In (Lee et al., 2008), the mouth of

In (Lee et al., 2008), the mouth of the fish can be used as a reference point. As long as the leftmost point on the fish is the mouth of the fish (which is generally true for that application) then the turn angle function is rotational invariant, turn angle function always starts from the same reference point of the shape. However, for oyster shape analysis, there is no distinct point that can be used as a reference point. A rotation in the oyster orientation or a different point is used as the starting point for the closed contour causes a horizontal shift in the turn angle function. Fig. 5 illustrates this horizontal shift caused by a starting point change or rotation of the contour. Fig. 5(a) is the turn angle function in the initial orientation. If the oyster rotates by a certain angle or the starting point changes, for example, the 30th point becomes the first point, then the turn angle function shifts left by 30 points as shown in Fig. 5(b).