An apparatus for providing current images of a surgical site during a robotically-implemented surgical procedure, comprising: a surgery facility comprising a patient table adapted to receive a patient thereon, a medical imaging device, and a manually-operated surgical robot comprising at least one instrument that is manually operable during a surgical procedure, and a force sensor that detects a force applied by said at least one instrument to anatomy of the patient that is involved in said surgical procedure; a control computer to operate said medical imaging device to acquire 3D data representing a volume of a patient situated on a patient table, said volume comprising anatomy that will be manipulated, during a surgical procedure, by a manually-operated surgical robot; said control computer being configured to reconstruct a 3D image of said volume from said 3D data; said processor being configured to segment a 3D volumetric image of said anatomy from said 3D image of said volume; said processor being configured to automatically determine at least one material property of said anatomy; wherein the apparatus comprises an electronic database in which at least one material property respectively for different anatomical objects is stored, and said processor being configured to access said electronic database to obtain said at least one material property from said database for said anatomy in said segmented volumetric image said processor being configured to bring a coordinate system of said surgical robot into registration with a coordinate system of said medical imaging device; said surgical robot being configured to allow a surgeon to implement said surgical procedure and, in said surgical procedure, manually-operate said surgical robot to apply at least one force to said anatomy that produces a geometrical change of said anatomy; said surgical robot being configured to provide an electronic signal representing said force to said processor and said processor being configured to automatically update the segmented volumetric image of said anatomy, based on said force and said at least one material property of said anatomy, to produce an updated segmented volumetric image of said anatomy that visually shows said change in the geometry of said anatomy; and a display screen in communication with said processor, said processor being configured to display said updated segmented volumetric image of said anatomy in real-time during said surgical procedure at said display screen. a surgery facility comprising a patient table adapted to receive a patient thereon, a medical imaging device, and a manually-operated surgical robot comprising at least one instrument that is manually operable during a surgical procedure, and a force sensor that detects a force applied by said at least one instrument to anatomy of the patient that is involved in said surgical procedure; a control computer to operate said medical imaging device to acquire 3D data representing a volume of a patient situated on a patient table, said volume comprising anatomy that will be manipulated, during a surgical procedure, by a manually-operated surgical robot; said control computer being configured to reconstruct a 3D image of said volume from said 3D data; said processor being configured to segment a 3D volumetric image of said anatomy from said 3D image of said volume; said processor being configured to automatically determine at least one material property of said anatomy; wherein the apparatus comprises an electronic database in which at least one material property respectively for different anatomical objects is stored, and said processor being configured to access said electronic database to obtain said at least one material property from said database for said anatomy in said segmented volumetric image said processor being configured to bring a coordinate system of said surgical robot into registration with a coordinate system of said medical imaging device; said surgical robot being configured to allow a surgeon to implement said surgical procedure and, in said surgical procedure, manually-operate said surgical robot to apply at least one force to said anatomy that produces a geometrical change of said anatomy; said surgical robot being configured to provide an electronic signal representing said force to said processor and said processor being configured to automatically update the segmented volumetric image of said anatomy, based on said force and said at least one material property of said anatomy, to produce an updated segmented volumetric image of said anatomy that visually shows said change in the geometry of said anatomy; and a display screen in communication with said processor, said processor being configured to display said updated segmented volumetric image of said anatomy in real-time during said surgical procedure at said display screen.