  Wiatowski and B\"olcskei, 2015, proved that deformation stability and
vertical translation invariance of deep convolutional neural network-based
feature extractors are guaranteed by the network structure per se rather than
the specific convolution kernels and non-linearities. While the translation
invariance result applies to square-integrable functions, the deformation
stability bound holds for band-limited functions only. Many signals of
practical relevance (such as natural images) exhibit, however, sharp and curved
discontinuities and are, hence, not band-limited. The main contribution of this
paper is a deformation stability result that takes these structural properties
into account. Specifically, we establish deformation stability bounds for the
class of cartoon functions introduced by Donoho, 2001.
