Evaluation index of optical flow optical flow estimation

Evaluation index

Endpoint error(EPE)

The calculation is the Euclidean distance between the estimated optical flow and the groundtruth optical flow:
$$EPE=\sqrt{((u_{es}-u_{gt}{)}^2+(v_{es}-v_{gt}{)}^2)}$$
This is a relatively common evaluation index, and the mean value of EPE is usually used to evaluate the results of optical flow estimation.

Angular error(AE)

The calculation is the angular error between the optical flow vectors: $(u_0,v_0,1)$表示一个列向量)
$$AE=\arccos (\frac{(u_{es},v_{es},1{)}^T\ast (u_{gt},v_{gt},1)}{\sqrt{1.0+u_{es}\ast u_{es}+v_{es}\ast v_{es}}\sqrt{1.0+u_{gt}\ast u_{gt}+v_{gt}\ast v_{gt}}})$$

Interpolation error(IE)

Interpolation error refers to the root-mean-square(RMS) difference
$$IE=\sqrt{\frac{1}{N}\sum _{(x,y)}(I(x,y)-I_{gt}(x,y){)}^2}$$
N is the number of pixels. For an RGB image, the L2 norm of the RGB color difference is taken.

Normalized interpolation error(NE)

$$IE=\sqrt{\frac{1}{N}\sum _{(x,y)}\frac{\left(I\right(x,y)-I_{gt}(x,y){)}^2}{||▽I_{gt}|{|}^2+ϵ}}$$
Take $ϵ=1.0$ .$\_$$\_$For RGB images, the L2 norm of the vector difference is taken, and the gradients are computed separately.
For the method of obtaining the interpolated image, see 3.3.2 of the paper

Optical Flow Dataset

Middlebury Optical flow dataset 最经典
MPI Sintel Dataset
Robust Vision Challenge
KITTI Flow 2012 evaluation
KITTI Flow 2015 evaluation
Heidelberg HD1K Flow benchmark

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参考：
论文 A Database and Evaluation Methodology for Optical Flow
https://vision.middlebury.edu/flow/eval/
https://stackoverflow.com/questions/49699739/what-is-endpoint-error-between-optical-flows
https://github.com/philferriere/tfoptflow/blob/master/README.md