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. Tilt is reported separately on its own tab so it never drags the centering number down.

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.