Spectral Analysis for Semantic Segmentation with Applications on Feature Truncation and Weak Annotation

The current neural networks for semantic segmentation usually predict the pixel-wise semantics on the down-sampled grid of images to alleviate the computational cost for dense maps. However, the accuracy of resultant segmentation maps may also be down graded particularly in the regions near object boundaries. In this paper, we advance to have a deeper investigation on the sampling efficiency of the down-sampled grid. By applying the spectral analysis that analyze on the network back propagation process in frequency domain, we discover that cross-entropy is mainly contributed by the low-frequency components of segmentation maps, as well as that of the feature in CNNs. The network performance maintains as long as the resolution of the down sampled grid meets the cut-off frequency. Such finding leads us to propose a simple yet effective feature truncation method that limits the feature size in CNNs and removes the associated high-frequency components. This method can not only reduce the computational cost but also maintain the performance of semantic segmentation networks. Moreover, one can seamlessly integrate this method with the typical network pruning approaches for further model reduction. On the other hand, we propose to employee a block-wise weak annotation for semantic segmentation that captures the low-frequency information of the segmentation map and is easy to collect. Using the proposed analysis scheme, one can easily estimate the efficacy of the block-wise annotation and the feature truncation method.