I develop an app which draw a bounding box in pictures of cats. I wonder which color is the fittest for that purpose.
Instead of using a single colour for the border of the bounding box, you could invert the colour underneath the border of the bounding box.
This way you can ensure that there is strong contrast between the bounding box and the surrounding image.
Also as noted by Nathan in the comments:
Note that inversion alone fails miserably for midtones, which change very little (or not at all). This is a perennial problem with tools that use this method. If you go with inversion, you should also attempt to amplify the resulting contrast if you can, and consider handling for colors precisely on the median as a special case.
If necessary, you could apply a hue or grayscale this inverted colour to make it more visually appealing. The important thing is that there's contrast.
This method is commonly used in image editing applications such as Photoshop: