Exercise 1 : How many pixels per hole? Consider the application of counting holes in truck crossbars at a more detailed level. Suppose that the area of the crossbar that is imaged is 50 inches long and 10 inches wide and suppose that this area almost fills up digital image of 100 rows and 500 columns pixels.
Suppose a particular bolt hole in the crossbar is 1/2 inch in diameter. What would you expect the radius and area of its image to be in terms of pixels?
Exercise 2: Imaging coins as pixels. This problem is related to the one above. Obtain some graph paper (0.25 inch squares would be good) and a quarter. Randomly place the quarter on the graph paper and trace its circumference: do this five times.
For each of the five placements, estimate the area of the image of the quarter in pixel units (a) by deciding whether a pixel is part of the quarter or not (no fractions) and (b) for each pixel cut by the circumference, estimate to the nearest tenth of a pixel how much of the pixel is part of the image of the quarter. After doing these measurements, compute the mean and standard deviation of the image area separately for methods (a) and (b).