Exposure Fusion

hardPROHDR ImagingHDRCV: Computational Photography

Implement exposure fusion to blend multiple exposures without HDR tonemapping, leveraging quality metrics to produce a seamless image. This technique is crucial in HDR Imaging as it allows for the combination of differently exposed images, capturing a wider dynamic range.

Exposure fusion directly blends images using weight maps based on contrast, saturation, and well-exposedness. Each input is an $H \times W \times 3$ image with 8-bit values (0–255); first scale every image to $[0, 1]$ . Then, for each image and each pixel, with $g$ the grayscale value (mean of R, G, B):

Contrast $C = |\nabla^2 g|$ : the absolute value of the 4-neighbour discrete Laplacian of $g$ (sum of the four neighbours minus 4 times the centre; at the border the edge pixels are mirrored), divided by its maximum over the image plus $10^{-8}$ .
Saturation $S = \text{std}(R, G, B)$ : the (population) standard deviation across the colour channels.
Well-exposedness $E = \exp\left(-\frac{(g - 0.5)^2}{2\sigma^2}\right)$ , a Gaussian centred at 0.5 with $\sigma = 0.2$ .

W = (C + 0.1)\,(S + 0.1)\,E

Normalise the weights across the images so they sum to 1 at every pixel (use $\max(\sum_k W_k, 10^{-8})$ as the denominator), then blend: $F = \sum_k \hat{W}_k I_k$ , with the same weight applied to all three channels. Clip $F$ to $[0, 1]$ , multiply by 255 and convert to 8-bit unsigned integers (truncating). Return an $H \times W \times 3$ array.

This technique is widely used in digital photography to capture high-contrast scenes.

Example

Input

images = [dark_exposure, medium_exposure, bright_exposure]

Output

Fused image with details from all exposures

Reasoning

Input: images holds exposures of one scene, each an $H \times W \times 3$ array of 8-bit values. Simplest case: flat grey $5 \times 5$ frames at 0 (dark), 128 (medium) and 255 (bright), which scale to $0$ , $0.502$ and $1$ .
Contrast and saturation: a flat frame has no edges, so $C = 0$ ; R = G = B, so $S = 0$ . Each weight shrinks to $0.1 \cdot 0.1 \cdot E = 0.01E$ ; the $+0.1$ offsets stop it collapsing to zero.
Well-exposedness ( $2\sigma^2 = 0.08$ ): dark $e^{-0.25/0.08} = e^{-3.125} \approx 0.0439$ , medium $\approx 0.99995$ , bright $\approx 0.0439$ .
Normalise: dividing by their total gives about $0.0404$ , $0.9192$ , $0.0404$ .
Blend: $0.0404 \cdot 0 + 0.9192 \cdot 0.502 + 0.0404 \cdot 1 \approx 0.5018$ ; times 255 is $127.96$ , stored as 127 at every pixel of a $5 \times 5 \times 3$ result.
Notice: the medium frame dominates, sitting nearest 0.5. In real photos $C$ and $S$ vary per pixel, so each region borrows from the exposure that shows it best: a fused image with details from all exposures.

Constraints

images: List of differently exposed images
Return: Fused image

More from CV: Computational Photography

Trimap-Based Alpha Estimationhard Drago Adaptive Log Mappinghard Gram Matrix for Stylehard Alpha Matte Compositingmedium Reinhard Global Tone Mappingmedium

Concept primerPREVIEW

Exposure Fusion: Background & Implementation Guide

Background Knowledge

Exposure Fusion Fundamentals

Exposure fusion is a computational photography technique that addresses the limited dynamic range of standard cameras without requiring the computationally expensive tone-mapping step of traditional HDR imaging. When a camera captures a scene with extreme lighting variations, a single exposure will either saturate bright regions or underexpose dark regions. Rather than capturing multiple exposures and reconstructing a full radiance map (which requires camera response function calibration), exposure fusion directly blends multiple LDR images using perceptual quality metrics. This approach is particularly valuable because it produces visually pleasing results while remaining computationally efficient—making it suitable for real-time and embedded applications.

Quality Metrics in Exposure Fusion

The three quality metrics you're implementing measure different aspects of image quality:

Contrast captures local detail and texture information using gradient magnitude. Images with higher contrast in specific regions typically contain more visually important information.
Saturation measures color diversity within local neighborhoods. Regions with vibrant, well-saturated colors are generally perceptually preferred over desaturated or grayscale areas.
Well-exposedness quantifies how close pixel intensities are to the optimal mid-range (0.5 in normalized space). This metric ensures that neither overexposed nor underexposed regions dominate the final blend.

These metrics are combined multiplicatively (via exponentiation with weights $w_c$ , $w_s$ , $w_e$ ) to create a unified quality score for each pixel across all input exposures.

Multi-Scale Blending with Laplacian Pyramids

Direct pixel-by-pixel blending using weight maps can produce visible seams and artifacts at boundaries where weights change abruptly. Laplacian pyramids enable seamless blending by decomposing images into multiple frequency bands. Low-frequency (coarse) components are blended at coarse scales where weight transitions are smooth, while high-frequency (detail) components are blended at finer scales. This multi-scale approach naturally produces smooth transitions and avoids ghosting artifacts that plague naive blending methods.

Algorithm/Approach

The exposure fusion pipeline follows this general pattern:

Compute quality metrics for each input image at each pixel location
Normalize weights across all exposures so they sum to 1 at each pixel
Build Laplacian pyramids for each input image and its corresponding weight map
Blend pyramids at each scale using the normalized weights
Reconstruct the final image from the blended pyramid

This approach separates the problem into manageable components: metric computation, normalization, pyramid construction, and reconstruction.

Step-by-Step Strategy

Step 1: Implement Quality Metric Functions

Create separate functions for each metric:

PRO

Continue the full explanation

You're reading the free preview. Unlock the complete walkthrough, the code editor, test runner and reference solution with Premium.

PRO

Editor locked

The code editor is locked for Pro problems. It is only available for free problems. Please upgrade to gain access to the code editor for all problems.

solution.py

Python 3.13

Test results