Implementation:Kornia Kornia Geman Mcclure Loss

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

Overview

Geman-McClure Loss is a robust regression loss function that saturates for large residuals, providing strong outlier rejection.

Description

The Geman-McClure loss, originally proposed for Bayesian image analysis (Geman and McClure, 1985), is a robust loss function that completely saturates for very large residuals, effectively ignoring outliers entirely. It is part of the family of robust estimators described by Barron (2019).

The mathematical formulation is:

$\text{GM}(x,y)=\frac{2(x-y{)}^2}{(x-y{)}^2+4}$

Where $x$ is the prediction and $y$ is the target. The loss is bounded between 0 and 2, meaning that no matter how large the residual becomes, the loss contribution is capped. This makes it one of the most aggressive robust loss functions available.

Usage

Import this loss for regression tasks where extreme outliers are present and should be completely ignored during training. It is particularly useful in robust estimation problems such as structure from motion, point cloud registration, and image matching where a significant portion of correspondences may be incorrect.

Code Reference

Source Location

• Repository: Kornia
• File: kornia/losses/geman_mcclure.py
• Lines: 1-134

Signature

def geman_mcclure_loss(
    img1: torch.Tensor,
    img2: torch.Tensor,
    reduction: str = "none",
) -> torch.Tensor: ...

class GemanMcclureLoss(nn.Module):
    def __init__(self, reduction: str = "none") -> None: ...
    def forward(self, img1: torch.Tensor, img2: torch.Tensor) -> torch.Tensor: ...

Import

from kornia.losses import GemanMcclureLoss
from kornia.losses import geman_mcclure_loss

I/O Contract

Inputs

Name	Type	Required	Description
img1	torch.Tensor	Yes	Predicted tensor with arbitrary shape (*)
img2	torch.Tensor	Yes	Target tensor with the same shape as img1
reduction	str	No	Reduction mode: 'none' (default), 'mean', or 'sum'

Outputs

Name	Type	Description
loss	torch.Tensor	Computed Geman-McClure loss; element-wise for 'none', scalar for 'mean'/'sum'; values bounded in [0, 2]

Usage Examples

import torch
from kornia.losses import GemanMcclureLoss

# Create sample tensors
img1 = torch.randn(2, 3, 32, 32, requires_grad=True)
img2 = torch.randn(2, 3, 32, 32)

# Using the module API
criterion = GemanMcclureLoss(reduction="mean")
output = criterion(img1, img2)
output.backward()

# Using the functional API
from kornia.losses import geman_mcclure_loss
output = geman_mcclure_loss(img1, img2, reduction="sum")

Related Pages

• Principle:Kornia_Kornia_Robust_Loss_Functions