PARCOR images

Since an image can be viewed as a set of pixel values $\{I_{<x,y>}\}$, a time sequence of images can be regarded as a set of time sequences of pixel values $\{I_{<x,y>}(t)\}$. Let $\bar{I}_{<x,y>}$ be average value of the sequence of pixel values I_<x,y>(t). By applying a linear AR model to each of the sequence of pixel values $I_{<x,y>}(t) - \bar{I}_{<x,y>}$, we can compute PARCOR coefficients P^m_<x,y>, where m is the order of the AR model. By rearranging the PARCOR coefficients P^m_<x,y> as an image, we can obtain PARCOR image of the order m. Fig.1 shows snapshots of a image sequence and its first order PARCOR image.

In general, by increasing the order of AR models, the mean squared errors for the learning samples decrease, but the generalization ability of the learned model also decreases. Thus we have to select a proper order of AR models. For each sequence of pixel values, we determined the order of AR model by checking the prediction error residual. If the prediction error residual is less than a threshold, then the PARCOR coefficients greater than that order are set to zero. Then PARCOR coefficients for stationary regions such as background become 0. This means that HLAC features extracted from PARCOR images do not change even if the background is changed. This property is good for gesture recognition. PARCOR coefficients in non-stationary regions have values between -1 to 1.

  

Figure 1: Some images in a image sequence and its first order PARCOR image.