A robotic production system uses a camera to identify the edge of machine parts. It does this to

ensure the quality control of the production line. Two things need to be measured accurately: the

position of the edge of the piece and the angle of the edge. A small region of the image is shown in

Figure Q$3$a$).$ Note it contains some noise.

i$)$ From the formula sheet provided select a suitable edge detection method. Justify your

choice. $[2$ marks$]$

ii$)$ Calculate the magnitude of the edge along row $3.$ Ignore the edge of the image where the

edge cannot be calculated. $[3$ marks$]$

iii$)$ Calculate the angle of the first edge found in row $3.$ Ignore the edge of the image where

the edge cannot be calculated. $[3$ marks$]$

iv$)$ An alternative method would be to calculate the $2$nd order moment of the image by

thresholding the image such that all pixels above the threshold $0\mathrm{.}5$ are $1\mathrm{.}0$ and all pixel

below the threshold are $0\mathrm{.}0.$ Calculate the angle of the object using this method.

$[6$ marks$]$

v$)$ Explain why the results are slightly different. $[2$ marks$]$