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Current saliency methods require to learn large scale regional features usingsmall convolutional kernels, which is not possible with a simple feed-forwardnetwork. Some methods solve this problem by using segmentation into superpixelswhile others downscale the image through the network and rescale it back to itsoriginal size. The objective of this paper is to show that saliencyconvolutional neural networks (CNN) can be improved by using a Green's functionconvolution (GFC) to extrapolate edges features into salient regions. The GFCacts as a gradient integrator, allowing to produce saliency features by fillingthin edges directly inside the CNN. Hence, we propose the gradient integrationand sum (GIS) layer that combines the edges features with the saliencyfeatures. Using the HED and DSS architecture, we demonstrated that adding a GISlayer near the network's output allows to reduce the sensitivity to theparameter initialization, to reduce the overfitting and to improve therepeatability of the training. By simply adding a GIS layer to thestate-of-the-art DSS model, there is an absolute increase of 1.6% for theF-measure on the DUT-OMRON dataset, with only 10ms of additional computationtime. The GIS layer further allows the network to perform significantly betterin the case of highly noisy images or low-brightness images. In fact, weobserved an F-measure improvement of 5.2% when noise was added to the datasetand 2.8% when the brightness was reduced. Since the GIS layer is modelagnostic, it can be implemented into different fully convolutional networks. Amajor contribution of the current work is the first implementation of Green'sfunction convolution inside a neural network, which allows the network tooperate in the feature domain and in the gradient domain at the same time, thusimproving the regional representation via edge filling.

Deep Green Function Convolution for Improving Saliency in Convolutional Neural Networks