Edit in JSFiddle

$(".panels img").mouseover(function(){
	$(this).css('border','1px solid #fff');
}).mouseout(function(){
	$(this).css('border','none');
});

$(".panels img").hover(
//マウスが載った時の動作
function () {
    var enLarge = this;
    $(function () {
        setTimeout(function () {
            //選択した画像のz-indexを小さくして一番後ろへ
            //.animateで拡大
            $(enLarge).stop()
            .css('zIndex', '50')
            .css('cursor', 'default')
            .animate({
                width: "298px",
                height: "248px"
            }, 200, "swing");
            //選択した以外の画像を縮小
            $(".panels img").not(enLarge).stop()
                .animate({
                width: "50px",
                height: "40px"
            }, 200, "swing");

        }, 220);
    });

},
//マウスが外れた時の動作
function () {
    var enSmall = this;
    //z-index,width,heightをもとの位置へ
    $(function () {
        setTimeout(function () {
            $(enSmall).stop()
            .css('zIndex', '100')
            .css('cursor', 'pointer')
            .animate({
                width: "149px",
                height: "124px"
            }, 200, "swing");
            //小さくなっていた画像達も元の大きさに
            $(".panels img").not(enSmall).stop()
                .animate({
                width: "149px",
                height: "124px"
            }, 200, "swing");
        }, 220);
    });

});
<div id="box">
    <div class="panels" id="one">
        <img src="http://dummyimage.com/300x250/e362e3/f5f6ff&text=ONE" />
    </div>
    <div class="panels" id="two">
        <img src="http://dummyimage.com/300x250/5cbdd1/f5f6ff&text=TWO" />
    </div>
    <div class="panels" id="three">
        <img src="http://dummyimage.com/300x250/f08741/f5f6ff&text=THREE" />
    </div>
    <div class="panels" id="four">
        <img src="http://dummyimage.com/300x250/6bbd52/f5f6ff&text=FOUR" />
    </div>
</div>
#box {
    margin:100px 0 0 50px;
    position:relative;
    width:300px;
    height:250px;
    background-color:#f5f5f5;
    border:1px solid #808080;
}
.panels {
    /*float:left;
    width:150px;
    height:125px;
    margin:0;*/
}
.panels img {
    width:149px;
    height:124px;
    position:absolute;
    z-index:100;
    cursor:pointer;
}
#one img {
    position:absolute;
    top:0;
    left:0;
}
#two img {
    position:absolute;
    top:0;
    right:0;
}
#three img {
    position:absolute;
    bottom:0;
    left:0;
}
#four img {
    position:absolute;
    bottom:0;
    right:0;
}