How about some more details.
In order to make the TCMs the spacecraft needs to determine quite accurately both its position and velocity.
I can understand how the apparent position of the stars will allow for determination of the orientation of the craft relative to the relatively fixed coordinate system of the stars.
The apparent positions of the planets would allow for the position to be determined. Tracking the position over time allows for the velocity to be determined; that is, both the direction of travel and the speed.
Does the typical spacecraft use a telescope to determine the positions of objects in its field of view? The stars will appear as single points. Does the craft use the edges of the planets when its proximity to them permits it?
The craft would need to find many points to verify its position and velocity. Does the craft use a mechanical system to measure the angles for a particular position of the telescope relative to the body of the craft?
I actually attempted to determine this information from a person involved in these space missions but I found his answer far too minimal and didn't want to embarrass him by finding that perhaps he didn't know the details.
The position and velocity of crafts is computed almost always on Earth. We use Doppler, radio interferometry and a host of other physics and maths tricks to get the position and velocity. Most of these procedures use the radio signals that these crafts send back to Earth.
The computers we send in space are programmed purposefully for the science mission and it would be far to wasteful to load them up with the heavy computations needed for obtaining a celestial navigation fix.
When these ships have cameras they are usually protected with entry shields and/or folded away during the cruise stage.
If a ship has navigation cameras, pictures are taken of planets and stars (like you theorized) but they are sent back to Earth for processing. Due to the limitations of imaging sensors if you want to see the planet’s edge the stars don’t show up. If you want to see the stars the planet is overexposed and looks like a white orb. Back on earth that can be processed and a precise fix can be calculated.