Matrix-array ultrasound is a new medical imaging modality that steers an ultrasound beam electronically in three dimensions. It is the first imaging modality that can view the heart in 3D in real time, making possible the `volumetricardiogram,' i.e., continuous beat to beat measurement of cardiac chamber volume. To create a fully automatic real-time volumetricardiogram, we have developed the flow integration transform (FIT), which operates on 2D images produced by slicing through the 3D ultrasound data. Although lacking rotational or scale invariance, the FIT is designed to operate eventually in dedicated hardware at very high speed, permitting the application of a large battery of test shapes within the period of a single ultrasound frame (approximately 45 milliseconds). To test the FIT, we have volumetrically scanned a series of 21 fluid-filled balloons. We used the FIT to detect circular cross-sections of the balloons by applying a battery of circles over a range of radii. The detected circles were used to compute volumes, which were then compared to volumes determined independently by weight. Our results are encouraging towards further development of this completely automated method of volume determination.