Digital Scanning

Digital Scanning

RESULTS

Figure 1. Scanned Hand draw graph.

Data from the hand drawn graph can be extracted by the use information taken from the positions of the pixels where data points are located. By the use of ratio and proportion, one can reconstruct the hand drawn graph and retrieve the values of the data points. For a scanned image, a pixel has an X and Y position, however, the positions of its (0,0) is not at the bottom left edge but at the upper left edge. Due to this the computation for the Y value is not just a simple ratio and proportion but we must include the difference in the orientation of the coordinate systems.

After taking the pixel positions of each data point, we must also get the positions of the axis ticks and the position of the graph edge. For this graph it is the value (10 degrees Celsius, 25 seconds). It is important to take the edge of the graphs since it is the graph values that you are scaling and not the image itself. Extra spaces in the graph if not considered may include errors in the computation of the values. After taking the positions of the tick marks in the axes and knowing the tick length from the original graph, one can calculate the constant of proportionality for X, Y by subtracting the pixel positions of consecutive tick marks. Divide the tick length by this value and you will obtain the proportionality constant (physical value / pixel).

In calculating the values of the data points from pixel positions. For the x position, we must first subtract the x position of the graph edge to the x pixel position of the data point,then multiply the result to the x proportionality constant, then add x value(physical value) of the graph edge. For the y position, we must first subtract the y pixel position of the data point to the y position of the graph edge, then we can proceed with multiplying the constant and the addition of the y initial value.

X proportionality constant: 0.043796

Y proportionality constant: 0.088496

X graph edge position: 259

Y graph edge position: 1073

X initial value: 10

Y initial value: 25

Equations:

Xval = ((Xpos - Xgraphedge) * Xconst) + Xin

Yval = ((Ygraphedge - Ypos) * Yconst) + Yin

Figure 2: Reconstructed graph from pixel information

The reconstructed graph shows that hand drawn graphs can be reconstructed using pixel position values.

Figure 3: Overlaying of the Hand drawn graph and the reconstructed graph

The overlaying of the two graphs shows that the pixel value information can be used to retrieve information about the data point on the graph by simple ratio and proportion. The graph shows that all computed data points coincide with those of the hand drawn graph. However the trend-line of the graphs did not coincide since both graphs used different fitting techniques. The reconstructed graph used error minimization techniques to form the fit, while the hand drawn graph used a French curve to make the line smoother compared to connect-the-dots technique.