I'm assuming the UI popup is gray near the border, and the background picture can have areas of various grays including black and white.
The problem is that the contrast between the UI popup and the background varies unpredictably, and can be zero.
Even the whole border of the popup could be adjacent to background of the same gray level, like when the picture shows a gray sky in that area.
Inverted line does not solve it
One way to separate the areas of popup and background would be adding a line of the inverse color of the adjacent background.
But that can fail near 50% gray, when background and inverse are the same or similar.
I propose to use two separating lines, one black, and one white.
Experiment which one should be on the outside. That may be different on the sides, creating a "3D efect".
This image shows the problem case, where the UI popup exterior is light gray on a background that is similar to light gray:
The popup is hard to see because there is not much contrast between it and the background image - that's the problem we want to solve:
Source of background image: Preview image of Wikimedia Commons: Selçuk Turkey 2015.
(Note that a large part of what separates the background and the popup is the direction of edges: the popup has only x and y edges, the photographic background has aproximately none.)
In the image below, I only added a black and white border, 4px wide.
On top and to the left, two white pixels are at the outside, two black at the inside of the frame. The colors are exchanged on the right and bottom edge.
With this, there will always be contrast at the border of the poup.
Because we put it there.
Separate by 3D border
The arrangement of the white and black lines is choosen to match the expectations of our visual system for an embossed edge with light from top left. It results in a typical "3D appearence", which is useful here, because it supports the separation:
Handles low and high contrast
The separation works good for light gray UI and background colors, but see below for a test with darker background colors giving more contrast - there is not much difference, it works just the same: