Simple BRIEF Descriptor

Implement a simplified BRIEF (Binary Robust Independent Elementary Features) descriptor, a type of feature descriptor used in computer vision to describe the appearance of an image patch. This descriptor is essential for tasks like image matching and object recognition.

The BRIEF descriptor creates binary strings by comparing pixel intensities at predefined point pairs. This process involves computing a series of binary tests, where each test compares the intensity of two pixels. The result of each comparison is a single binary digit.

Here are the steps to compute the BRIEF descriptor:

Select a set of predefined point pairs $(p_i, q_i)$ .
Compare the pixel intensities at each pair of points.
Record the result of each comparison as a binary digit.

b_i = \begin{cases} 1 & \text{if } I(p_i) < I(q_i) \\ 0 & \text{otherwise} \end{cases}

This technique is widely used in image processing and object detection applications.

Example:

Input:

patch = 31×31 grayscale patch
pairs = [((15,10), (15,20)), ((10,15), (20,15)), ...]

Output:

[1, 0, 1, 1, 0, ...]

Reasoning:

For each pair, compare intensities:

Pair 0: patch[10,15]=100 < patch[20,15]=150 → 1
Pair 1: patch[15,10]=120 > patch[15,20]=80 → 0 ...

Result: Binary string encoding local texture.

Constraints:

patch: Image patch centered on keypoint (31×31)
pairs: List of ((x1,y1), (x2,y2)) point pairs
Return: Binary descriptor as list of 0/1

Example:

Constraints:

Test Results