GEOMETRIC OPERATIONS. Transformations and directions Affine (linear) transformations Translation,...
-
Upload
noreen-dixon -
Category
Documents
-
view
231 -
download
5
Transcript of GEOMETRIC OPERATIONS. Transformations and directions Affine (linear) transformations Translation,...
Transformations and directions
•Affine (linear) transformations• Translation, rotation and scaling
•Non linear (Warping transformations)
•source to target (coordinate for each input image pixel)
I(x,y) O(x´,y´)
•target to source (coordinate for each output image pixel)
O(x,y) I(x´,y´) BETTER, WHY?
General affine equations
Linear equations in general form
x´ = (x cos(+ y sin()) Sx +Tx
= (Sx cos(x + (Sx sin()) y +Tx
= a2x + a1y + a0
y´ = (-x sin(+ y cos()) Sy +Ty
= (-Sy sin(x + (Sy cos()) y + Ty
= b2x + b1y + b0
Number of reference points
• 3 for first order warping• 6 for second order warping• 10 for third order warping
Number of reference points• Example: correction of a lense degradation by a third
order equation
x´= a9x3 + a8y3 + a7x2y + a6y2x + a5x2
+ a4y2 + a3x + a2y + a1xy + a0
y´= b9x3 + b8y3 + b7x2y + b6y2x + b5x2
+ b4y2 + b3x + b2y +b1xy +b0
Sampling and resizing• In downsizing, first low pass filtering to avoid aliasing
(Nyquist theorem)
• Interpolation in resizing (up- and downsizing )
Interpolation, Bilinear
*
5 6
4
5
a b
c d
Address: 5.3, 4.4
Weighted average of neighbour
pixels:
cd = (1-0.3)*c + 0.3 *d
ab = (1-0.3)*a + 0.3 *b
abcd= (1-0.4)ab + 0.4*cd
abcd is the final pixel value
Interpolation, Bicubic• Second order interpolation• In 16*16 neighbourhood, sometimes 64*64• Optimizing moving images