Accurate Three-Dimensional Instrument Positioning

A system comprising:

• a three-dimensional image sensor configured to scan a closed or partially closed container;
• an output display;
• and
• a computing device communicatively coupled to the three-dimensional image sensor and the output display, wherein the computing device includes a processor and data storage, and wherein instructions stored in the data storage are executable by the processor to perform operations including:
• recognizing an instrument that is detected by the three-dimensional image sensor, wherein a first section of the instrument is located inside of the container and a second section of the instrument is located outside of the container, and
• representing, on the output display, three-dimensional positions and orientations of the instrument, wherein a first position and a first orientation of the first section of the instrument is inferred from a second position and a second orientation of the second section of the instrument.