  Images are formed by counting how many photons traveling from a given set of
directions hit an image sensor during a given time interval. When photons are
few and far in between, the concept of `image' breaks down and it is best to
consider directly the flow of photons. Computer vision in this regime, which we
call `scotopic', is radically different from the classical image-based paradigm
in that visual computations (classification, control, search) have to take
place while the stream of photons is captured and decisions may be taken as
soon as enough information is available. The scotopic regime is important for
biomedical imaging, security, astronomy and many other fields. Here we develop
a framework that allows a machine to classify objects with as few photons as
possible, while maintaining the error rate below an acceptable threshold. A
dynamic and asymptotically optimal speed-accuracy tradeoff is a key feature of
this framework. We propose and study an algorithm to optimize the tradeoff of a
convolutional network directly from lowlight images and evaluate on simulated
images from standard datasets. Surprisingly, scotopic systems can achieve
comparable classification performance as traditional vision systems while using
less than 0.1% of the photons in a conventional image. In addition, we
demonstrate that our algorithms work even when the illuminance of the
environment is unknown and varying. Last, we outline a spiking neural network
coupled with photon-counting sensors as a power-efficient hardware realization
of scotopic algorithms.
