THE STAGES OF THE DETECTION SYSTEM

9.3.1 Stage 1; template selection

The image regions with the highest SNR^n and the greatest probability of being matched are those with the largest variance. Accordingly, the templates used by the system are located by processing the later image to detect the regions of highest variance and then selecting the templates from sites at the same regions in the original unprocessed image.

The variance detection method consists of applying a two-dimensional gradient operator to the later image to produce a gradient map which is then thresholded to reveal the regions of greatest local variance. Because it is important to avoid detecting regions with a high local variance due to noise rather than signal, the Sobel gradient operator (Kittler, 1983) was used followed by a median threshold to select the regions of greatest local variance. The Sobel gradient operator is a differential gradient operator which is convolved with the image to produce a new image whose pixels have a grey level that is proportional to the local variance or gradient across the surrounding eight pixels.

9.3.2 stage 2: high probability detection

The decorrelator produces images with inherently high variance which allows very precise localisation of the peak. Unfortunately, there is a greater probability of detecting a false-match with high variance data than with low variance data (Knapp and Carter, 1974). Thus, where a match is sought over an area of 12 mm x 12 mm at a pixel size of 0.13 mm x 0.13 mm, 5976 cross-correlation values will be obtained. Consequently, even if the probability of detecting a false peak which exceeds the height of the true peak is only one-in-a-thousand, on average a wrong peak will be located almost six times as often as the true peak.

The second stage of the detection system is designed to avoid this problem by searching for a match without decorrelating the images. Thus, the detection search in the second stage is conducted with lower variance images which, although they provide a low probability of detecting a false match, can only provide an approximate location for the match in the presence of noise.

detection system, a threshold was set for the acceptance of the peak as indicating a true match. The threshold was chosen such that only rarely does a peak value obtained from an incorrect match reach above this threshold, giving rise to a false match.

The threshold can be determined from theoretical considerations if the probability density functions of correct and incorrect outputs are known or assumed. However, in the absence of previous studies on detection of structures in bone the threshold was determined empirically. This was done by measuring the distribution of the correlations between the template and the regions surrounding the true peak and is reported in Appendix F. Using the results of that experiment, the thresholds were set at p = 0.68 and p = 0 .7 5 for the mandible and maxilla respectively.

9.3.2 stage 3: decorrelation of the template and search region

The third stage of the detection system involves the decorrelation of the template and search region for which a match has been detected in the previous stage. The decorrelation is carried out by passing the images through the decorrelator. That is, by convolving the decorrelator impulse response array with each image in turn. However, this involves two problems.

The first problem is one of unfiltered noise. Despite the initial noise filtering provided as the radiographs were converted to digital signals, some residual noise will inevitably remain. Electric-line noise and quantum noise have largely high frequency components which are amplified during decorrelation because the decorrelation operation accentuates the highest frequency components of the images. The result is a differential amplification of noise which tends to overwhelm the image signals. To tackle this problem, the high frequency noise must be suppressed prior to decorrelation. This is achieved by convolving the data from the template and search region with a Gaussian impulse response array, which has the effect of replacing each pixel in the images with a Gaussian weighted sum of the eight surrounding pixels.

Secondly, as explained in section 3.4.3., spatial domain convolution leads to a band of pixels with spurious values at the border of the decorrelated (output) image, half the width of the impulse response array wide. To overcome this "border effect" the convolution operation is only computed when the impulse response array is contained fully within the confines of the input image. Thus, the output image will be smaller than

the convolution is conducted over an image area larger than the ultimate search region and template; from which the search region and template are then extracted leaving the spurious pixels behind.

9.3.4 stage 4: accurately locate the site of match

The fourth stage of the detection system is required to provide the accurate location of the matching structure in the earlier image. The accurate location is carried out using the decorrelated versions of the template and search region for which a match has been detected and approximately located in stage two. However, this search is conducted over a much smaller region around the location of the cross-correlation peak found in stage two. Because the true peak has been approximately located the size of search area can be reduced to an area just greater than the error of location in stage two. This error is described by the correlation length which is variously defined as the standard deviation of the width of the ACF (Mostavi and Smith, 1978b) or full-width at half-maximum height (FWHM) of the ACF (Bogler, 1986). For an exponentially declining ACF the second definition in more useful. However, in practice, the two values will be similar.

The FWHM correlation length for screen/film radiographs of bone was estimated using the data derived in section 8.2.2.4. The maximum FWHM of the ACF found was 7 pixels (mean and median 4 pixels). Accordingly, to be confident of locating the true peak the search in the third stage of the detection system was set at 15 pixels on either side o f the peak detected in stage 2.