Prediction of pixels in an arbitrary region from pixels on the region boundary

Solution of Dirichlet problem is proposed as a method for predicting the pixel values in an arbitrary region from the pixel values on the boundary of the region. Using the actual boundary pixel values as input to the predictor does not necessarily yield the best prediction. A computationally complex method is proposed for 'selecting' the pixel values on the boundary so as to yield an optimal prediction in a least squares sense. An iterative low complexity approximation to this method is also proposed. Experimental results show that both methods provide significant improvements overusing original boundary pixel values for prediction.