Caffe is perfectly happy with models that make matrix outputs and learn from matrix ground truths for problems where the output and truth have spatial dimensions e.g. reconstruction / de-noising, pixelwise semantic segmentation, sliding window detection, and so forth. The forward and backward passes for these models follow directly from the definitions and Caffe has always been capable of computing these.

However, there isn't yet a bundled example and exactly how to accomplish this is confusing to many new users.
#189 is already solved technically by on-the-fly reshaping #594, instance-wise losses like SOFTMAX_LOSS, EUCLIDEAN_LOSS, SIGMOID_CROSS_ENTROPY_LOSS and so on, and proper data preparation. At the same time, this isn't immediately obvious from the documentation and examples so a walkthrough would do a lot of good.
#308 is technically redundant and does not mesh with the Caffe code but it was put to use in a standalone way and it's good that the code was made available to accompany the tech report.