The phrase "be stamped on your memory/mind" implies that a particular memory or image is permanently imprinted in your mind. There are several synonyms that can be used to express the same idea. One could say that the memory is engrained, fixed, embedded, or etched into their mind. Similarly, the image could be burned, imprinted, inscribed, or impressed onto their memory. Each of these synonyms conveys the concept that the memory or image is indelibly imprinted in one's mind and is not likely to be forgotten easily. Whether it is a happy or painful memory, it can leave a lasting impression on one's consciousness.