TY - JOUR
A1 - Peppert, Felix
A1 - von Kleist, Max
A1 - SchÃ¼tte, Christof
A1 - Sunkara, Vikram
T1 - On the Sufficient Condition for Solving the Gap-Filling Problem Using Deep Convolutional Neural Networks
T2 - IEEE Transactions on Neural Networks and Learning Systems
N2 - Deep convolutional neural networks (DCNNs) are routinely used for image segmentation of biomedical data sets to obtain quantitative measurements of cellular structures like tissues. These cellular structures often contain gaps in their boundaries, leading to poor segmentation performance when using DCNNs like the U-Net. The gaps can usually be corrected by post-hoc computer vision (CV) steps, which are specific to the data set and require a disproportionate amount of work. As DCNNs are Universal Function Approximators, it is conceivable that the corrections should be obsolete by selecting the appropriate architecture for the DCNN. In this article, we present a novel theoretical framework for the gap-filling problem in DCNNs that allows the selection of architecture to circumvent the CV steps. Combining information-theoretic measures of the data set with a fundamental property of DCNNs, the size of their receptive field, allows us to formulate statements about the solvability of the gap-filling problem independent of the specifics of model training. In particular, we obtain mathematical proof showing that the maximum proficiency of filling a gap by a DCNN is achieved if its receptive field is larger than the gap length. We then demonstrate the consequence of this result using numerical experiments on a synthetic and real data set and compare the gap-filling ability of the ubiquitous U-Net architecture with variable depths. Our code is available at https://github.com/ai-biology/dcnn-gap-filling.
Y1 - 2022
UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/8220
VL - 33
IS - 11
SP - 6194
EP - 6205
ER -