Linear Blend Weight

easyPROPanoramasStitchingCV: Image Alignment and Stitching

You are given a position in an overlap region and need to compute the blending weight for smooth image compositing.

Linear blending creates smooth transitions between overlapping images:

$\alpha = \frac{x - x_{start}}{x_{end} - x_{start}}$

Where:

$\alpha$ is the weight for the second (right) image
$1 - \alpha$ is the weight for the first (left) image
The final color is: $C = (1-\alpha) \cdot C_1 + \alpha \cdot C_2$

Outside the overlap:

x < x_start: α = 0 (use only first image)
x > x_end: α = 1 (use only second image)

Example

Input

x = 150
x_start = 100
x_end = 200

Output

0.5

Reasoning

x = 150 is in the overlap region [100, 200]
Apply linear interpolation: α = (x - x_start) / (x_end - x_start) α = (150 - 100) / (200 - 100) α = 50 / 100 α = 0.5

At x = 150 (middle of overlap), both images contribute equally.

First image weight: 1 - 0.5 = 0.5
Second image weight: 0.5

Constraints

x is the current pixel position
x_start and x_end define the overlap region (x_start < x_end)
Return weight for second image (0 to 1)
Round to 4 decimal places

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Linear Blend Weight: Background and Implementation Guide

Background Knowledge

Image Stitching and Blending Fundamentals

Image stitching combines multiple overlapping images into a single panoramic view. When two images overlap, a critical challenge is creating smooth transitions at the seams to avoid visible artifacts like ghosting, color inconsistencies, and hard edges. Linear blending is one of the simplest and most effective fusion techniques for achieving this smoothness. The core idea is that in the overlap region, pixels from both images contribute to the final result, with their contributions weighted based on position. Pixels closer to the left image contribute more from the left image, while pixels closer to the right image contribute more from the right image, creating a gradual fade between them.

Why Linear Blending Works

Linear blending leverages the principle that human perception of image quality depends on smooth structural transitions. By using position-based weights that vary linearly across the overlap region, the algorithm ensures that color and intensity changes are gradual rather than abrupt. This approach is computationally efficient compared to more sophisticated methods like non-linear sigmoid-based weighting or adaptive saliency-weighted blending, making it ideal for real-time applications. The linear interpolation formula ensures that at the left boundary of the overlap, the first image dominates (α ≈ 0), and at the right boundary, the second image dominates (α ≈ 1).

Algorithm/Approach

The linear blend weight problem follows a conditional linear interpolation pattern:

Determine the position relative to the overlap region boundaries
Apply conditional logic to handle three cases: before overlap, within overlap, and after overlap
Compute the normalized position as a fraction of the overlap width
Return the appropriate weight based on the position

This is a straightforward mapping problem where you transform a spatial coordinate into a blending coefficient.

Step-by-Step Strategy

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solution.py

Python 3.13

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