This annimation demonstrates the concepts behind importance sampling. The tree is assumed to resemble a second degree parabola (rotated by 360 degrees to make a solid) - this is the proxy taper function or shape. A point on the tree is randomly selected, with its chance of selection proportional to the volume of that section. Then the proxy shape is adjusted so that is matches the tree at that point.NOTE: Error in the above animation! The Volume of a second degree parabola is: PI*0.5*Length*Diameter^2/4, where Diameter is the diameter at the base of the shape.
The animation incorrectly left off the 0.5 (which makes the equation the volume of a cylinder!)
The following figures represent volumes up to 11.1m^3 (which is the total volume initially estimated by the proxy taper function above). Randomly click on values to select an importance sampling point and see how the volume estimate changes depending upon the sample. Note how many of the samples (picked proportionally to volume) tend to fall on the lower portion of the tree.
| 10.0 | 0.2 | 1.6 | 2.4 | 3.9 | 4.1 | 5.8 | 6.5 | 7.2 | 8.3 | 9.7 | 6.2 | 5.8 | 7.3 | 8.8 | 4.0 | 3.2 | 9.2 | 0.1 | 2.8 | 1.5 | 10.6 | 4.1 | 2.3 | 7.7 | 1.2 | 9.8 | 6.3 | 8.2 | 10.2 | 3.7 | 5.8 | 0.5 | 9.4 | 2.5 | 6.7 | 4.2 | 3.3 | 5.7 | 1.0 | 0.1 | 7.3 | 8.8 | 10.9 |
Return to Importance and Centroid sampling discussion
| Document URL | http://online.anu.edu.au/Forestry/mensuration/IMPOR_AN.HTM |
| Editor | Cris Brack © |
| Last Modified Date | Fri, 9 Feb 1996 |