Try this:
To unskew the image use a nested div for the image and give it the opposite skew value. So if you had 20deg on the parent then you can give the nested (image) div a skew value of -20deg.
.container {
overflow: hidden;
}
#parallelogram {
width: 150px;
height: 100px;
margin: 0 0 0 -20px;
-webkit-transform: skew(20deg);
-moz-transform: skew(20deg);
-o-transform: skew(20deg);
background: red;
overflow: hidden;
position: relative;
}
.image {
background: url(http://placekitten.com/301/301);
position: absolute;
top: -30px;
left: -30px;
right: -30px;
bottom: -30px;
-webkit-transform: skew(-20deg);
-moz-transform: skew(-20deg);
-o-transform: skew(-20deg);
}
<div class="container">
<div id="parallelogram">
<div class="image"></div>
</div>
</div>
The example: