Implement cylindrical projection for 360° panorama stitching, a crucial step in image alignment and stitching that enables the creation of seamless panoramic images. This process involves mapping image coordinates to a cylinder, allowing for efficient stitching of multiple images.

The cylindrical projection is a geometric transformation that maps 2D image coordinates to a cylindrical surface, which is essential for 360° panorama stitching. The projection equations are given by $x' = f \cdot \arctan(\frac{x - c_x}{f})$ and $y' = f \cdot \frac{y - c_y}{\sqrt{(x - c_x)^2 + f^2}}$ , where $f$ is the focal length and $(c_x, c_y)$ is the image center.

Here are the steps to achieve this projection:

Define the input image coordinates $(x, y)$ and the focal length $f$ .
Calculate the image center $(c_x, c_y)$ .
Apply the cylindrical projection equations to obtain the projected coordinates $(x', y')$ .

x' = f \cdot \arctan(\frac{x - c_x}{f})

y' = f \cdot \frac{y - c_y}{\sqrt{(x - c_x)^2 + f^2}}

This technique is widely used in virtual reality and computer vision applications.

Each pixel (x, y) maps to (x', y') on cylinder. Center pixels barely move, edges curve significantly. The projection removes perspective distortion.

image: Input image (H, W)
focal_length: Camera focal length in pixels
Return: Cylindrically projected image

Editor

Python 3.13.1

Test Results

0/0

Run code to see test results.

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Cylindrical Projection for Panoramas

HardWarping

Here are the steps to achieve this projection:

Define the input image coordinates $(x, y)$ and the focal length $f$ .
Calculate the image center $(c_x, c_y)$ .
Apply the cylindrical projection equations to obtain the projected coordinates $(x', y')$ .

x' = f \cdot \arctan(\frac{x - c_x}{f})

y' = f \cdot \frac{y - c_y}{\sqrt{(x - c_x)^2 + f^2}}

This technique is widely used in virtual reality and computer vision applications.

Example:

Input:

image = 1000×1000 image
focal_length = 500

Output:

Cylindrically warped image (curved edges)

Reasoning:

Each pixel (x, y) maps to (x', y') on cylinder. Center pixels barely move, edges curve significantly. The projection removes perspective distortion.

Constraints:

image: Input image (H, W)
focal_length: Camera focal length in pixels
Return: Cylindrically projected image

Editor

Python 3.13.1

Test Results

0/0

Run code to see test results.