Preliminary Experiments

To evaluate the performance of the proposed HLAC features of PARCOR images, preliminary experiments of human gestures recognition were performed. The subject sat on a chair in the office. The image sequences were captured as movie files by SGI Indy. The size of the images is $320 \times 240$. Gestures used for the experiments included: (1) yes (shake the head), (2) no (nod the head), (3) important (move the forefinger back and forth), (4) stop (show the palm), (5) up (point the forefinger to up), (6) down (point the forefinger to down), (7) right (point the forefinger to right), (8) left (point the forefinger to left), (9) still (no motion).

In the classification experiments, we used linear discriminant analysis to get new effective features for recognition and neglected the nonuniform changes in the speed of the gesture. New features were constructed by linear combinations of the proposed HLAC features ${\bf x}$ with weights A=[a_ij] and constants ${\bf b}=(b_1,\ldots,b_L)^T$ as

$${\bf y} = A^T {\bf x} + {\bf b}.$$ (8)

The optimal coefficients are determined from the learning data samples so as to optimize a discriminant criterion $J = tr(\hat{\Sigma}_W^{-1}\hat{\Sigma}_B)$, where $\hat{\Sigma}_B$ and $\hat{\Sigma}_W$ are the within-class and between-class covariance matrices defined on ${\bf y}$. The optimal coefficient matrix A is obtained by solving the eigen-equation

$$\Sigma_B A = \Sigma_W A \Lambda \ \ \ (A^T \Sigma_W A =I),$$ (9)

where $\Sigma_B$ and $\Sigma_W$ are the within-class and between-class covariance matrices defined on ${\bf x}$ and $\Lambda$ is a diagonal matrix of eigenvalues.

To identify the class of the gesture, we used a simple classifier which checks the distances from an input vectors ${\bf y}$ to the class mean vectors $\{\bar{{\bf y}}_k\}$ in the discriminant space and classifies the input to such class C_k that gives the shortest distance.