1st Activity: Digital Scanning

In this activity, we were tasked to recreate a hand drawn plot. First, I searched for an old book and took a hand sketched plot. It is shown in figure 1. 

Figure 1. Hand-sketched graph

Using GIMP editor, I moved the pointer over several points in the plot. I noted the pixel locations of each. I gathered 46 data points from the plot. I took as many as I could (especially at the curved portions of the plot) so that I could obtain a more precise plot.

The interval between two successive tick marks is related to the interval in pixels by a constant. This constant value is the scaling factor. This is just a simple ratio and proportion principle.

(Scaling factor) (interval in pixels) = interval as shown in graph                                    (1)

Since both the interval between successive tick marks and the interval in pixels could be easily determined, the scaling factor can then be calculated. In the x-axis, the interval between each tick marks shown by the graph is 50 gauss. After taking the pixel location of successive tick marks, the interval was found to be 60pixels.  In the y-axis, the interval between successive tick marks as shown by the graph is 10 while the interval in pixels is 40. Using equation 1, the scaling factors are shown in Table 1.

Table 1. Scaling factors

Scaling factor in x	0.83 gauss/pixel
Scaling factor in y	0.25 beam intensity/pixel

Since the scaling factor is now derived, the actual location for each point in the plot can now be obtained. However, there is a need to introduce a reference point. This is needed because there is a difference in the origin of the graph and the origin of the image. I chose the reference point to be at the lower left corner of the plot which is at (66pixel, 199pixel). I subtracted this to the pixel location of each point in the plot. This length is then multiplied to the scaling factor to eliminate the pixel unit. This would be the scaled value of the point.

scaled value of each point = scaling factor * (pixel value of each point – pixel value of reference point)            (2)

For the final step in obtaining the reconstructed plot, we use the equation given by

x coordinate of each point = Actual value of reference point + scaled value of each point in x      (3a)

y coordinate of each point = Actual value of reference point – scaled value of each point in y      (3b)

Also, note that the actual value of the reference point is (3300, 60).

All the calculations were done simply in Excel and the plot was generated as shown in Figure 2.

I compared the reconstructed plot with the original plot by superimposing these two as shown in Figure 3.

Figure 3. Superimposed plots of original and reconstructed plot

It can be clearly seen that the plot that I was able to generate was exactly over the hand-sketched plot. Also note that the tick marks in x-axis and y-axis of generated plot is continuous with the horizontal and vertical lines in the hand-sketched graph (except that it was way too thicker). This indicates that the reconstruction of the hand-sketched graph was successful.

Self-evaluation:

For this activity, I give myself a score of 10. For technical correctness, I rate myself a 5 since I was able to understand the lecture completely. I was able to reconstruct the hand-drawn plot accurately. Also, I was able to produce all the required output. For quality of presentation, I also rate myself a 5 since all of the  text and images are of good quality. Captions can stand alone. All plots are properly labeled and are visually understandable.