Cylindrical Projection for Panoramas

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.

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

Example:

Constraints:

Test Results