4.4.1.1 Methods

The images were taken from the background data set^4.1 from the `Computational Vision' group at Caltech, Pasadena. The set comprises 396 images of size 223×147 pixels showing indoor and outdoor scenes. To create the training set, 200 windows 10×10 pixels large were cut out at random positions from each of these images. Thus, totally, 79 200 100-dimensional training patterns were created. The background data set also comprises images of size 378×251. Three of them were used for testing.

The local PCA methods used for training, NGPCA, NGPCA-constV, and
MPPCA-ext contained ten units and extracted 50 principal components. The NGPCA parameters were $\rho$(0) = 10.0, $\rho$(t_max) = 0.0001, $\epsilon$(0) = 0.5, $\epsilon$(t_max) = 0.001, and t_max = 400 000. The mixture models were compared, first, to a model using a single unit extracting either 50 or all 100 eigenvectors, but with the same recall algorithm, and, second, to a multi-layer perceptron (MLP). The MLP had 64 input, 30 hidden, and 36 output neurons. The corresponding activation functions were the identity, the sigmoid function, and again the identity. The weights were initialized with random values drawn uniformly from the interval [- 0.1;0.1]. 2 000 steps of resilient propagation (Riedmiller and Braun, 1993) were used for training.

Unless otherwise noted, a center square of size 6×6 pixels defines the output, and the pixels surrounding this square are the input. To illustrate the performance of the recall, 850 such squares were cut out of two test images (figure 4.7), and the abstract RNN completed all of them individually. It was ensured that a two pixels wide border (used as input) remained around each hole. The restored test images were compared to images gained by filling each hole with a color that is the average over all border-pixel gray-values. For quantitative performance tests, 5 000 windows were cut out at random positions from another test image. The mean square error between a recalled window and the corresponding original window was calculated as the average over all output pixels and test windows.