Card Analysis Calculations

🔧Perspective Correction via Homography

When you photograph a flat object like a trading card from an angle, the image undergoes a projective transformation, also known as a homography. This distortion makes rectangles appear as general quadrilaterals (often like parallelograms or trapezoids).

To get accurate centering measurements, we compute the homography matrix that maps the card's outer corners to a perfect rectangle (e.g., a standard 750×1050 canvas). We then apply this same transform to the inner content corners, effectively "un-distorting" the card to a top-down view before measuring anything.

This ensures that all margin measurements reflect the card's true physical proportions, regardless of the angle the photo was taken from.

🧮 How Centering is Calculated

When you place the 8 keypoints (4 outer corners of the card, 4 inner corners of the content box), here's what happens:

1. Homography Matrix: We compute a homography matrix that maps the 4 outer card corners to a perfect rectangle (the card's known aspect ratio).
   H = getHomographyMatrix(outerCorners, targetRectangle)
2. Transform Inner Corners: We apply the same matrix to the 4 inner content corners, projecting them into the corrected, top-down space.
   correctedInnerCorners = applyHomography(H, innerCorners)
3. Margin Measurement: In corrected space, the outer edges are straight lines at known positions. We measure margins from those edges to the corrected inner corners:
   left_margin = correctedInnerLeft - targetLeft

   right_margin = targetRight - correctedInnerRight

   top_margin = correctedInnerTop - targetTop

   bottom_margin = targetBottom - correctedInnerBottom
4. Ratio Calculation: Centering ratios are computed from these perspective-corrected margins.
   left_centering_ratio = left_margin / (left_margin + right_margin)

   top_centering_ratio = top_margin / (top_margin + bottom_margin)
5. Balance Score: A balance score is calculated using the ratio of the smaller margin to the larger margin:
   leftRight_balance = (min(left, right) / max(left, right)) × 100

   topBottom_balance = (min(top, bottom) / max(top, bottom)) × 100
   This ratio-based approach aligns with industry standards and provides more intuitive scoring.

By correcting for perspective first, these measurements reflect the card's true physical centering — not just how it appears from the camera angle. This produces consistent results regardless of how the photo was taken.

📏 Ratio-Based Centering Scoring

Our centering scores use a ratio-based approach that aligns with professional card grading standards used by PSA, BGS, and other major grading companies.

🟣 Why Perspective Correction Matters

This tool applies perspective correction (homography) to every measurement. By mathematically "un-distorting" the card corners back into a perfect rectangle, we get:

1. Angle-Independent Results: The same card photographed from different angles produces consistent centering scores.
2. True Physical Proportions: Measurements reflect the card's actual border widths, not distorted image-space distances.
3. Cross-Photo Comparability: You can compare centering between cards photographed under different conditions.

If the homography computation fails (e.g., due to degenerate corner placement), the tool falls back to a direct ratio method that measures centering in raw image space — still useful, but less accurate for heavily angled photos.