Some ideas:
1) Several pictures: instead of only one. As Rodrigo commented and Brad Larson tried to circumvent with his method, the problem with the user taking only one picture for the input is that you are necessarily lacking information to make a triangulation and form a point cloud in 3D. With 4 pictures taken from a slightly different angle, you can already reconstruct parts of the object. Comparing point clouds would make the endeavor much easier for any ML algorithm, Neuronal Networks (NN), Support Vector Machine (SVM) or others. A common standard to create point clouds is ASTM E2807, which uses the e57 file format.
On the downside a 3D vision algorithm might be heavy on the user's device, and is not the easiest to implement.
2) Artificial picture training: By training on pre-computed artificial pictures like Brad Larson suggested, you take over much of the computation, to the user's benefit. Be aware that you should probably use "features" extracted from the pictures, not the complete picture, both to train and to classify. The problem with this method is that you might be very sensitive to lighting and background context. You should take care to produce CAD pictures that have the same lightning conditions for all objects, so that the classifier doesn't overfit certain aspects of the "pictures" that do not belong to the object.
This aspect is where solution 1) is much more stable, it is less sensitive to the visual context.
3) Scale: The size of your object is an important descriptor. You should thus add scale information to your object descriptor before training. You could ask the user to take pictures with a reference object. Alternatively you can ask the user to make a rule-of-thumb estimate of the object size ("What are the approximate dimensions of the object, in [cm]?"). Providing size could make your algorithm significantly faster and more accurate.