This document discusses digital signal processing and digital image processing. It introduces a new interpolation method called the EASE (Edge-Adaptive Scheme) which is based on bilinear interpolation but tries to reduce error by using the interpolation error theorem in an edge-adaptive manner. The EASE scheme estimates interpolation errors at points between samples and uses this to improve the accuracy and reliability of the interpolation compared to other linear interpolation methods like nearest neighbor and bilinear.
3. Digital signal processing :
DSP take real –world signals like voice, video,
temperature, pressure or position that have been digitized
and then mathematically manipulate them.
Digital image processing :
The term digital image processing generally refers to
processing of a 2-D picture by a digital computer.
An image is any one of the form of transparency, slide,
photography, or a chart.
4. Image is continuous with respect to x and y
directions, and also in amplitude. To convert into a
digital form, we have to sample the function in both
coordinates and in amplitude.
5. What is Image resampling?
Resampling is the mathematical technique used to
create a new version of the image with a different
width and/or height in pixels.
6. Why is resampling important?
Reducing the size of an image from a scanner or
digital camera for emailing or display on the web.
Increasing the size of an image before or during the
printing process.
How resampling works ?
A 2-dimensional image can be broken down into two
1-dimensional resampling passes.
7. FromFrom interinter meaning between andmeaning between and polepole, the points or, the points or
nodes. Any means of calculating a new point between twonodes. Any means of calculating a new point between two
existing data points is therefore interpolation.existing data points is therefore interpolation.
8. Image interpolation techniques often are required in medicalImage interpolation techniques often are required in medical
imaging for image generation and processing such asimaging for image generation and processing such as
compression or re sampling.compression or re sampling.
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12. Linear Interpolation Method:
Usually the interpolation kernel H2Dis selected to be
symmetric and seperable to reduce the complexity.
H(x,y)=H(x)*H(y)
H(-x)=H(x)
14. Rgb to Gray
Mapping original
points
Interpolation
through EASE
Extending to 2-D
Interpolation of
non aligned points
15. EASE for 1-D Signals
Let point ‘p’ be mid point of
the interval (xi,xi+1) .
p=(xi+xi+1) /2
ui=u(xi)
ui+1/2 =(ui +ui+1 )/2 +ci+1/2
xi-1 xi xi+1 xi+2
16. ui+1/2 =(ui +ui+1 )/2 +ci+1/2
where ci+1/2 is the error amender and defined as
ci+1/2 = -u’’(p)/2*h2
/4
Here h= 1 hence ci+1/2 = -u”(p)/8
but we really don’t know the value of u”(p) .
17. ci+1/2 can be estimated through cL and cR .
ui = (ui-1+ui+1 )/2 + cL
So we obtain
cL= ui –(ui-1+ui+1 )/2
cR = ui+1 –(ui+ui+2 )/2
18. cL =u”(xi)*22
/8=u”(xi)/2
so comparing we get
ci+1/2 ≈ cL/4
So ui+1/2 =(ui +ui+1 )/2 +minmod(cL, cR )/4
Where minmod(a , b)= a, if ab>0 & |a|<=|b|
b, if ab>0 & |a|>|b|
0, if ab<0
19. For magnification factor >2 we can derive equations
similarly.
ui+j/k =(1-j/k) ui +(j/k) ui+1 +M i+j/k /4
Where j=1,2,…..(k-1)
ui+1/4 =(1-1/4) ui +(1/4) ui+1 +M i+1/4 /4
= 3ui/4 + ui+1/4+M i+1/4 /4
26. The edge direction is between the two directions that
evaluate the two smallest directional sobel derivatives.
The flattest directions are to be adjacent to each other.
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31. This project introduces a new interpolation method, called the
EASE scheme , which is based on the bilinear method and tries
to amend the error by utilizing the interpolation error theorem in
an edge-adaptive way.
This new interpolation scheme has proved better in accuracy
and reliability than linear interpolation methods such as the
nearest neighborhood and bilinear scheme.
