Optical flow#

kornia.metrics.aepe(input, target, reduction='mean')[source]#

Calculate the average endpoint error (AEPE) between 2 flow maps.

AEPE is the endpoint error between two 2D vectors (e.g., optical flow). Given a h x w x 2 optical flow map, the AEPE is:

\[\text{AEPE}=\frac{1}{hw}\sum_{i=1, j=1}^{h, w}\sqrt{(I_{i,j,1}-T_{i,j,1})^{2}+(I_{i,j,2}-T_{i,j,2})^{2}}\]

Convention:

Flow is channel-last, \((*, 2)\) such as \((B, H, W, 2)\), in the units of the flow (pixels for optical flow). Permute a channel-first \((B, 2, H, W)\) flow to \((B, H, W, 2)\) first: it raises unless \(W = 2\), where it is read wrongly. Losses and metrics ports RAFT’s endpoint error.
The endpoint error is the Euclidean distance between the two vectors at every position, symmetric in input and target and not normalized by the image size. reduction='mean' (the default) averages it over every position of every sample at once and 'sum' adds it up, both into a 0-d tensor; 'none' returns the \((*)\) map. There is no valid mask: mask sparse ground truth on the 'none' map. An unknown reduction raises NotImplementedError.
aepe() and average_endpoint_error() are the same function.

Parameters:

input (Tensor) – the input flow map with shape \((*, 2)\).
target (Tensor) – the target flow map with shape \((*, 2)\).
reduction (str, optional) – Specifies the reduction to apply to the output: 'none' | 'mean' | 'sum'. 'none': no reduction will be applied, 'mean': the sum of the output will be divided by the number of elements in the output, 'sum': the output will be summed. Default: "mean"

Return type:

Tensor

Returns:

the computed AEPE as a 0-d tensor, or the endpoint-error map of shape \((*)\) for reduction='none'.

Examples

>>> ones = torch.ones(4, 4, 2)
>>> aepe(ones, 1.2 * ones)
tensor(0.2828)

Reference:: https://link.springer.com/content/pdf/10.1007/s11263-010-0390-2.pdf

kornia.metrics.average_endpoint_error(input, target, reduction='mean')[source]#

Calculate the average endpoint error (AEPE) between 2 flow maps.

AEPE is the endpoint error between two 2D vectors (e.g., optical flow). Given a h x w x 2 optical flow map, the AEPE is:

\[\text{AEPE}=\frac{1}{hw}\sum_{i=1, j=1}^{h, w}\sqrt{(I_{i,j,1}-T_{i,j,1})^{2}+(I_{i,j,2}-T_{i,j,2})^{2}}\]

Convention:

Flow is channel-last, \((*, 2)\) such as \((B, H, W, 2)\), in the units of the flow (pixels for optical flow). Permute a channel-first \((B, 2, H, W)\) flow to \((B, H, W, 2)\) first: it raises unless \(W = 2\), where it is read wrongly. Losses and metrics ports RAFT’s endpoint error.
The endpoint error is the Euclidean distance between the two vectors at every position, symmetric in input and target and not normalized by the image size. reduction='mean' (the default) averages it over every position of every sample at once and 'sum' adds it up, both into a 0-d tensor; 'none' returns the \((*)\) map. There is no valid mask: mask sparse ground truth on the 'none' map. An unknown reduction raises NotImplementedError.
aepe() and average_endpoint_error() are the same function.

Parameters:

input (Tensor) – the input flow map with shape \((*, 2)\).
target (Tensor) – the target flow map with shape \((*, 2)\).
reduction (str, optional) – Specifies the reduction to apply to the output: 'none' | 'mean' | 'sum'. 'none': no reduction will be applied, 'mean': the sum of the output will be divided by the number of elements in the output, 'sum': the output will be summed. Default: "mean"

Return type:

Tensor

Returns:

the computed AEPE as a 0-d tensor, or the endpoint-error map of shape \((*)\) for reduction='none'.

Examples

>>> ones = torch.ones(4, 4, 2)
>>> aepe(ones, 1.2 * ones)
tensor(0.2828)

Reference:: https://link.springer.com/content/pdf/10.1007/s11263-010-0390-2.pdf

class kornia.metrics.AEPE(reduction='mean')[source]#

Computes the average endpoint error (AEPE) between 2 flow maps.

EPE is the endpoint error between two 2D vectors (e.g., optical flow). Given a h x w x 2 optical flow map, the AEPE is:

\[\text{AEPE}=\frac{1}{hw}\sum_{i=1, j=1}^{h, w}\sqrt{(I_{i,j,1}-T_{i,j,1})^{2}+(I_{i,j,2}-T_{i,j,2})^{2}}\]

Convention:: See the Convention block of aepe(), which this module calls with its reduction.

Parameters:: reduction (str, optional) – Specifies the reduction to apply to the output: 'none' | 'mean' | 'sum'. 'none': no reduction will be applied, 'mean': the sum of the output will be divided by the number of elements in the output, 'sum': the output will be summed. Default: "mean"

Shape:

Examples

>>> input1 = torch.rand(1, 4, 5, 2)
>>> input2 = torch.rand(1, 4, 5, 2)
>>> epe = AEPE(reduction="mean")
>>> epe = epe(input1, input2)