The resolution integral is a figure of merit that characterizes ultrasound images in terms of the ratio of the penetration of an ultrasound beam in soft tissue to the ultrasound beam width. This concept has been implemented using a novel tissue mimicking test object (the Edinburgh pipe phantom) that comprises a series of anechoic cylinders of different diameters embedded in a block of tissue-mimicking material. The resolution integral is calculated by imaging each cylinder in turn and measuring the depth range over which it can be detected. We have carried out these measurements using two complementary approaches: by visual assessment and using a computational approach. Data were collected from 12 transducers used on 12 different models of ultrasound scanner of various makes, ages and clinical performance. Transducer centre frequencies were in the range of 3 to 7.5 MHz. The computational approach makes use of standard image processing techniques to detect and segment anechoic structures in images of the test object. This was optimized against visual assessment results for one of the transducers, and subsequently used to evaluate the resolution integral for the others. The values of the resolution integral ranged from 40 to 69 and computed values were within +/- 11% of the corresponding visual assessments. The repeatability of both approaches was +/- 2-3%. The computational approach functions well compared to visual assessment and adds to the overall robustness of resolution integral measurements by providing an objective assessment algorithm.