You can stop the image from overlapping it's edges by clipping the image and applying a wrapper element which sets the blur effect to 0 pixels. This is how it looks like:
HTML
<div id="wrapper">
<div id="image"></div>
</div>
CSS
#wrapper {
width: 1024px;
height: 768px;
border: 1px solid black;
// 'blur(0px)' will prevent the wrapped image
// from overlapping the border
-webkit-filter: blur(0px);
-moz-filter: blur(0px);
-ms-filter: blur(0px);
filter: blur(0px);
}
#wrapper #image {
width: 1024px;
height: 768px;
background-image: url("../images/cats.jpg");
background-size: cover;
-webkit-filter: blur(10px);
-moz-filter: blur(10px);
-ms-filter: blur(10px);
filter: blur(10px);
// Position 'absolute' is needed for clipping
position: absolute;
clip: rect(0px, 1024px, 768px, 0px);
}