$$p_j^t = [ x_j^t y_j^t ]'$$ $$[ x_j^t y_j^t ]'$$ denotes the transposed vector of 2D coordinates in the image of a body joint j from a set of joints J (Fig. 1); t denotes the frame number
$$P^t(j_1,j_2) = p^t_{j_2} - p^t_{j_1} = [ x^t_{j_2} - x^t_{j_1} y^t_{j_2} - y^t_{j_1} ]'$$ Vector directed from joint $$j_1$$ to joint $$j_2$$
$$\Vert P^t(j_1,j_2)\Vert$$ $$d^t(j_1,j_2) = \Vert p_{j_1}^t - p_{j_2}^t \Vert$$ $$\Vert P^t(j_1,j_2)\Vert$$ is the euclidean norm of vector $$P^t(j_1,j_2)$$ and, alternatively, $$d^t(j_1,j_2)$$ is the euclidean distance between two selected joints, $$j_1$$ and $$j_2$$
$$\Delta x^t(j_1,j_2) = x^t_{j_1} - x^t_{j_2}$$ $$\Delta y^t(j_1,j_2) = y^t_{j_1} - y^t_{j_2}$$ Displacement between two selected joints, $$j_1$$ and $$j_2$$, in the X ($$\Delta x$$) and Y ($$\Delta y$$) axis
$$a^t(j_1,j_2,j_3) = \arccos \bigg ( \frac{P^t(j_2,j_1) \cdot P^t(j_2,j_3)}{\Vert P^t(j_2,j_1) \Vert \cdot \Vert P^t(j_2,j_3) \Vert } \bigg )$$ Angle between two vectors, $$P^t(j_2,j_1)$$ and $$P^t(j_2,j_3)$$, defined by two points, $$j_2$$ to $$j_1$$ and $$j_2$$ to $$j_3$$ 