Lecture 5
Mathematical tools for image processing,
continued

Spatial versus transform operations
•
Spatial operations are performed in spatial domain
–
Image is represented as f(x,y)
–
X=0,1,2,…,M
–
Y=0,1,2,…,N
–
Single pixel based operations, neighborhood operations,
geometric transformation
•
Transform operation
–
Image is transformed to other domain g(u,v)
–
Operations are performed in the other domain
–
Transformed operated image is inverse-transformed to the
spatial domain

Single pixel spatial operations
Intensity mapping
s=T(z)
z: input image intensity
s : Output image intensity
T : the operation
Example: getting the negative of 8 bit image
T(z)= 2
8
-z

Neighborhood spatial operations
The value of the pixel
at x,y in the output
image is calculated from a set of
neighbor pixels centered at x,y in the
input image
Example, the calculated value = the
average of the neighbors rectangle of
dimensions M by N centered at the pixel
S
set
neighbor
MxN
in the
index
column
and
row
are
c
r,
)
,
(
1
)
,
(
,
)
,
(
y
x
S
c
r
c
r
f
MN
y
x
g

Geometric spatial transformation
•
Geometric transformation is the mapping of the
coordinates of each pixel in an input image to another
(displaced/rotated,..) pixel in the output image.
•
Intensity interpolation is used to assign intensities for the
relocated pixels in processed image
•
Forward mapping: for each pixel in the input image, find
its location in the output image and assign its value
•
Multiple output values are assigned to the same
output pixel
•
Some output locations may not assigned values
•
Inverse mapping: for each pixel in the output image, find
the location in the input image by applying the inverse
transform, use the interpolation to calculate intensity
value based on the intensities in the input image location
ed
concatenat
be
can
tion
tranforma
Affine
matrix
tion
transorma
the
is
T
1
0
0
1
,
,
1
,
,
1
,
,
tion

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- Fall '15
- Hamed Hemeda
- Linear Algebra, Image processing, Computer Graphics, input image