Corner Detection Implementation

Type: Feature Extraction / Interest Point Detection
Library: OpenCV (cv2.cornerHarris)
Application: Image Stitching, Tracking & 3D Reconstruction

Unlike edge detection which finds lines, Corner Detection identifies points where intensity changes significantly in all directions. The Harris Corner Detector is rotation-invariant, meaning it can find the same corners even if the image is rotated, making it a staple in computer vision tasks like panoramic stitching.

1. Mathematical Formulation

The algorithm analyzes the change in intensity for a small window shift (u, v) using a second-moment matrix M (Structure Tensor). This matrix summarizes the predominant directions of the gradient in a local neighborhood.

A "Corner Response" score R is calculated from the eigenvalues (λ₁, λ₂) of this matrix. If both eigenvalues are large, it indicates a corner.

Where k is an empirical constant (usually 0.04 - 0.06). Positive R indicates a corner; negative R indicates an edge; small R indicates a flat region.

2. Python Backend Logic (Snippet)

def detect_corners(image, block_size, ksize, k, color):
    # Convert to Grayscale & Float32
    # Harris algorithm requires float32 input for precision
    gray = cv2.cvtColor(image, cv2.COLOR_BGR2GRAY)
    gray = np.float32(gray)

    # Calculate Harris Response
    # block_size: Neighborhood size (e.g., 2)
    # ksize: Aperture parameter for Sobel (e.g., 3)
    # k: Harris detector free parameter (e.g., 0.04)
    dst = cv2.cornerHarris(gray, block_size, ksize, k)

    # Dilate the result to make corners visible
    dst = cv2.dilate(dst, None)

    # Thresholding & Marking
    # Mark pixels where response > 1% of max response
    image[dst > 0.01 * dst.max()] = color

    return image

3. Complexity & Constraints

The complexity is dominated by the calculation of image derivatives (Sobel) and the Gaussian windowing, roughly O(N) where N is the number of pixels.

Optimization Strategy: While faster than iterative segmentation methods, the cornerHarris function can still be heavy on 4K images. We restrict the block_size to small integers (2-5) to keep the convolution kernel small, ensuring the server can process requests in under 200ms.

Algorithm Reference: Harris Corner Detection

1. Mathematical Formulation

2. Python Backend Logic (Snippet)

3. Complexity & Constraints