tector data as inputs to the ANS neurons.
In accordance with the second variation of the ANS-based detection system, "features" are developed from the detector signals as described above. These features comprise the input signals to the ANS. A diagram of a preferred ANS used with this variation is shown in FIG. 8. This ANS comprises a three-layer, fully connected, feedforward network. The network includes a first layer (input layer) of neurons (or PE's) 120. This input layer receives a set of pre-computed feature vectors from the explosive detection system that have been normalized to gray scale values between -0.5 and +0.5. A middle layer (hidden layer) of neurons 122 learns to encode features that are not explicitly present in the input patterns. A last layer (output layer) of neurons 124 produces a gray scale value that can be compared to a threshold to obtain a decision. The output layer is coded with +0.5 if the object being examined contains an explosive threat, and -0.5 if it does not. While the steps of computing and developing such "features" for use with this second variation may consume a noticeable amount of time, once a set of features has been developed, the number of input neurons for the ANS can be significantly reduced, and the complexity of the ANS network can be greatly simplified, over that which would be required if the first variation were used (raw detector data connected directly to the input neurons of the ANS).
Advantageously, by using the network shown in FIG. 8, no preclassification (large, small, etc.) of the objects, such as is used in the discriminant analysis approach, is required. The list of features fed into the network may include all those that are used with the discriminant functions, which features may include some which have significant collinearity. Training of the network is accomplished by presenting a training data set to the network over and over again, at a relatively low learning rate. Advantageously, such training can occur with only minimal human supervision. Back Propagation (BP) is used as the paradigm of learning for the system. BP is based on the generalized delta rule, mentioned above, and is well documented in the art. Essentially, this rule is a steepest descent method of computing the interconnection weights between neurons of the ANS that minimizes the total squared output error over a set of training vectors. Evaluation of the effectiveness of the ANS network may be judged by simply observing the residual error (as the network can be expected to make errors and have false positives), and/or by simply measuring the PD and PFA rates for a test set of objects.
A performance comparison between an explosive detection system using the discriminant analysis approach and one using an ANS trained by the BP technique is depicted in FIG. 9. The performance of both techniques is evaluated on a test set of objects that is different from the training set. Since the outputs of both techniques produce gray scale values, different thresholds can be applied to get different performance points on the PD PFA tradeoff curve. Each curve in FIG. 9 was generated by changing the thresholds for the decision over the applicable range.
FIG. 9 clearly shows that the ANS approach performs better than the discriminant analysis approach for false alarm rates greater than 1.75%. For example, at the operating point of 95% detection (which is a typical operating point for a viable explosive detection system), the ANS reduces the false alarm rate by around 1.5-2.0%. Advantageously, for an explosive detection system having a high throughput of objects, this results in substantially fewer objects having to be scanned or checked by secondary techniques. At slightly higher detection rates, e.g., 96%, the ANS reduces the difference between the PFA rates still further (even though the value of the PFA goes up for both approaches).
One advantage offered by the BP-trained ANS network over the discriminant analysis approach is that ANS takes relatively less human supervision. As noted above, calibration of 