Panorama Canvas Size
Implement a function to calculate the required canvas size for a panorama given multiple images with their respective dimensions and positions. The goal is to determine the minimum canvas size that can accommodate all images without any overlap or truncation.
To achieve this, we need to understand the concept of image alignment and how images are positioned within a panorama. Each image has a width w, height h, and a horizontal offset xoff​, which represents the x-coordinate of the left edge of the image in the panorama's coordinate system. The total width of the canvas is determined by the rightmost edge of any image, which can be calculated as xoff​+w. The total height of the canvas is simply the maximum height among all images, denoted as max(h).
Here are the steps to calculate the canvas size:
- Initialize variables to store the maximum rightmost edge and maximum height.
- Iterate through each image and calculate its rightmost edge.
- Update the maximum rightmost edge and maximum height if necessary.
This technique is widely used in image stitching applications to create seamless panoramas.
Example:
images = [(100, 50, 0), (100, 50, 80), (100, 50, 160)]
(260, 50)
Analyzing each image:
Image 1: width=100, height=50, x_offset=0
- Right edge: 0 + 100 = 100
Image 2: width=100, height=50, x_offset=80
- Right edge: 80 + 100 = 180
- Overlaps with Image 1 by 20 pixels
Image 3: width=100, height=50, x_offset=160
- Right edge: 160 + 100 = 260
- Overlaps with Image 2 by 20 pixels
Canvas dimensions:
- Width = max right edge = 260
- Height = max height = 50
Result: (260, 50)
Constraints:
- images: list of (width, height, x_offset) tuples
- All x_offsets are non-negative
- Return (total_width, max_height) tuple
More from CV: Image Alignment and Stitching
You can think of this problem as purely geometry on a 1D axis (the x-axis of the panorama) plus a simple max over heights, not about feature matching or real stitching.
1. Background Knowledge
In image stitching / panoramas, each input image is mapped into a common coordinate system called the panorama (or canvas) coordinate frame. After estimating where each image should lie (its offset/transform), you must allocate a canvas large enough so that all pixels of all images fit inside.
For this simplified problem, all images:
- Are axis-aligned (no rotation).
- Are placed by a known horizontal offset xi​ (left edge position on the panorama).
- Have known width wi​ and height hi​.
So each image occupies a rectangle:
[xi​,xi​+wi​)×[0,hi​)The canvas must be wide enough to cover the rightmost x-coordinate of any image and tall enough to cover the largest height among all images.
2. Algorithm / Approach
This is a classic single pass aggregation problem:
- For each image, compute its right edge = xi​+wi​.
- Track the maximum right edge to get the overall canvas width.
- Track the maximum height to get the overall canvas height.
Algorithm pattern:
- Initialize maxRight = 0, maxHeight = 0.
- For each image:
- maxRight = max(maxRight, x_i + w_i)
- maxHeight = max(maxHeight, h_i)
- Answer = (canvasWidth = maxRight, canvasHeight = maxHeight).
3. Step-by-Step Strategy
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