1. PA2920 SPACECRAFT IMAGING SYSTEMS GROUP S1 Presented by Leon Hicks

2. PROBLEMS: Calibration of the cameras to calculate distances Focal length Actual pixel size

3. To find the factor (or focal length), the offset needs to be measured in number of pixels. The offset should be horizontal and is the measured displacement from one point of the chosen object in the left camera image to the same point of the object in the right camera image (for our experiment the chosen point is the centre cross of a box).

4. tan θ 1 = offset / factor θ 2 = π/2 – θ 1 tan θ 2 = distance / eye seperation →factor = offset / tan(π/2 – tan -1 (distance / eye seperation)) Thus →distance = tan(π/2 – tan -1 (offset / factor)) x eye seperation

5. For the parallel eye seperation of 0.251m; an average factor value of 1013 was found. To confirm this factor value, the focal length was also calculated via a second method of calculation, but similar in that it required the counting of pixels in the offset between the two left and right images. x` l / f = (x + d/2) / z x` r / f = (x – d/2) / z y` l / f = y` r / f = y / z

6. x = d(x` l + x` r ) / 2(x` l – x` r ) y = d(y` l + y` r ) / 2(x` l – x` r ) z = d x f / (x` l – x` r ) Where z is the distance to the object and (x` l – x` r ) is the offset in pixels. Using z = d x f / (x` l – x` r ) the average focal length (f) was valued at 1013 (the same as calculated earlier) Note: the focal length is in terms of pixels rather than a physical measurement.

7. Also, graphs were created to show the relation between offset and the distance. The graph below shows a better trendline in the relation between the logs of the offset and the distance. The equation for this graph line is y = -1.0568x + 4.5297

8. To put our calibrations to the test, we obtained new images of the crossed box at varied distances (which were recorded for comparison), and calculated the distance from the offset value. Offset (pixels) z = d x f / (x` l – x` r )Distance obtained by graph Real measured distance 3520.720.750.70 1891.351.361.25 1401.821.801.63 Its not perfect: Errors have not yet been added, and might allow these results to be acceptable? Further measurements could make for better results? The factor/focal length was a taken average. In truth f decreased with decreasing offset. It is hoped that a pattern may be there so that f could be varied for each calculation of distance. Unfortunately, no such pattern has been found.

9. NEXT - ErrorsErrors More results for calibration and testingMore results for calibration and testing Consideration of other potential methodsConsideration of other potential methods Calculation of heightsCalculation of heights Further work on producing a 3-D stereo effectFurther work on producing a 3-D stereo effect