Please add to the #myImg div (just for the example..) a 100% width :
<img id='myImg' style="width:100%" src=".....">
and add the following css :
#imgDiv{
border: 1px solid red;
min-height:300px;
vertical-align: middle;
#myImg{
position: absolute;
top: 50%;
left:50%;
transform: translate(-50%,-50%);
}
}
#div1{
border: 1px solid blue;
min-height:600px;
}
#div2{
border: 1px solid green;
min-height:400px;
}
#imgDiv{
border: 1px solid red;
min-height:300px;
vertical-align: middle;
}
#myImg{
position: absolute;
top: 50%;
left:50%;
transform: translate(-50%,-50%);
}
#div1{
border: 1px solid blue;
min-height:600px;
}
#div2{
border: 1px solid green;
min-height:400px;
}
<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width">
<link href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/css/bootstrap.min.css" rel="stylesheet"/>
<title>JS Bin</title>
</head>
<body>
<div class='col-md-12 col-sm-12 col-xs-12'>
<div id='imgDiv' class='col-md-2 col-sm-3 col-xs-3'>
<img id='myImg' style="width:100%" src="https://v4-alpha.getbootstrap.com/assets/brand/bootstrap-social.png">
</div>
<div id='div1' class='col-md-7 col-sm-6 col-xs-6'>aaa
</div>
<div id='div2' class='col-md-3 col-sm-3 col-xs-3'>bbb
</div>
</div>
<script src="https://code.jquery.com/jquery.min.js"></script>
<link href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.6/css/bootstrap.min.css" rel="stylesheet" type="text/css" />
<script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/js/bootstrap.min.js"></script>
</body>
</html>