  Current saliency methods require to learn large scale regional features using
small convolutional kernels, which is not possible with a simple feed-forward
network. Some methods solve this problem by using segmentation into superpixels
while others downscale the image through the network and rescale it back to its
original size. The objective of this paper is to show that saliency
convolutional neural networks (CNN) can be improved by using a Green's function
convolution (GFC) to extrapolate edges features into salient regions. The GFC
acts as a gradient integrator, allowing to produce saliency features by filling
thin edges directly inside the CNN. Hence, we propose the gradient integration
and sum (GIS) layer that combines the edges features with the saliency
features. Using the HED and DSS architecture, we demonstrated that adding a GIS
layer near the network's output allows to reduce the sensitivity to the
parameter initialization, to reduce the overfitting and to improve the
repeatability of the training. By simply adding a GIS layer to the
state-of-the-art DSS model, there is an absolute increase of 1.6% for the
F-measure on the DUT-OMRON dataset, with only 10ms of additional computation
time. The GIS layer further allows the network to perform significantly better
in the case of highly noisy images or low-brightness images. In fact, we
observed an F-measure improvement of 5.2% when noise was added to the dataset
and 2.8% when the brightness was reduced. Since the GIS layer is model
agnostic, it can be implemented into different fully convolutional networks. A
major contribution of the current work is the first implementation of Green's
function convolution inside a neural network, which allows the network to
operate in the feature domain and in the gradient domain at the same time, thus
improving the regional representation via edge filling.
