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OK, let's try 8-) I don't think that you can estimate the depth without a stereo camera. You can also try the SfM to reconstruct the 3d model of the apple. But most likely results will be not satisfactory, because of weak features. However, you can improve them is the apple is under structured light.

So, my guess is that linear regression may help you. You're biting many-many apples, and try to find dependency between radius of the bite, and its depth. If the results are not satisfactory, you can take more apples to obtain larger training set. Please note that you also need a testing set of bitten apples, which is not intersected with the training set.

If the prediction is still bad, you can try to build other types of regression, for instance your X may be the following ratio: radius_of_bite/radius_of_apple, and your Y may be equal to volume_of_bite / volume_of_apple. You can later try polynomial and non-linear regressions.

If the prediction is still bad, you can try to build other types of regression, for instance your X may be the following ratio: radius_of_bite/radius_of_apple, and your Y may be equal to volume_of_bite / volume_of_apple. You can later try polynomial and non-linear regressions.