Nivo Slider custom height/width problems

I have searched for a resolution to my problem, but have not yet been successful.

I have images of different sizes in Nivo Slider, but I need to create a viewport that displays the image centered in a div. It's hard to explain, but I have included a diagram below.

The image must be centered in a div, while the div must also be responsive. I don't want the div to change its size and would like the image to create an overflow that is hidden on the div.

I have tried different methods of CSS and HTML, but neither are my greatest strengths.

If I understand correctly what you want to achieve is something like this (uncommenting /*overflow: hidden;*/): DEMO

HTML:

<div>
    <img src="http://i.imgur.com/cjgKmvp.jpg"/>
</div>

CSS:

div{
    position: relative;
    margin: 100px auto;
    width: 400px;
    height: 300px;
    border: 3px solid red;
    /*overflow: hidden;*/
}

img {
    position: absolute;
    top: 50%;
    left: 50%;
    -webkit-transform: translateX(-50%) translateY(-50%);
    -ms-transform: translateX(-50%) translateY(-50%);
    transform: translateX(-50%) translateY(-50%);
    min-width: 100%;
    min-height: 100%;
    width: auto;
    height: auto;
    z-index: -1;
}

Note: I comment overflow: hidden; so you can see how the image is positioned.