Change your scaling transform to use additive="sum" and apply an additional transform that translates the circle to the center of the image. So instead of defining the shape at the center of the image, define its center to be 0 0 and then use the transform attribute to translate it to 50, 50 (the exact center of your particular image).
<svg version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="100px" height="100px">
<circle style="fill:blue;" cx="0" cy="0" r="45" transform="translate(50 50)">
<animateTransform attributeName="transform"
type="scale"
additive="sum"
from="0 0"
to="1 1"
begin="0s"
dur="1s"
repeatCount="indefinite"
/>
</circle>
</svg>
Here's another example using the defs and use tags to reuse the circle definition:
<svg version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="100px" height="100px">
<defs>
<circle id="def-circle" style="fill:blue;" cx="0" cy="0" r="45" />
</defs>
<use xlink:href="#def-circle" transform="translate(50 50)">
<animateTransform attributeName="transform"
type="scale"
additive="sum"
from="0 0"
to="1 1"
beg="0s"
dur="1s"
repeatCount="indefinite" />
</use>
</svg>