2.7. Findthefingertips The method used to find the fingertips is the k-curvature al- gorithm. The main idea is for each point P(i) of the con- tour, get the P(i-k) and P(i+k) points, and using these points generate two vectors and calculate the minimum angle they form. The vector are formed by P(i-k) - P(i) and P(i+k) - P(i). If the angle is lesser than an α value, it is a fingertip. The more robust values found were k=22 andα= 40. One of the problems of this algorithm is that it could pro- duce some false positive in the valley between two fingers, because they have similar properties to the fingers. To avoid thisfalsepositive,wecalculatethedistancebetweenthecen- ter of the hand an two points, P(i) and the middle point of P(i-k) and P(i+k). If the distance is greater in the first case, it is fingertip, in other case is valley. Moreovertoimprovetheefficiencyweintroduceaheuris- tic. Each time we deduce that P(i) is a fingertip, the next point weshoulddealwithis not P(i+1),itshouldbeP(i+m), because fingertips are not near to each other. The value of m depends on the size of the contour of the hand, around a 10% of the number of points of the contour seems to be reasonable. Using the Figure 3 (obtained from [TP10]) we can under- stand more clearly how the algorithm works. We have two cases, the firstone try to calculate the angleαthat is formed by the lines P(i+k) - P(i) and P(i-k) - P(i). In this case the angle is around 30º, so the point P(i) it could be a fingertip. But, in the second case we calculate the angle β using he lines P(x+k) - P(x) and P(x-k) - P(x), and the resulting an- gle is equal to 180º more or less, so the point P(x) cannot a fingertip. The value of k in this sample is too small, and we can find more points than we should, so the idea is to find the value k that fits better with the right side of the figure.