Method



Objective:

After we have got the x_max value of the box cluster, we want to find the coordinate x’ which is near to the x_max but has more points close to the plane x=x’ than x=x_max.

Process:

Step 1. Measure the maximum x value of the cluster, as x_max.
Step 2. Count the number of points in the region of x∈(x_max-d, x_max), record as ni.
Step 3. Make x_max=x_max-d, repeat step 2-3

Box1 (real length=14.5cm, x_max-x_min=16.23cm)

For Box1 and box2, the x_max and x_min values have been tested. The parameter d has been set from 0.5mm to 10mm(d=0.5mm, 1mm, 1.5mm, 2mm, ….10mm). And for each d, the first 30 steps have been recorded and drawn.

For x_max:
The raw data
It can be seen that, the number of points has a jump when x=16(around 8mm). It can be considered that, the x range of the bounding box (which was calculated by x_max-x_min, equal to 16.23cm) may be on one side for about 8mm over measured. The real size of the box is 14.5cm, so it’s still large after subtracting 8mm.
Then on the side of the x_min, the same experiment was also done. However, the result is quite different because another side is further to the camera, some points are missing.


For x_min:
This is some text inside of a div We can see that, when x is smaller than 1.5cm, there’s no step jump on the points. And the error cannot be larger than 1.5cm, or the bounding box length will be too small. 

Box2(real length=14.5cm, x_max-x_min=16.72cm)

Same process is also done on box2(whose measured bounding box length on x direction is 16.72cm )`
It’s interesting to see that the curves fluctuate a lot, even with some regularities.


For x_min