Implementation:Kornia Kornia Depth Smoothness Loss

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

Overview

Inverse Depth Smoothness Loss computes an image-aware smoothness loss on inverse depth maps, penalizing depth discontinuities in regions where the image is smooth.

Description

The image-aware inverse depth smoothness loss encourages smooth depth predictions while preserving edges that are present in the corresponding image. It works by computing the gradients of the inverse depth map and weighting them by the exponential of the negative image gradients.

The mathematical formulation is:

$\text{loss}=|{\partial }_x{d}_{ij}|e^{-\Vert {\partial }_x{I}_{ij}\Vert }+|{\partial }_y{d}_{ij}|e^{-\Vert {\partial }_y{I}_{ij}\Vert }$

Where $d$ is the inverse depth map and $I$ is the corresponding image. The image gradient term acts as an edge-aware weighting: in areas where the image has strong edges, the depth smoothness penalty is reduced, allowing depth discontinuities to align with image edges.

This loss is inspired by the implementation from TensorFlow's struct2depth model.

Usage

Import this loss for monocular depth estimation and self-supervised depth prediction tasks. It is commonly used alongside photometric losses in self-supervised monocular depth estimation pipelines to regularize the predicted depth maps.

Code Reference

Source Location

• Repository: Kornia
• File: kornia/losses/depth_smooth.py
• Lines: 1-122

Signature

def inverse_depth_smoothness_loss(
    idepth: torch.Tensor,
    image: torch.Tensor,
) -> torch.Tensor: ...

class InverseDepthSmoothnessLoss(nn.Module):
    def forward(self, idepth: torch.Tensor, image: torch.Tensor) -> torch.Tensor: ...

Import

from kornia.losses import InverseDepthSmoothnessLoss
from kornia.losses import inverse_depth_smoothness_loss

I/O Contract

Inputs

Name	Type	Required	Description
idepth	torch.Tensor	Yes	Inverse depth tensor with shape (N, 1, H, W)
image	torch.Tensor	Yes	Input image tensor with shape (N, 3, H, W); must share spatial dimensions and device with idepth

Outputs

Name	Type	Description
loss	torch.Tensor	Scalar loss value representing the mean image-aware depth smoothness

Usage Examples

import torch
from kornia.losses import InverseDepthSmoothnessLoss

# Create sample inverse depth and image tensors
idepth = torch.rand(1, 1, 4, 5)
image = torch.rand(1, 3, 4, 5)

# Using the module API
smooth = InverseDepthSmoothnessLoss()
loss = smooth(idepth, image)

# Using the functional API
from kornia.losses import inverse_depth_smoothness_loss
loss = inverse_depth_smoothness_loss(idepth, image)

Related Pages

• Principle:Kornia_Kornia_Depth_Regularization