1. Image Interpolation Techniques with Optical and Digital Zoom Concepts
Musaab M. Jasim
Yildiz Technical University
Computer department
Seminar

2. Outline Digital Image concepts . Optical Zoom vs. Digital Zoom .
Digital Image definition .
Image Acquisition Using Sensor Arrays .
Basic Concepts in Sampling and Quantization .
Digital Image Clarity.
Optical Zoom vs. Digital Zoom .
Image Interpolation (spatial processing).
Nearest Neighbor .
Bilinear .
Bicubic.
Conclusion.

3. Digital Image concepts
Digital Image Definition
The digital Image is a visual representation in form of a function f(x,y) where “ f ” is Intensity value (bit depth) and it is related to the brightness (or color) at point (x,y) .
The value of each point is acquired based on the light that reflect from the objects on the sensors inside the Digital Camera .
Right idea
Wrong idea

4. Image Acquisition Using Sensors Array
Sensors arranged in the form of a 2-D array.
The light that reflect from the objects on the sensors will be aggregated.

5. Basic Concepts in Sampling and Quantization
The result of sensor array (acquisition process) is an image which be continuous with respect to the x , y-coordinates, and also in amplitude.
Digitizing the coordinate values is called sampling .
Digitizing the amplitude values is called quantization.

6. Continues Image on sensor array
Basic Concepts in Sampling and Quantization
after the sampling and quantization processes the image pixels will been created
Continues Image on sensor array
Digital image

7. Digital Image Clarity
A Pixel is actually a unit of the digital image .
A Resolution is the capability of the sensor to observe or measure the smallest object clearly with distinct boundaries.
the Resolution is the measurement unit of the clarity in digital image .
There are three types of resolution:
the Pixel Resolution determine the number of pixels in the image .(related with the size of the pixel).
but unfortunately, the count of pixels isn't a real measure of the image clarity as most people think . There are another resolution types affects.
The Spatial Resolution can be defined as the number of independent pixel values per unit length .
The Intensity Resolution is the bit depth or the colors range of pixels in image.

8. Optical Zoom vs. Digital Zoom
An Optical zoom means moving the zoom lens so that it increases the magnification of light before it even reaches the digital sensor.
A digital zoom is not really zoom , it is simply interpolating the image after it has been acquired at the sensor (pixilation process).
Optical Zooming
Digital Zooming
Original image

9. Image Interpolation (spatial processing).
Image interpolation occurs when we resize or distort our image from one pixel grid to another.
Image resizing is necessary when we need to increase or decrease the total number of pixels .
so it mean resampling the image by creating new pixel locations and assigning gray-level values (or color) to these locations.
There are two types of resizing methods
Adaptive .(beyond my presentation)
Non-adaptive :
Nearest Neighbor interpolation.
Bilinear interpolation .
Bicubic interpolation .

10. Nearest Neighbor Interpolation
the simplest method, determines the grey level value(or color) from the closest pixel to the specified input coordinates, and assigns that value to the output coordinates.
Enlargement
Reduction

11. Nearest Neighbor Algorithm
This algorithm assumed that :
(R=r+1 and C=c+1). So, 𝑆 𝑟 , 𝑆 𝑐 has two states .
Some conditions to delete the frame.
In another Image processing books , It assumed that the:
(R=r and C=c). So, 𝑆 𝑟 , 𝑆 𝑐 has just the first state .
This what I assumed in my Example to facilitate it.

