1:10 Y.Yin et al. As shown in Fig.9(a),the black line and the green line respectively mean the first basis vector wi and the second basis vector w2,while the red plane containing wi and w2 is the detected principal plane.In the principal plane,we can obtain the projected 2D contour, as shown in Fig.9(b).However,due to the information loss of dimensionality reduction, there may exist the problems like reversal and skew of the projected contour,which needs a further calibration.It is worth mentioning that lowercase letters are different from capital letters,the shapes of different lowercase letters observed from different viewing angles can be similar,e.g.,'b'and'q','d'and 'p',thus the orientation and writing order of a character are both important for lowercase letter recognition.It is essential to calibrate the projected 2D contour in right orientation and normalized size under a uniform view for character recognition. 0.2 02 n" -0.2 0.2 02 m022 02 m -02 x.m) 0.2 (a)3D contour (b)Projected contour Fig.9.Relationship between contours and principal plane 4.2 Reference Coordinate Plane Detection According to Section 4.1 and Fig.9,the projected 2D contour in the principal plane has a high probability of keeping the shape feature of the in-air contour,while still having the problems like reversal and skew,i.e.,the orientation of the contour is changed.Thus we need to calibrate the 2D contour in the principal plane.To achieve this goal,we detect the reference coordinate plane and determine the viewing angle at first.Here,the reference coordinate plane is used to indicate the viewing angle and possible orientation of the projected contour in the principal plane.In regard to the user,she/he can perform the gesture towards arbitrary directions,the writing plane may be not parallel to any coordinate plane. 0 02 82 4m0202 m) m m (a)3D contour (b)2D contour by PCA (c)2D contour with re-(d)2D contour with ro- versal tation Fig.10.Contour of character'm'written with right hand,h z-axis mean the projection of ch. yh,Zh-axis,respectively ACM Trans.Sensor Netw.,Vol.1,No.1,Article 1.Publication date:January 2019.1:10 Y. Yin et al. As shown in Fig. 9(a), the black line and the green line respectively mean the first basis vector 𝜔1 and the second basis vector 𝜔2, while the red plane containing 𝜔1 and 𝜔2 is the detected principal plane. In the principal plane, we can obtain the projected 2D contour, as shown in Fig. 9(b). However, due to the information loss of dimensionality reduction, there may exist the problems like reversal and skew of the projected contour, which needs a further calibration. It is worth mentioning that lowercase letters are different from capital letters, the shapes of different lowercase letters observed from different viewing angles can be similar, e.g., ‘b’ and ‘q’, ‘d’ and ‘p’, thus the orientation and writing order of a character are both important for lowercase letter recognition. It is essential to calibrate the projected 2D contour in right orientation and normalized size under a uniform view for character recognition. (a) 3D contour (b) Projected contour Fig. 9. Relationship between contours and principal plane 4.2 Reference Coordinate Plane Detection According to Section 4.1 and Fig. 9, the projected 2D contour in the principal plane has a high probability of keeping the shape feature of the in-air contour, while still having the problems like reversal and skew, i.e., the orientation of the contour is changed. Thus we need to calibrate the 2D contour in the principal plane. To achieve this goal, we detect the reference coordinate plane and determine the viewing angle at first. Here, the reference coordinate plane is used to indicate the viewing angle and possible orientation of the projected contour in the principal plane. In regard to the user, she/he can perform the gesture towards arbitrary directions, the writing plane may be not parallel to any coordinate plane. (a) 3D contour (b) 2D contour by PCA (c) 2D contour with re￾versal (d) 2D contour with ro￾tation Fig. 10. Contour of character ‘m’ written with right hand, 𝑥 ′ ℎ, 𝑦 ′ ℎ, 𝑧 ′ ℎ-axis mean the projection of 𝑥ℎ, 𝑦ℎ, 𝑧ℎ-axis, respectively ACM Trans. Sensor Netw., Vol. 1, No. 1, Article 1. Publication date: January 2019