BezierAlign is a feature sampling method for arbitrarilyshaped scene text recognition that exploits parameterization nature of a compact Bezier curve bounding box. Unlike RoIAlign, the shape of sampling grid of BezierAlign is not rectangular. Instead, each column of the arbitrarilyshaped grid is orthogonal to the Bezier curve boundary of the text. The sampling points have equidistant interval in width and height, respectively, which are bilinear interpolated with respect to the coordinates.
Formally given an input feature map and Bezier curve control points, we concurrently process all the output pixels of the rectangular output feature map with size $h_{\text {out }} \times w_{\text {out }}$. Taking pixel $g_{i}$ with position $\left(g_{i w}, g_{i h}\right)$ (from output feature map) as an example, we calculate $t$ by:
$$ t=\frac{g_{i w}}{w_{o u t}} $$
We then calculate the point of upper Bezier curve boundary $tp$ and lower Bezier curve boundary $bp$. Using $tp$ and $bp$, we can linearly index the sampling point $op$ by:
$$ op=bp \cdot \frac{g_{i h}}{h_{\text {out }}}+tp \cdot\left(1\frac{g_{i h}}{h_{\text {out }}}\right) $$
With the position of $op$, we can easily apply bilinear interpolation to calculate the result. Comparisons among previous sampling methods and BezierAlign are shown in the Figure.
Source: ABCNet: Realtime Scene Text Spotting with Adaptive BezierCurve NetworkPaper  Code  Results  Date  Stars 

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