There is an increasing interest in the applications of 3D ultrasound imaging of the pelvic floor to improve the diagnosis, treatment, and surgical planning of female pelvic floor dysfunction (PFD). Pelvic floor biometrics are obtained on an oblique image plane known as the plane of minimal hiatal dimensions (PMHD). Identifying this plane requires the detection of two anatomical landmarks, the pubic symphysis and anorectal angle. The manual detection of the anatomical landmarks and the PMHD in 3D pelvic ultrasound requires expert knowledge of the pelvic floor anatomy, and is challenging, time-consuming, and subject to human error. These challenges have hindered the adoption of such quantitative analysis in the clinic. This work presents an automatic approach to identify the anatomical landmarks and extract the PMHD from 3D pelvic ultrasound volumes. To demonstrate clinical utility and a complete automated clinical task, an automatic segmentation of the levator-ani muscle on the extracted PMHD images was also performed. Experiments using 73 test images of patients during a pelvic muscle resting state showed that this algorithm has the capability to accurately identify the PMHD with an average Dice of 0.89 and an average mean boundary distance of 2.25mm. Further evaluation of the PMHD detection algorithm using 35 images of patients performing pelvic muscle contraction resulted in an average Dice of 0.88 and an average mean boundary distance of 2.75mm. This work had the potential to pave the way towards the adoption of ultrasound in the clinic and development of personalized treatment for PFD.