12. Nearest Neighbor Example
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (1,7) (1,8) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (2,7) (2,8) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (3,7) (3,8) (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (4,7) (4,8) (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (5,7) (5,8) (6,1) (6,2) (6,3) (6,4) (6,5) (6,6) (6,7) (6,8) (7,1) (7,2) (7,3) (7,4) (7,5) (7,6) (7,7) (7,8) (8,1) (8,2) (8,3) (8,4) (8,5) (8,6) (8,7) (8,8)
(1,1) (1,2) (1,3) (1,4) (2,1) (2,2) (2,3) (2,4) (3,1) (3,2) (3,3) (3,4) (4,1) (4,2) (4,3) (4,4)
I (R X C) =
J ( 𝑅 𝐗 𝐶 ) =
R=r & C=c
𝑅 𝑅
𝐶 𝐶
𝑆 𝑟 =
=0.5
𝑆 𝐶 =
=0.5
(0.5 ,0.5) (0.5 ,1) (0.5 ,1.5) (0.5 ,2) (0.5 ,2.5) (0.5 ,3) (0.5 ,3.5) (0.5 ,4) (1 ,0.5) (1 ,1) (1,1.5) (1,2) (1,2.5) (1,3) (1,3.5) (1,4) (1.5,0.5) (1.5 ,1) (1.5,1.5) (1.5,2) (1.5,2.5) (1.5,3) (1.5,3.5) (1.5,4) (2 ,0.5) (2 ,1) (2,1.5) (2,2) (2,2.5) (2,3) (2,3.5) (2,4) (2.5 ,0.5) (2.5 ,1) (2.5,1.5) (2.5,2) (2.5,2.5) (2.5,3) (2.5,3.5) (2.5,4) (3,0.5) (3 ,1) (3,1.5) (3,2) (3,2.5) (3,3) (3,3.5) (3,4) (3.5 ,0.5) (3.5 ,1) (3.5,1.5) (3.5,2) (3.5,2.5) (3.5,3) (3.5,3.5) (3.5,4) (4 ,0.5) (4 ,1) (4,1.5) (4,2) (4,2.5) (4,3) (4,3.5) (4,4)
( 𝑟 𝑓 , 𝑐 𝑓 ) = (𝑆 𝑟 ∗ 𝑟 , 𝑆 𝑐 ∗ 𝑐 ) =
(1 ,1) (1 ,1) (1,2) (1 ,2) (1 ,3) (1 ,3) (1 ,4) (1 ,4) (1 ,1) (1 ,1) (1,2) (1,2) (1,3) (1,3) (14) (1,4) (2,1) (2 ,1) (2,2) (2,2) (2,3) (2,3) (2,4) (2,4) (2 ,1) (2 ,1) (2,2) (2,2) (2,3) (2,3) (2,4) (2,4) (3 ,1) (3 ,1) (3,2) (3,2) (3,3) (3,3) (3,4) (3,4) (3,1) (3 ,1) (3,2) (3,2) (3,3) (3,3) (3,4) (3,4) (4 ,1) (4 ,1) (4,2) (4,2) (4,3) (4,3) (4,3.5) (4,4) (4 ,1) (4 ,1) (4,2) (4,2) (4,3) (4,3) (4,4) (4,4)
( 𝑟 , 𝑐 ) = 𝑅𝑜𝑢𝑛𝑑{ 𝑟 𝑓 , 𝑐 𝑓 } =
𝐽( 𝑟 , 𝑐 ) = I ( 𝑟 , 𝑐 )

13. Bilinear Interpolation
Bilinear Interpolation determines the grey level value (or color) from the weighted average of the four closest pixels to the specified input coordinates, and assigns that value to the output coordinates.
Linear interpolation between two known points
Interpolation is the process of estimating the values of a continuous function from discrete samples.
𝑦− 𝑦 0 𝑥− 𝑥 0 = 𝑦 1 − 𝑦 0 𝑥 1 − 𝑥 0
𝑦= 𝑦 0 + 𝑦 1 − 𝑦 0 ∗ 𝑥− 𝑥 0 𝑥 1 − 𝑥 0

14. Bilinear Interpolation
weighted average
The previews formula can also be understood as a weighted average .
The closer point has more influence than the farther point. Thus, the weights are 𝑥− 𝑥 0 𝑥 1 − 𝑥 0 and 𝑥 1 −𝑥 𝑥 1 − 𝑥 0 which are normalized distances between the unknown point and each of the end points.
𝑦= 𝑦 0 1− 𝑥− 𝑥 0 𝑥 1 − 𝑥 𝑦 1 1− 𝑥 1 −𝑥 𝑥 1 − 𝑥 0 =𝑦= 𝑦 0 1− 𝑥− 𝑥 0 𝑥 1 − 𝑥 𝑦 1 𝑥− 𝑥 0 𝑥 1 − 𝑥 0

15. Bilinear Interpolation
Example
we observe that the intensity value at the pixel computed to be at row 20.2, column 14.5 can be calculated by first linearly interpolating between the values at column 14 and 15 on each rows 20 and 21, giving
𝐼 20,14.5 = 15− −14 ∗ −14 15−14 ∗210=150.5
𝐼 21,14.5 = 15− −14 ∗ −14 15−14 ∗95=128.5
and then interpolating linearly between these values, giving
𝐼 20.2 ,14.5 = 21− −20 ∗ −20 21−20 ∗128.5=146.1

16. Bilinear Algorithm

17. Bicubic Interpolation
BiCubic Interpolation method determines the gray level value (or color) from the weighted average of the 16 closest pixels to the specified input coordinates .
The image is sharper and more clarity than that produced by Nearest neighbor and Bilinear Interpolation .
It needs much more calculation and time to find weighting..

18. Conclusion
The digital images are result of the optical intensity that is received at the image plane (Sensor array) inside a digital camera .
Digital Zooming includes : enlargement and shrinking processes where these processes require two steps: the creation of new pixel locations, and the assignment of gray (or color) levels to those new locations .
Descending order for the methods of zooming with respect to the picture quality, processing time is :
Bicubic Interpolation .
Bilinear Interpolation .
Nearest Neighbor Interpolation .

19. “ thank you to all attendees “
The end
“ thank you to all attendees “