44:12 Y.Yin et al. 8 x”m 0 m m .84m (a)3D contour (b)2D contour by PCA (c)2D contour with re-(d)2D contour with ro- versal tation Fig.14.Contour of characterwritten with left hand:axis mean the projection ofaxis respectively. A & 01D 0 G Fig.15.Relationship between projected axis and plane included angle reference coordinate plane for contour calibration.In the following,we will provide the proof for this intuition. As shown in Figure 15,the plane ABCD and the plane EFGH intersect on line CD (i.e.,EF).For simplification,we use Op to represent one of the three axes(ie..xhaxis,yh-axis,zhaxis),the plane ABCD represents the corresponding plane perpendicular to OP(i.e.,yh-zh plane,xh-zh plane,or xh-yh plane),while EFGH represents the principal plane.To obtain the projection of O P,we first extend the line OP to intersect with EFGH at P',then O P'L CD,because OPL ABCD.Besides,we make the line O1I1 CD,then,we get OI1 CD and OP'L CD,thus CD L AOIP'.From point O1,we make the line 01O',where OO1IP'.Then,we obtain that 01O1 CD and O1O'LIP',thus O1O1 EFGH.Similarly,from point P,we make the line PO2,where PO2 L IP'and PO2//01O'.Therefore,O'Oz is the projection of OP in the principal plane,|O'O2= lO1Pl·sin01. n regard to01and3,01+02=90°，02+03=90°，thus01=03,where3 means the plane in cluded angle between ABCD and EFGH.If3(or 0)is equal to zero,then the plane ABCD is parallel to the plane EFGH,and ABCD will be selected as reference coordinate plane,in what the projected 2D contour has the similar orientation with the 2D contour in the principal plane.In regard to 10021 0=arcsin the length of OP is a fixed value (e.g.a unit),if the projection's length of OP (i.e.,projection of xhaxis,yh-axis,or zh-axis)achieves the minimal value,then (and 03) achieves the minimal value,the plane perpendicular to this axis will be selected as the reference coordinate plane. Therefore,in human-frame,the coordinate plane perpendicular to the axis that has the shortest projection in principal plane will be selected as the reference coordinate plane.In Figure 10(b), Figure 13(b),and Figure 14(b),the shortest projected axis from human-frame is yh-axis,zh-axis, ACM Transactions on Sensor Networks,Vol 15.No.4.Article 44.Publication date:October 2019.44:12 Y. Yin et al. Fig. 14. Contour of character “t” written with left hand; x  h, y h, z h-axis mean the projection of xh, yh, zh-axis, respectively. Fig. 15. Relationship between projected axis and plane included angle. reference coordinate plane for contour calibration. In the following, we will provide the proof for this intuition. As shown in Figure 15, the plane ABCD and the plane EFGH intersect on line CD (i.e., EF ). For simplification, we use −−→O1P to represent one of the three axes (i.e., xh-axis, yh-axis, zh-axis), the plane ABCD represents the corresponding plane perpendicular to −−→O1P (i.e., yh − zh plane, xh − zh plane, or xh − yh plane), while EFGH represents the principal plane. To obtain the projection of O1P, we first extend the line O1P to intersect with EFGH at P , then O1P ⊥ CD, because O1P ⊥ ABCD. Besides, we make the line O1I ⊥ CD, then, we get O1I ⊥ CD and O1P ⊥ CD, thus CD ⊥ O1IP . From point O1, we make the line O1O 1, where O1O 1 ⊥ IP . Then, we obtain that O1O 1 ⊥ CD and O1O 1 ⊥ IP , thus O1O 1 ⊥ EFGH. Similarly, from point P, we make the line PO2, where PO2 ⊥ IP and PO2//O1O 1. Therefore,O 1O2 is the projection ofO1P in the principal plane, |O 1O2 | = |O1P | · sinθ1. In regard to θ1 and θ3, θ1 + θ2 = 90◦, θ2 + θ3 = 90◦, thus θ1 = θ3, where θ3 means the plane in￾cluded angle betweenABCD and EFGH. If θ3 (or θ1) is equal to zero, then the planeABCD is parallel to the plane EFGH, and ABCD will be selected as reference coordinate plane, in what the projected 2D contour has the similar orientation with the 2D contour in the principal plane. In regard to θ1 = arcsin |O 1O2 | |O1P | , the length of O1P is a fixed value (e.g., a unit), if the projection’s length |O 1O2 | of O1P (i.e., projection of xh-axis, yh-axis, or zh-axis) achieves the minimal value, then θ1 (and θ3) achieves the minimal value, the plane perpendicular to this axis will be selected as the reference coordinate plane. Therefore, in human-frame, the coordinate plane perpendicular to the axis that has the shortest projection in principal plane will be selected as the reference coordinate plane. In Figure 10(b), Figure 13(b), and Figure 14(b), the shortest projected axis from human-frame is yh-axis, zh-axis, ACM Transactions on Sensor Networks, Vol. 15, No. 4, Article 44. Publication date: October 2019