.center-cropped {
  width: 100px;
  height: 100px;
  background-position: center center;
  background-repeat: no-repeat;
}

<div class="center-cropped" 
     style="background-image: url('http://placehold.it/200x200');">
</div>

.center-cropped {
  width: 100px;
  height: 100px;
  background-position: center center;
  background-repeat: no-repeat;
  overflow: hidden;
}

/* Set the image to fill its parent and make transparent */
.center-cropped img {
  min-height: 100%;
  min-width: 100%;
  /* IE 8 */
  -ms-filter: "progid:DXImageTransform.Microsoft.Alpha(Opacity=0)";
  /* IE 5-7 */
  filter: alpha(opacity=0);
  /* modern browsers */
  opacity: 0;
}

<div class="center-cropped" 
     style="background-image: url('http://placehold.it/200x200');">
  <img src="http://placehold.it/200x200" />
</div>

.center-cropped {
  object-fit: none; /* Do not scale the image */
  object-position: center; /* Center the image within the element */
  height: 100px;
  width: 100px;
}

<img class="center-cropped" src="http://placehold.it/200x200" />