To elaborate on Tez's answer, Amazon S3 provides support for mapping custom domains via Virtual Hosting of Buckets.
To make this work, the name of your bucket must be the full hostname you wish to map.
So, using the example in the original question, create an S3 bucket called image.mydomain.com and set up a CNAME for it:
image.mydomain.com CNAME image.mydomain.com.s3.amazonaws.com.
