Assignment 1

Fabian Prada

Implemented Filters and Results:

1. Box (N=0,L=1,W=1,Interpolator,Positive)

2. Hat (N=1,L=2,W=2,R=0,Interpolator,Positive)

3. Bspline3 (N=3,L=4,W=4,R=2,No Interpolator,Positive)

4. Mitchel-Netravali (N=3,L=2,W=4,R=1,No Interpolator,Negative Lobes)

5. Keys (Catmull-Rom) (N=3,L=3,W=4,R=1,Interpolator,Negative Lobes)

6. Keys6 (N=3,L=4,W=6,R=1,Interpolator,Negative Lobes)

7. Lanczos4 (W=4,Interpolator,Negative Lobes)

8. Lanczos6 (W=6,Interpolator,Negative Lobes)

9. Dodgson Interpolating (Interpolating Quadratic) (N=2,L=2,W=3,R=0,Interpolator,Negative Lobes)

10. Dodgson C1 (Bspline2) (N=2,L=2,W=3,R=1,No Interpolator,Positive)

11. Meijering5 (N=5,L=3,W=6,R=3,Interpolator,Negative Lobes)

Observations and Conclusions:

• Interpolation Kernels performed much better than Non-Interpolation ones, with the noticeable exception of Box (as expected). Results from Interpolation Kernels such as Keys, Meijering, and Lanczos were sharper and drew fine countours for the cactus thorns and flower petals.



• Non Interpolation Kernels such as Dodgson C1, Bspline3 and Mitchell-Netravalli, produced blurred images that partially lost the contours of the objects from the original image. In the case of the Bspline3, the smoothing is excessive and it produces an unpleasent result.



• Kernels with regularity less than 0 loose sharpness and produce results with high intensity variance between neighbour pixels. This high intensity variance perceptually induces an unnatural ''block'' structure to the image (alias). This phenomena is perfectly observed for the Box Kernel result, and is also noticeable for Hat and Dodge Interpolating.



• Kernels with regularity 1 such as Keys(4 and 6) lead to smoother intensity transition between neighbour pixels which is perceptually pleasent. Kernels with higher regularity such as Meijering5 (R=3) did NOT achieve significant improvement (at least noticeable!) respect to regularity=1.



• Meijering5 despite of a larger polynomial degree, support and regularity, lead to a result perceptually equivalent to Keys(W=4). On the other hand, Keys(W=6) only using a larger support (larger approx order) improved the results obtained by those two Kernels. This is slightly evidenced by the sharper reconstruction of the cactus thorns.



• Similarly to the improvement from Keys(W=4) to Keys(W=6), Lanczos6 obtained a sharper and more natural reconstruction of the image than Lanczos4. In my opinion, the computational cost that involves enlarging the support was well paid with better reconstructions in this experiment.

Ranking:

High Performance:
1. Lanczos6
2. Keys(W=6)


Good Performance:
3. Lanczos4
4. Keys(W=4)
5. Meijering5


Acceptable Performance:
6. Dodgeson Interpolating (Interpolating Cuadratic)
7. Mitchell-Netravali


Defficient Performance:
8. Dodgeson C1 (Bspline2)
9. Hat
10. Bspline3
11. Box