1:16 Y.Yin et al. each segment,we use velocity compensation to mitigate the computation error of velocity. With the calibrated velocity,we calculate the gesture contour in 3D space by integral.In this way,although the calculated contour can be smaller or larger than the actual contour, it keeps the important contour features (e.g.,shape and orientation),which are essential to recognizing contours as characters,as shown in Fig.10(a)-14(a). 5.2.3 Transforming 3D Contour to 2D Contour.As described in Section 4,we first introduce Principal Component Analysis(PCA)to detect the principal/writing plane of the 3D contour. Then,we calibrate the projected 2D contour in the principal plane through reversing,rotating and normalizing operations.After that,the calibrated 2D contour will be used for character recognition. 5.3 Contour Recognition To recognize the calibrated 2D contours as characters,we utilize the overall space-time distribution in the contour,i.e.,the relative positions among the contour points and the shape changes along with time,to recognize contours as characters.Specifically,we propose an online approach AC-Vec and an offline approach AC-CNN. Vector sequence-based recognition approach:Considering the distribution of con- tour,we first propose a vector sequence-based recognition approach AC-Vec.As shown in Fig.17,we sequentially and evenly select m points in the contour.Suppose the origin of coordinates in the principal plane is(po,ypo),the coordinates of the ith selected point is ()Then,we can get the vector from the origin of coordinates to the ith selected point as nd,=(p-po,p-yp),as shown in Fig.17.By putting the m coordinate vectors in a vector,we can get a feature vector (d.dd)which describes the distribution of the contour in principal plane.After that,we use the feature vector containing 2*m elements to train a classifier (i.e.,Random Forest)for character recognition. Fig.17.The principle of AC-Vec CNN-based recognition approach:As shown in Fig.10(d)-Fig.14(d),we can get the image containing the 2D character contour.With the images containing the calibrated contours,we propose AC-CNN,which utilizes convolutional neural network(CNN)[20]22 to recognize the handwritten character in an image as a letter belonging to'a'z'.The architecture of AC-CNN is shown in Fig.18.Here,the input image containing the 2D contour is 64 64(pixels).To put the time information into the 2D contour,we change the gray levels of points along the contour,i.e.,as time goes,the gray level of a point decreases from 100 to 0,as shown in Fig.18,the contour's color changes from gray to black.Then, the first convolutional layer filters the 64 64 input image with 6 kernels of size 5*5,and followed by 2*2 max-pooling.After that,the second convolutional layer and max-pooling layer perform the similar operations. ACM Trans.Sensor Netw.,Vol.1,No.1,Article 1.Publication date:January 2019.1:16 Y. Yin et al. each segment, we use velocity compensation to mitigate the computation error of velocity. With the calibrated velocity, we calculate the gesture contour in 3D space by integral. In this way, although the calculated contour can be smaller or larger than the actual contour, it keeps the important contour features (e.g., shape and orientation), which are essential to recognizing contours as characters, as shown in Fig. 10(a)-14(a). 5.2.3 Transforming 3D Contour to 2D Contour. As described in Section 4, we first introduce Principal Component Analysis (PCA) to detect the principal/writing plane of the 3D contour. Then, we calibrate the projected 2D contour in the principal plane through reversing, rotating and normalizing operations. After that, the calibrated 2D contour will be used for character recognition. 5.3 Contour Recognition To recognize the calibrated 2D contours as characters, we utilize the overall space-time distribution in the contour, i.e., the relative positions among the contour points and the shape changes along with time, to recognize contours as characters. Specifically, we propose an online approach AC-Vec and an offline approach AC-CNN. Vector sequence-based recognition approach: Considering the distribution of con￾tour, we first propose a vector sequence-based recognition approach AC-Vec. As shown in Fig. 17, we sequentially and evenly select 𝑚 points in the contour. Suppose the origin of coordinates in the principal plane is (𝑥𝑝0 , 𝑦𝑝0 ), the coordinates of the 𝑖th selected point is (𝑥 ′ 𝑝𝑖 , 𝑦′ 𝑝𝑖 ). Then, we can get the vector from the origin of coordinates to the 𝑖th selected point as ⃗𝑛𝑑𝑖 = (𝑥 ′ 𝑝𝑖 − 𝑥𝑝0 , 𝑦′ 𝑝𝑖 − 𝑦𝑝0 ), as shown in Fig. 17. By putting the 𝑚 coordinate vectors in a vector, we can get a feature vector (⃗𝑛𝑑1 , ⃗𝑛𝑑2 , . . . , ⃗𝑛𝑑𝑚−1 , ⃗𝑛𝑑𝑚) which describes the distribution of the contour in principal plane. After that, we use the feature vector containing 2 * 𝑚 elements to train a classifier (i.e., Random Forest) for character recognition. + 1 d n 2 d n 3 d n 4 d n m d n m-1 d n xp -axis yp -axis Fig. 17. The principle of AC-Vec CNN-based recognition approach: As shown in Fig. 10(d)-Fig. 14(d), we can get the image containing the 2D character contour. With the images containing the calibrated contours, we propose AC-CNN, which utilizes convolutional neural network (CNN) [20][22] to recognize the handwritten character in an image as a letter belonging to ‘a’-‘z’. The architecture of AC-CNN is shown in Fig. 18. Here, the input image containing the 2D contour is 64 * 64 (pixels). To put the time information into the 2D contour, we change the gray levels of points along the contour, i.e., as time goes, the gray level of a point decreases from 100 to 0, as shown in Fig. 18, the contour’s color changes from gray to black. Then, the first convolutional layer filters the 64 * 64 input image with 6 kernels of size 5 * 5, and followed by 2 * 2 max-pooling. After that, the second convolutional layer and max-pooling layer perform the similar operations. ACM Trans. Sensor Netw., Vol. 1, No. 1, Article 1. Publication date: January 2019