Frame Similarity (SSD)

easyPROVideo TexturesVideoCV: Image-Based Rendering

Implement a function to compute the similarity between two video frames using the Sum of Squared Differences (SSD) metric. This task is crucial in video texture analysis, particularly for identifying seamless loop points in videos.

The concept of frame similarity is rooted in image-based rendering, where the goal is to measure the difference between two images or frames. The SSD metric calculates the sum of the squared differences between corresponding pixel values in two frames, $F1$ and $F2$ . This metric is sensitive to brightness changes and noise, making it a simple yet effective way to compare frames.

To compute the SSD, follow these steps:

Iterate over each pixel in the frames.
Calculate the difference between corresponding pixel values.
Square the difference.
Sum up the squared differences.

SSD = \sum_{i,j} (F1_{i,j} - F2_{i,j})^2

This technique is widely used in video editing and processing applications.

Example

Input

frame_ssd([[100, 100], [100, 100]], [[100, 100], [100, 100]])

Output

Reasoning

Comparing identical frames: All pixel differences are 0

SSD = 0² + 0² + 0² + 0² = 0 Identical frames have zero SSD.

Constraints

frame1 and frame2: 2D grayscale images (same dimensions)
Return SSD (integer)

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To solve this problem you only need basic image representation and a simple pixel-wise numeric computation.

1. Background Knowledge

A video frame can be treated as an image: a 2D grid of pixels, where each pixel has an intensity (grayscale) or multiple channels (e.g., RGB). Mathematically, a frame is a matrix $F$ where $F_{i,j}$ is the pixel value at row $i$ , column $j$ . Comparing two frames $F1$ and $F2$ means comparing their matrices element-wise.

The Sum of Squared Differences (SSD) is a common similarity (actually, dissimilarity) measure in image processing and template matching. For two frames of the same size, it is defined as:

SSD(F1, F2) = \sum_{i,j} (F1_{i,j} - F2_{i,j})^2

If frames are identical, every difference is 0 so SSD = 0. As frames become more different, the squared differences grow, making SSD larger. Because of the squaring, SSD heavily penalizes large pixel differences and is sensitive to global brightness shifts (adding a constant to all pixels changes SSD).

2. Algorithm / Approach

General pattern to compute SSD between two frames:

Ensure same shape (same height, width, and channels).
For each pixel (and channel):

Compute the difference between $F1$ and $F2$ .
Square this difference.

Sum all squared differences to get a single scalar SSD value.
Optionally, use SSD to:

Compare many candidate frames and pick the one with minimum SSD as “most similar”.
Threshold SSD to decide if frames are “similar enough” for a loop transition.

3. Step-by-Step Strategy

Assume frames are given as 2D (grayscale) or 3D (color) arrays.

Input validation

Check that F1 and F2 have the same dimensions.
If not, either resize or raise an error (depending on problem spec).

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solution.py

Python 3.13

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