images
• When we see a video clip on a PC, we like to see it in
the full screen mode
– We want GOOD images
• If some block of an image gets damaged during the
transmission, we want to repair it
– We want COOL images
• Manipulate images digitally can render fancy artistic
effects as we often see in movies
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25. Techniques of
interpolation
•Image quality highly depends on the used interpolation
techniques.
•The techniques used for interpolation are:
1.Nearest neighbor
2.Linear interpolation
3.Cubic interpolation
4.B-splines

26. Nearest neighbor
•The simplest interpolation from a computational
standpoint.
• Here each interpolated output pixel is assigned the
value of the nearest sample point in the input image.
The simplest interpolation from
a computational standpoint
•This technique is also known as point shioft algorithm
and pixel replication.
•The interpolation kernel for the nearest neighbor
algorithm is defined as

27. •Frequency response of the nearest neighbor kernel is:
•Kernel and its fourier transform is given in figure as:
•This technique achieves magnification by pixel replication,
by sparse point sampling. For large-scale changes, nearest
neighbor interpolation produces images with blocky effects.

28. Linear Interpolation
•Linear interpolation is a first degree method that passes a
straight line through every two consucutive points of the input
signal.
•In the spatial domain, linear interpolation is equivalent to
convolving the sampled input with the following kernel.
• Frequency response of linear interpolation is :
•This kernel is also called triangle filter, roof function or
Bartlett windoe.

29. •The frequency response of the linear interpolation kernel
is superior to that of the nearest neighbor interpolation
function.
•The side lobes are less prominent, so the performance
is improved in the stopband.
• A passband is moderately attenuated, resulting in
image smoothing.

30. Cubic convolution
•Cubic convolution is a third degree interpolation
algorithm that fairly well approximates the theoretically
optimum sinc interpolation function.
•The kernel is composed of piecewise cubic polynomials
defined on subintervals (-2, -1), (-1, 0), (0, 1) and (1, 2).
•The kernel is of form:
•The frequency response is:

31. •Choices for a are a=-1, a=-0.75 and a=-0.5.
•The performance of the interpolation kernel depends
on a, and the frequency content of the image.
• For different images, different values of the parameter
a gives the best performance.

32. B-splines
•A B-spline of degree n is derived through n
convolutions of the box filter, B
0 ..
•The cubic B-spline B is generated from convolving
B *B . That is B =B *B *B *B .
•The cubic B-spline interpolation kernel is defined as:
3
0
2
3
0
0
0
0
•Unlike cubic convolution, the cubic B-spline kernel is
not interpolatory since it does not satisfy the necesssary
constraint that h(0)=1 and h(1)=h(2)=0.

33. •Figure summarizes the shapes of these low-order Bsplines.
•The positivity of the B-spline kernel is attractive for our
image processing application. When using kernels with
negative lo obes, it is possible to generate negative
values while interpolating positive data.

34. Summary of Image processing
• Image processing has anenormous range of
applications; almost every area of science and
technology can make use of its methods.
• Wide applications from consumer electronics to
biomedical imaging
• Interpolation is a hot topic after the IT bubbles
break
• A fundamental tool in digital processing of
images: bridging the continuous world and the
discrete world.
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