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Image Interpolation Techniqueswith

Optical and Digital Zoom Concepts

Musaab M. JasimYildiz Technical UniversityComputer departmentSeminar

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Outline Digital Image concepts .

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.

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 .

3Right idea Wrong idea

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.

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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.

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Basic Concepts in Sampling and Quantization after the sampling and quantization processes the image pixels will

been created

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Continues Image on sensor array

Digital image

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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:

I. 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.

II. The Spatial Resolution can be defined as the number of independent pixel values per unit length .

III. The Intensity Resolution is the bit depth or the colors range of pixels in image.

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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).

Original image

Optical Zooming

Digital Zooming

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Image Interpolation (spatial processing).

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 methodsA. Adaptive .(beyond my presentation)B. Non-adaptive :

A. Nearest Neighbor interpolation.B. Bilinear interpolation .C. Bicubic interpolation .

Image interpolation occurs when we resize or distort our image from one pixel grid to another.

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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

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Nearest Neighbor Algorithm

This algorithm assumed that : (R=r+1 and C=c+1). So, , has two states

. Some conditions to delete the frame.

In another Image processing books , It assumed that the: (R=r and C=c). So, , has just the first

state . This what I assumed in my Example to

facilitate it.

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Nearest Neighbor Example

[(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) = [

(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)

]J () =

=𝑅�̂� =

𝐶�̂�¿0 .5 ¿0 .5

=

R=r & C=c

[(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)

] = [

(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)

] = I (

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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 pointsInterpolation is the process of estimating the values of a continuous function from discrete samples.

𝑦−𝑦 0𝑥−𝑥0

=𝑦1− 𝑦 0𝑥1− 𝑥0

𝑦=𝑦0+( 𝑦1− 𝑦0 )∗𝑥−𝑥0𝑥1−𝑥0

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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

and which are normalized distances between the unknown point and each of the end points.

𝑦=𝑦0(1− 𝑥−𝑥0𝑥1−𝑥0 )+𝑦1(1−

𝑥1−𝑥𝑥1−𝑥0 )=𝑦=𝑦 0(1− 𝑥−𝑥0

𝑥1−𝑥0 )+𝑦1(𝑥− 𝑥0𝑥1−𝑥0 )

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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 .515−14 ∗91+ 14 .5−1415−14 ∗210=150 .5

𝐼 21 ,14 .5=15−14 .515−14 ∗162+ 14 .5−1415−14 ∗95=128 .5

and then interpolating linearly between these values, giving

𝐼 20 .2 ,14 .5=21−20 .221−20 ∗150 .5+ 20 .2−2021−20 ∗128 .5=146 .1

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Bilinear Algorithm

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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..

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 :

i. Bicubic Interpolation .

ii. Bilinear Interpolation .

iii. Nearest Neighbor Interpolation .

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The end

“ thank you to all attendees “

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