Logarithmic simulated annealing for computer-assisted x-ray diagnosis

We present a new stochastic learning algorithm and first results of computational experiments on fragments of liver CT images. The algorithm is designed to compute a depth-three threshold circuit, where the first layer is calculated by an extension of the Perceptron algorithm by a special type of simulated annealing. The fragments of CT images are of size 119×119 with eight bit grey levels. From 348 positive (focal liver tumours) and 348 negative examples a number of hypotheses of the type w1x1++wnxn≥ were calculated for n=14161. The threshold functions at levels two and three were determined by computational experiments. The circuit was tested on various sets of 50+50 additional positive and negative examples. For depth-three circuits, we obtained a correct classification of about 97%. The input to the algorithm is derived from the DICOM standard representation of CT images. The simulated annealing procedure employs a logarithmic cooling schedule c(k)=Γ/ ln(k+2), where Γ is a parameter that depends on the underlying configuration space. In our experiments, the parameter Γ is chosen according to estimations of the maximum escape depth from local minima of the associated energy landscape.