Continuing from my last post, I did the same analysis on the Herbert Run point cloud that was generated from spring 2011. It turns out at first, the set of GPS data was not ordered properly, so the spline function didn't work correctly. This yielded the following results:

The x-y-z axes show how the orientation of the data is set up. Ideally, this picture would show an untilted image as if one were looking down on the campus perpendicularly. This point cloud was given an incorrect set of helmert parameters, due to having a poorly constructed spline of the GPS and camera data. This problem was fixed and once I analyzed the data again, I got much better results.

This point cloud transformation was much better, now that the GPS points were in the correct order. The x and y axes appear to be close enough to where they should be and it seems that we are perpendicularly looking down onto campus, but there is one glitch that this picture does not show. All of the z coordinates appear to have been inverted. The high points in the point cloud are actually the low points, and the low points in the cloud are the real high points. This is indicated in the analysis of the orange field bucket position in the point cloud versus their actual position in space when the pictures were taken.

These scatter plots are for this second attempt of transforming the point cloud. The graph is of the X-values of the manually detected buckets in the point cloud, versus the actual GPS coordinates of those buckets in the field. The equation of the trend line for the x coordinates is y=0.996x + 1398.7 with an R-squared = 0.9995. The graph of the y-values of the data is not shown, but is very similar to the first graph, with the trend line for the y values for the buckets being y=1.0073x - 31820 with an R-squared = 0.9994. The graphs of x and y show a strong correlation between the two data sets for each. Both slopes are very close to 1.

The second graph shown is for the values of the estimated z coordinates of the buckets versus the GPS z coordinates. You can see a correlation between the two by the trend line, but the slope is negative. The trend line is y = -1.0884x +187.29 and R-squared = 0.9872. This negative slope seems to be tied to the fact that all of the point cloud data had inverted z coordinate values.

Overall, this data is much, much better than the original result. We are currently trying to find a solution to the inverted z-axis, but the following is the first attempt to fix this problem.

When the helmert parameters were compared to the original data set from Herbert Run in Fall 2010, the fourth parameter which was for scaling turned out to be negative for the spring. We wanted to see how the transformed point cloud would react if we forced the scaling constant to be greater than zero. This change results in the following point cloud orientation:

This did exactly what we wanted for the z-axis, all the real world high points became point cloud high points and lows becames lows. The obvious problem here is that it inverted the x and y axes. This "solution" really did not solve much due to the fact that it caused the problem it was attempting to fix in different axes. The correlation between the 3 sets of variables only changed by making the slopes of the trend lines of opposite sign to what they were before. The R-squared values did not change when the scale parameter was altered. Besides this, despite having the z axis in the correct orientation, the data seems a little wierd. The z coordinates were falling in a range of about (-3,7). I took the differences between the real GPS height of the buckets and the calculated heights of the buckets and it looks like there is a consistent difference between the two. The calculated data is about 50.7 units below that of the expected GPS heights, for each bucket.

I want to see how just altering the applyHelmert code to multiply anything involving the z-axis by the absolute value of the scale parameter and leaving the x and y axes multiplications alone will do. If we can maintain the x,y axes from the first attempt with ordered data, and use the z-axis orientation with ordered data and only being multiplied by the absolute value of the scale parameter for the z-components, the point cloud should be oriented in the correct way, just translated down too low by a constant amount. (Which is something that has not been explained yet.)