Computational intensiveness of deep learning has motivated low-precision arithmetic designs. However, the current quantized/binarized training approaches are limited by: (1) significant performance loss due to arbitrary approximations of the latent weight gradient through its discretization/binarization function, and (2) training computational intensiveness due to the reliance on full-precision latent weights. This paper proposes a novel mathematical principle by introducing the notion of Boolean variation such that neurons made of Boolean weights and/or activations can be trained ---for the first time--- natively in Boolean domain instead of latent-weight gradient descent and real arithmetic. We explore its convergence, conduct extensively experimental benchmarking, and provide consistent complexity evaluation by considering chip architecture, memory hierarchy, dataflow, and arithmetic precision. Our approach achieves baseline full-precision accuracy in ImageNet classification and surpasses state-of-the-art results in semantic segmentation, with notable performance in image super-resolution, and natural language understanding with transformer-based models. Moreover, it significantly reduces energy consumption during both training and inference.

In order to overcome the limited depth of field of usual photographic devices, a common approach is multi-focus image fusion (MFIF). From a stack of images acquired with different focus settings, these methods aim at fusing the content of the images of the stack to produce a final image that is sharp everywhere. Such methods can be very efficient, but when a global geometric alignment of images is out-of-reach, or when some objects are moving, the final image shows ghosts or other artefacts. In this paper, we propose a generic method to overcome these limitations. We first select a reference image, and then, for each image of the stack, reconstruct an image that shares the geometry of the reference and the sharpness content of the image at hand. The reconstruction is achieved thanks to a specially crafted modification of the PatchMatch algorithm, adapted to blurred images, and to a dedicated postprocessing for correcting reconstruction errors. Then, from the new image stack, MFIF is performed to produce a sharp result. We show the efficiency of the result on a database of challenging cases of hand-held shots containing moving objects.