5,516 research outputs found
The Perception-Distortion Tradeoff
Image restoration algorithms are typically evaluated by some distortion
measure (e.g. PSNR, SSIM, IFC, VIF) or by human opinion scores that quantify
perceived perceptual quality. In this paper, we prove mathematically that
distortion and perceptual quality are at odds with each other. Specifically, we
study the optimal probability for correctly discriminating the outputs of an
image restoration algorithm from real images. We show that as the mean
distortion decreases, this probability must increase (indicating worse
perceptual quality). As opposed to the common belief, this result holds true
for any distortion measure, and is not only a problem of the PSNR or SSIM
criteria. We also show that generative-adversarial-nets (GANs) provide a
principled way to approach the perception-distortion bound. This constitutes
theoretical support to their observed success in low-level vision tasks. Based
on our analysis, we propose a new methodology for evaluating image restoration
methods, and use it to perform an extensive comparison between recent
super-resolution algorithms.Comment: CVPR 2018 (long oral presentation), see talk at:
https://youtu.be/_aXbGqdEkjk?t=39m43
Thresholds in Random Motif Graphs
We introduce a natural generalization of the Erd\H{o}s-R\'enyi random graph
model in which random instances of a fixed motif are added independently. The
binomial random motif graph is the random (multi)graph obtained by
adding an instance of a fixed graph on each of the copies of in the
complete graph on vertices, independently with probability . We
establish that every monotone property has a threshold in this model, and
determine the thresholds for connectivity, Hamiltonicity, the existence of a
perfect matching, and subgraph appearance. Moreover, in the first three cases
we give the analogous hitting time results; with high probability, the first
graph in the random motif graph process that has minimum degree one (or two) is
connected and contains a perfect matching (or Hamiltonian respectively).Comment: 19 page
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