A three-dimensional second-derivative surface-detection algorithm for volume determination on SPECT images

Most existing techniques for determining volumes on single-photon-emission computed tomography (SPECT) data employ thresholding, two-dimensional edge detection, or manual delineation of edges. These methods, however, are limited in both accuracy and applicability. In seeking to overcome these limitations, a truly three-dimensional (3D) second-derivative-based algorithm which can be implemented with relative ease has been developed. The method incorporates 3D matrix operators; these are convoluted with the SPECT count data in order to produce a 3D voxel map whose data elements correspond to the second derivative of counts in the image. This map is then searched, a suitable derivative-based edge-defining criterion being applied to each voxel position, in order to locate the derivative surface boundary which defines the volume. Validation is obtained using phantom data from 99Tcm-filled bottles of volumes 200, 580 and 2500 cm3 placed within a body-sized tank containing background activities set to give a range of contrasts between 1.00 and 0.75 (i.e. background 0% to 25%). The performance of the algorithm is encouraging: the volumes of the two larger bottles are determined to within a 3% accuracy without the need for any prior calibration, and the results obtained over all bottle sizes are found to be contrast independent to within approximately 4%.