  Heatmap-based regression overcomes the lack of spatial and contextual
information of direct coordinate regression, and has revolutionized the task of
face alignment. Yet it suffers from quantization errors caused by neglecting
subpixel coordinates in image resizing and network downsampling. In this paper,
we first quantitatively analyze the quantization error on benchmarks, which
accounts for more than 1/3 of the whole prediction errors for state-of-the-art
methods. To tackle this problem, we propose a novel Heatmap In Heatmap(HIH)
representation and a coordinate soft-classification (CSC) method, which are
seamlessly integrated into the classic hourglass network. The HIH
representation utilizes nested heatmaps to jointly represent the coordinate
label: one heatmap called integer heatmap stands for the integer coordinate,
and the other heatmap named decimal heatmap represents the subpixel coordinate.
The range of a decimal heatmap makes up one pixel in the corresponding integer
heatmap. Besides, we transfer the offset regression problem to an interval
classification task, and CSC regards the confidence of the pixel as the
probability of the interval. Meanwhile, CSC applying the distribution loss
leverage the soft labels generated from the Gaussian distribution function to
guide the offset heatmap training, which makes it easier to learn the
distribution of coordinate offsets. Extensive experiments on challenging
benchmark datasets demonstrate that our HIH can achieve state-of-the-art
results. In particular, our HIH reaches 4.08 NME (Normalized Mean Error) on
WFLW, and 3.21 on COFW, which exceeds previous methods by a significant margin.
