Try using CSS-Tricks’ Infinite Borders technique and applying border-radius.
This method will require borders and box-shadow and not outline.

img {
border-radius: 4px;
/* #1 */
border: 5px solid hsl(0, 0%, 40%);
/* #2 */
padding: 5px;
background: hsl(0, 0%, 20%);
/* #3
outline: 5px solid hsl(0, 0%, 60%); */
/* #4 AND INFINITY!!! (CSS3 only) */
box-shadow:
0 0 0 10px red,
0 0 0 15px orange,
0 0 0 20px yellow,
0 0 0 25px green,
0 0 0 30px blue;
/* If you could do pseudo elements
you could get a few more... */
/* Also, HSL is awesome but don't use it if
you need super old browser support */
}
body { padding: 50px; text-align: center; }
<img src="https://www.randomlists.com/img/animals/chipmunk.jpg">