Cascaded computation, whereby predictions are recurrently refined over
several stages, has been a persistent theme throughout the development of
landmark detection models. In this work, we show that the recently proposed
Deep Equilibrium Model (DEQ) can be naturally adapted to this form of
computation. Our Landmark DEQ (LDEQ) achieves state-of-the-art performance on
the challenging WFLW facial landmark dataset, reaching $3.92$ NME with fewer
parameters and a training memory cost of $\mathcal{O}(1)$ in the number of
recurrent modules. Furthermore, we show that DEQs are particularly suited for
landmark detection in videos. In this setting, it is typical to train on still
images due to the lack of labelled videos. This can lead to a ``flickering''
effect at inference time on video, whereby a model can rapidly oscillate
between different plausible solutions across consecutive frames. By rephrasing
DEQs as a constrained optimization, we emulate recurrence at inference time,
despite not having access to temporal data at training time. This Recurrence
without Recurrence (RwR) paradigm helps in reducing landmark flicker, which we
demonstrate by introducing a new metric, normalized mean flicker (NMF), and
contributing a new facial landmark video dataset (WFLW-V) targeting landmark
uncertainty. On the WFLW-V hard subset made up of $500$ videos, our LDEQ with
RwR improves the NME and NMF by $10$ and $13\%$ respectively, compared to the
strongest previously published model using a hand-tuned conventional filter.

本文提出了一种基于 Deep Equilibrium Model 的级联计算方法 --Landmark DEQ (LDEQ)，在面部关键点检测上取得了最先进的性能，并针对视频数据集提出了 Recurrence without Recurrence (RwR) 范式，通过引入新的评估指标 NMF 和发布新的面部标记视频数据集 WFLW-V，大大减少了面部关键点的抖动。