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Since there are tones within the image that are lighter than the surround, you may want this method.
1. Open the file and if the Background layer is locked, drag the lock to the trash.
2. Cmd+J to dupe the layer, turn off the eye on the layer and return to the bottom layer.
3. Double click to bring up Layer Styles and in the Blend If section, gently move the top right slider to the left until the background is transparent. It ail impinge on areas within the image, but don't be upset.
4. Choose the top layer, turn on the top layer eye and Option click on the mask symbol at the bottom of the Layers panel to produce a black mask. Paint with white on the mask with a soft edge brush to bring back any part of the illustration that you want to retrieve.
One more thing you may consider: Depending upon the method used to put the image on the cup, you may have the option to paint on the mask along the outer rim if the image with a brush set to less than 100% opacity so that the illustration vignettes even more gently than a soft edge brush alone. Good luck.
Thanks for the answer but this method didn't really work either. Since the cracks are so thin and fine, it is difficult to show them without showing the white part of the rocks which is what I want to avoid.
One last suggestion: you may be able to hold that detail if you split the Blend If slider. Hold down the Option key, click and drag the left slide of the slider for a less abrupt break from tones to transparent. It just may work.