Digital Scanning

In this activity, replication of the image of a graph was performed by relating the pixel locations and physical values of the data points. By using Paint, the scanned image of the graph showing the number of observed asteroids (in logarithmic form) with brightness from 9.0 (magnitude) from the book entitled “The System of Minor Planets” by Gunter D. Roth (1962) was opened. The tick marks were recorded as well as their pixel locations. The x-axis which corresponds to the brightness of asteroids began at 9 and end to 17 with an increment of 1. On the other hand, the y-axis of the graph which shows the number of asteroids in logarithmic form started from 0 up to 3.5 with an increment of 0.5. Since the increments in each axis are equal, the difference between the pixel locations of the tick marks must also be the same. However, there are small deviations from what I got using Paint. So, I took the average of the differences of the pixel locations of the tick marks in the x and y axes, noting that for the horizontal axis, the y-coordinates are the same and in the vertical axis, the x-coordinates are equal. The average values for x and y-axis are 72.57 and 74.17, respectively. The ratio between the increment of the physical value of the tick marks and their averaged pixel location difference were taken. This was used to measure the physical value of the points in the graph given their pixel locations.

For the physical value of the data points along the x-axis, the pixel location of each point was subtracted to the x-axis pixel location of (9, 0) since it is the starting point in the horizontal axis. This was then multiplied with the ratio obtained. Finally, 9 was added from the product to account for the starting point of the x-axis. Similar procedure was done to obtain the physical value of the points in the y-axis. However, it must be reminded that in Paint software, the value of the y-axis increases as we go downward (opposite of that in the graph). So, the y-coordinate pixel location of the starting point (9, 0) was subtracted to the pixel location of the point and then multiplied with the ratio obtained. All this computations were done using Microsoft Excel 2007.

The physical x and y values of the data points in the graph were then plotted in Excel. To check whether the obtained physical values matched with that in the scanned image of the graph, the image was overlaid from the plot. This was done by right clicking the plot and choosing “Format Plot Area”. From the dialog box, go to “Fill” and click “Picture of texture fill”. Then, insert the image from the File and then close the dialog box. The scanned image must be cropped properly such that only the graph is being shown for accurate comparison with the reconstructed plot. The last figure shows the scanned image overlaid with the reconstructed plot. It can be seen that the calculated physical values of the data points matched almost perfectly with that from the image.

I would like to acknowledge Mr. Jay Samuel Combinido for giving helpful suggestions in improving my plot and our teachers, Dr. Soriano and Dr. Perez for their assistance. For this activity, I give myself a grade of 8 because there is still very small difference between the scanned image and the reconstructed one.