Image Processing Reference
In-Depth Information
Exercise 3: An image is first rotated 10° and then scaled with a factor 2 in both
horizontal and vertical direction. Next, the image is scaled with a factor 0.5 in
both horizontal and vertical direction and rotated
10°. Do we now have the same
image as we started out with?
Exercise 4: An image is first rotated 10° and then scaled with a factor 2 in both
horizontal and vertical direction. Would the same image appear if the order of the
rotation and scaling is reversed (i.e., first scaling and then rotation)?
Exercise 5: An input image f(x,y) consists of a black background with a white
rectangle on top. The corners of the rectangle are located at: ( 50 , 50 ) , ( 50 , 60 ) ,
( 60 , 50 ) and ( 60 , 60 ) . We want to scale the image with a factor 2 in the horizontal
direction and a factor 1.5 in the vertical direction. What will the area of the white
rectangle be after the scaling?
Exercise 6: f(x,y) is rotated 15 around the point ( 55 , 55 ) . Where will the corner
( 50 , 50 ) be located after the rotation?
Exercise 7: f(x,y) is sheared with B x =
2 and B y =−
1 . 5. Where will the corner
( 50 , 50 ) be located after the shearing?
Exercise 8: In an image the following pixel values are present: f( 10 , 10 )
=
10,
f( 10 , 11 )
=
12, f( 11 , 10 )
=
11 and f( 11 , 11 )
=
9. During a backward mapping
f( 10 . 3 , 10 . 8 ) . What value will g( 100 , 100 ) have if
we use i) zero-order interpolation? ii) first-order interpolation?
Exercise 9: The mapping between two coordinate systems (x, y) and (x ,y ) is de-
fined via the LUT below. Which position does the point (x, y)
it is found that g( 100 , 100 )
=
=
( 8 , 6 ) correspond
to in (x ,y ) ?
(x, y) ( 1 , 4 ) 3 , 4 ) 6 , 4 ) 10 , 4 ) 2 , 7 ) 5 , 7 ) 10 , 7 ) 3 , 10 ) 5 , 10 ) 9 , 9 )
(x ,y ) 0 , 1 ) 3 , 1 ) 5 , 1 ) 10 , 2 ) 1 , 4 ) 4 , 4 ) 9 , 5 )
( 1 , 7 )
( 3 , 8 )
( 7 , 7 )
Additional exercises: What is camera calibration? What can it be used for and how
does it work?
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