For many image-guided interventions there exists a need to compute the registration between preprocedure image(s) and the physical space of the intervention. Real-time intraprocedure imaging such as ultrasound (US) can be used to image the region of interest directly and provide valuable anatomical information for computing this registration. Unfortunately, real-time US images often have poor signal-to-noise ratio and suffer from imaging artefacts. Therefore, registration using US images can be challenging and significant preprocessing is often required to make the registrations robust. In this paper we present a novel technique for computing the image-to-physical registration for minimally invasive cardiac interventions using 3-D US. Our technique uses knowledge of the physics of the US imaging process to reduce the amount of preprocessing required on the 3-D US images. To account for the fact that clinical US images normally undergo significant image processing before being exported from the US machine our optimization scheme allows the parameters of the US imaging model to vary. We validated our technique by computing rigid registrations for 12 cardiac US/magnetic resonance imaging (MRI) datasets acquired from six volunteers and two patients. The technique had mean registration errors of 2.1-4.4 mm, and 75% capture ranges of 5-30 mm. We also demonstrate how the same approach can be used for respiratory motion correction: on 15 datasets acquired from five volunteers the registration errors due to respiratory motion were reduced by 45%-92%.