Image retrieval looks like a supervised task. If you have an image query and want to find similar images, you can use a SOM network where each neuron represents some images then the winner neuron will return those similar images.
Hopfield neural networks? They are designed to provide a content addressable memory... and I guess they are considered non-supervised because you just apply the hebb rule to let them memorize.
To use SOMs is adaquate BUT to take the winner neuron only not, as SOMs show a "jumping behaviour" , means you will have uncertain results. For that reason we developed the method of "Computing with Actvities" which takes the overall activity pattern of the SOM in to account. It furtheron the SOM achitecture is closed you will have a powerfull storage (16high number of neurons patterns) which will enable you to make a differentialy patern recognition.
Jennifer Dy, Carla Brodley, A. C. Kak, Lynn Broderick, and Alex Aisen, "Unsupervised Feature Selection Applied to Content-Based Retrieval of Lung Images," IEEE Transactions on Pattern Analysis and Machine Intelligence, pp. 373-378, March 2003.