What physical process governs which details are retained in memory? With long term memory, there is loss of information. For example, we don't seem to retain all the details of every image we see. What is the physical process those details undergo which cause them to be retained over the ones that are not, and what is the mechanism that "chooses" which information undergoes that process?
I think this question is not getting answered because it suggests a misunderstanding or lack of understanding about all the forces leading up to your specific question about long term memory. For instance, you imply that we see images in detail to begin with—or that we are able to 'store' a detailed image in short term memory... and that detail simply does not get transferred to long-term memory. 

Obviously, humans are still far off from fully understanding how memory functions. We can make some statements about your question now, though. To begin, when we see images, we are not seeing everything—we are only seeing precisely what we are looking at (or focusing on), then our brain is filling in the rest of the information. We think that we see the world pretty clearly; however, this is a combination of our brains ability to fill in missing information with what it expects, and our eyes' ability to rapidly scan its environment—quickly changing focus in order to paint your world (see: saccadic eye movements).

These images, that are intimately connected with the other senses and emotions which are firing at the same time in the brain, are dull from the start. The vividity with which we can recall these images can be considered a function of how impactful the event was on our lives. Like all functions in our bodies, long-term memory is a product of evolution. This implies a likelihood the moments which are most important to remember for our survival and procreation are the ones we can recall most vividly. Did you almost die? Was it your first kiss? Additionally, especially novel moments are remembered well. Were you at the beach for the first time, never having smelled the salt air before?

Moving beyond the question of the vividness of long term memory, we may consider the notion that are long-term memories are actually mutable. Each moment of recall is a moment of re-storing that memory; it is like copying a copy.