Implementation:Kornia Kornia AEPE Metric

Knowledge Sources	Kornia
Domains	Vision, Metrics
Last Updated	2026-02-09 15:00 GMT

Overview

Computes the Average Endpoint Error (AEPE) between two optical flow maps, measuring the Euclidean distance between predicted and ground truth 2D flow vectors.

Description

The AEPE (Average Endpoint Error) metric calculates the average Euclidean distance between corresponding 2D flow vectors in two flow maps. Given flow maps of shape (H, W, 2), the AEPE is defined as:

AEPE = (1/HW) * sum(sqrt((I_{i,j,1} - T_{i,j,1})^2 + (I_{i,j,2} - T_{i,j,2})^2))

This is the standard evaluation metric for optical flow estimation, as established in the Middlebury optical flow benchmark. The module provides both a functional interface (aepe function) and an nn.Module-based interface (AEPE class). The function also has an alias average_endpoint_error. Three reduction modes are supported: mean (default), sum, and none.

Usage

Import this metric when evaluating optical flow estimation models. It is suitable for comparing predicted optical flow fields against ground truth flow fields from benchmarks such as Middlebury, KITTI, or Sintel.

Code Reference

Source Location

• Repository: Kornia
• File: kornia/metrics/endpoint_error.py
• Lines: 1-113

Signature

def aepe(
    input: torch.Tensor,
    target: torch.Tensor,
    reduction: str = "mean"
) -> torch.Tensor:

class AEPE(nn.Module):
    def __init__(self, reduction: str = "mean") -> None: ...
    def forward(self, input: torch.Tensor, target: torch.Tensor) -> torch.Tensor: ...

average_endpoint_error = aepe

Import

from kornia.metrics import aepe, AEPE
# or
from kornia.metrics import average_endpoint_error

I/O Contract

Inputs

Name	Type	Required	Description
input	torch.Tensor	Yes	The predicted flow map with shape (*, 2). The last dimension must be 2 representing the (u, v) flow components.
target	torch.Tensor	Yes	The ground truth flow map with shape (*, 2). Must match the shape of input.
reduction	str	No	Specifies the reduction to apply: none (no reduction), mean (average over all elements, default), or sum (sum all elements).

Outputs

Name	Type	Description
epe	torch.Tensor	The computed endpoint error. A scalar if reduction is mean or sum, or a tensor matching the spatial dimensions of the input if reduction is none.

Usage Examples

import torch
from kornia.metrics import aepe, AEPE

# Functional interface
ones = torch.ones(4, 4, 2)
error = aepe(ones, 1.2 * ones)
# error: tensor(0.2828)

# Module interface
input1 = torch.rand(1, 4, 5, 2)
input2 = torch.rand(1, 4, 5, 2)
metric = AEPE(reduction="mean")
error = metric(input1, input2)

# No reduction - get per-pixel endpoint errors
error_map = aepe(input1, input2, reduction="none")

Related Pages

• Principle:Kornia_Kornia_Optical_Flow_Evaluation