\chapter{Results} \label{ch:result} During the training sessions, we have recorded five static gestures in 4 different positions in front of the robot. NAO is equipped with Asus Xtion and set in "Stand" posture. Head pitch of NAO is set to -18 degrees to look at the upper body of the user 1800 mm away from the sensor. First 3 positions of training are recorded at 1800 mm distance from the sensor in z axis and + /- 800 mm in x axis. Last training position is recorded at 2200 mm distance. Therefore, training data is recorded for 80 seconds of each gesture.

In this chapter, we present the results of real time hand gesture recognition for Human-robot interaction based on skeletal points tracking using depth camera. Training data for 5 classes with 11918 samples of 6 dimensional vector are trained with Adaptive Naive Bayes Classifier. Min-Max scaling and Null Rejection with coefficient of 2.0 are enabled. Following sections illustrates the results of end-to-end interaction with robot using five gestures named as Walk, Turn Right, Turn Left, Move Right, Move Left gestures which are represented by the class labels 1,2,3,4,5 respectively.


\section{Gesture-To-Motion Results} 
Following sections shows that NAO is looking at the user to detect any possible gestures. When it recognized the gesture, Command module commands the robot to execute the appropriate Gesture-To-Motion task. Additionally, results shows the normalized x, y positions of left and right. It is plotted using 60 input samples of the detected gesture. Finally, Control Center displays the prediction results and detected gesture with x,y,z positions of left and right hand in 3D.

\input{chapter/figures/res-walk}
\input{chapter/figures/res-turn-right}
\input{chapter/figures/res-turn-left}
\input{chapter/figures/res-move-right}
\input{chapter/figures/res-move-left}

\clearpage
\section{Gesture-To-Gesture} Figure \ref{res:gg} shows how human hand gestures are translated to robotic hand gestures. When a gesture is detected, the Command module sets the predefined angles to the shoulder and elbow joints of both the hands of NAO to perform Gesture-To-Gesture translation. 

\input{chapter/figures/res-gg}

\section{Evaluation} In this section, we present the experiments carried out to evaluate and validate our system to recognize hand gestures using skeletal points. The goal is to demonstrate the effectiveness of the classifier and to evaluate its potential for real time prediction. In the classification phase, input samples are normalized using Min-Max Scaling and Null Rejection is enabled to detect non-gestures. Therefore, the evaluation demonstrates the prediction accuracy of ANBC with various null rejection coefficient and the comparison it with other supervised learning classifier such as Minimum Distance (MinDist).

\input{chapter/tables/ev-mean-sd}

\subsection{Mean and Standard Deviation} During the training phase, first all the input samples are normalized with the range from 0 to 1 and then GRT computes mean $\mu$ and standard deviation $\sigma$ to create a model for each class. During the prediction phase, it basically computes the maximum a posterior probability of an input vector belonging to any of the trained class. Figure \ref{fg:ev:mean} shows the mean positions of left and right hand for every gesture. Table \ref{tb:ev:mean} and \ref{tb:ev:sd} show mean and standard deviations of the labeled training data of all the five classes. 

\input{chapter/figures/ev-all-ges-mean} 

\subsection{Classification and Prediction} Our gesture recognition pipeline is trained with 11918 input samples of 6 dimensional vector for 5 classes. Classes are labeled as 1,2,3,4,5 and they represent Walk, Turn Right, Turn Left, Move Right, Move Left gestures respectively. Class label 0 is reserved for non-gesture by GRT. We have carried out experiments to evaluate the classification, prediction and post processing efficiency of our system. Figure \ref{ev:test:prediction} show change is positions of left and hand in Cartesian coordinates while test data is recorded and corresponding prediction for every input sample.

Test dataset is a 10\% of training dataset and it is chosen randomly from class. Test dataset is validated against the remaining training dataset, therefore, Precision, Recall, F-Measure and Confusion Matrix are computed. Table \ref{tb:ev:metrics} and \ref{tb:ev:confusion} show the results of prediction using ANBC with null rejection coefficient 2.0. Figure \ref{ev:test:prediction} shows the plot of normalized distances of x,y,z axes of both hands from the test data and their prediction in real time.

\input{chapter/tables/ev-confusion} 

\subsection{Prediction Accuracy Vs Null Rejection Accuracy} \label{sec:ev:accuracy} Classifiers of GRT offers various customization that could produce different results for the same test data. Accuracy of a gesture recognition system does not depend only on th precise predictions of trained gestures, but also differentiating them from unintended hand gestures. GRT allows us to set null rejection coefficient for the classifier. Evaluation results are obtained by computing accuracies of 5 trained gestures using ANBC with varying null rejection coefficient from 0 to 10.

Figure \ref{ev:accuracy:anbc} shows that increase in null rejection coefficient causes an increase in the accuracy of trained gestures, however, causes a decrease in the accuracy of non-gesture. Therefore, it is optimal to use a null rejection coefficient of 2.0 with ANBC.

Figure \ref{ev:accuracy:mindist} shows some interesting results of Minimum Distance classifier with 4 clusters. Figure shows that prediction results are unpredictable as there is increase in null rejection coefficient. However, it produces accuracy above 95\% with null rejection coefficient from 2.0 till 4.0. This shows that MinDist could be a better alternative to ANBC. 

\input{chapter/figures/ev-test-all} 
\input{chapter/figures/ev-accuracy}

