Upcoming SlideShare
×

# Comparing 3-D Interpolation Techniques

3,709 views
3,608 views

Published on

Comparing 3-D Interpolation Methods - Nearest Neighbour, Cubic convolution, B-spline, Tri-linear

Published in: Technology, Art & Photos
0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
Your message goes here
• Be the first to comment

• Be the first to like this

Views
Total views
3,709
On SlideShare
0
From Embeds
0
Number of Embeds
8
Actions
Shares
0
51
0
Likes
0
Embeds 0
No embeds

No notes for slide

### Comparing 3-D Interpolation Techniques

1. 1. Comparing 3-D Interpolation Methods Binu Enchakalody January, 12 2010
2. 2. Interpolation Methods <ul><li>Nearest Neighbor </li></ul><ul><li>Tri-Linear </li></ul><ul><li>Cubic-Keys </li></ul><ul><li>Clamped Cubic Spline </li></ul><ul><li>Catmull-Rom Spline </li></ul><ul><li>Cubic B-Spline </li></ul>
3. 3. Methods <ul><li>Vxyz  = V000 (1 - x) (1 - y) (1 - z) + </li></ul><ul><li>V100 x (1 - y) (1 - z) +  </li></ul><ul><li>V010 (1 - x) y (1 - z) +  </li></ul><ul><li>V001 (1 - x) (1 - y) z + </li></ul><ul><li>V101 x (1 - y) z +  V011 (1 - x) y z + </li></ul><ul><li>V110 x y (1 - z) + V111 x y z </li></ul>Tri-Linear Weights an interpolated intensity value, based on the distance from the nearest x,y and z pixels within a 2 x 2 x 2 neighborhood Nearest Neighbor Picks the intensity of the nearest x,y and z pixel within a 2 x 2 x 2 neighborhood
4. 4. Piecewise-Cubic <ul><li>Basic Algorithm </li></ul><ul><li>[ t 0 t 1 t 2 t 3 ] x Basis Matrix x [a -1 a 0 a 1 a 2 ] ’, where 0 < t < 1 </li></ul><ul><li>Cubic-Keys </li></ul><ul><li>*Cubic Convolution Interpolation for Digital Image Processing - R.G. Keys </li></ul><ul><li>C2 Continuity (curvature) </li></ul><ul><li>4 Cubic Kernel </li></ul><ul><li>Dimension Separable </li></ul><ul><li>Catmull-Rom Spline </li></ul><ul><li>Different Basis Matrix </li></ul>
5. 5. Piecewise Cubic-Spline <ul><li>Clamped Cubic-Spline </li></ul><ul><li>C2 Continuity (curvature) </li></ul><ul><li>4 Cubic Kernel </li></ul><ul><li>Dimension Separable </li></ul>General Equation
6. 6. Piecewise Cubic-Spline <ul><li>B-Spline Interpolation </li></ul><ul><li>*A parallel B-Spline fitting algorithm – F.Cheng, A. Gosthashby </li></ul><ul><li>Uses Control Points defined by the neighboring intensity pixels </li></ul>
7. 7. Calculating Control Points, C Parallel Algorithm A parallel B-Spline fitting algorithm – F.Cheng, A. Gosthashby
8. 8. Original – Volume Center slice
9. 9. Nearest Neighbour
10. 10. Tri-Linear
11. 11. Cubic-Keys
12. 12. Catmull-Rom Spline
13. 13. Clamped-Cubic Spline
14. 14. B-spline
15. 15. Analysis <ul><li>Rotated a 151 x 221 x 50 Test Matrix, 6 times in increments of 60 degrees </li></ul><ul><li>Along the Z-axis </li></ul><ul><li>Along the X-axis (permuted) </li></ul><ul><li>Recorded computation time for interpolating the data-set </li></ul><ul><li>Error Analysis on a 23 x 29 x 11 sub-matrix </li></ul><ul><li>Calculated MSE, Mean, Standard Deviation </li></ul>
16. 16. Error analysis on test matrix, after 6 rotations of 60 ° - along Z-axis (top), along X-axis (bottom)
17. 17. Approx. computation time@ rotation(MATLAB profiler)