geometric operations. transformations and directions affine (linear) transformations translation,...
Post on 14-Dec-2015
231 Views
Preview:
TRANSCRIPT
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
top related