How Centering is Calculated

🔧Homography Distortion & Ratios

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).

The crucial property of homographies is that they preserve ratios of lengths along a line. This means even though absolute lengths and angles are distorted, the proportions between segments on the same line remain accurate within the distorted image.

Example: Imagine the left border, the content area, and the right border all lie along a single conceptual horizontal line on the card. Even if the card is tilted in the photo:

These ratios in the distorted image still accurately reflect the original card's proportions as seen from that specific angle.

🧮 How This Applies to Centering

This tool leverages this principle. When you place the 8 keypoints (4 outer corners of the card, 4 inner corners of the content box):

1. Midpoints Calculation: We calculate the midpoints of the top, bottom, left, and right edges for both the outer card boundary and the inner content boundary directly in the distorted image space.
2. Distance Measurement: We measure the distances between corresponding midpoints (e.g., outer top midpoint to inner top midpoint gives the top border width in the image).
   top_margin = distance(outerTopMid, innerTopMid)

   bottom_margin = distance(outerBottomMid, innerBottomMid)

   left_margin = distance(outerLeftMid, innerLeftMid)

   right_margin = distance(outerRightMid, innerRightMid)
3. Ratio Calculation: We calculate the centering ratios based on these image-space distances.
   left_centering_ratio = left_margin / (left_margin + right_margin)

   right_centering_ratio = right_margin / (left_margin + right_margin)

   top_centering_ratio = top_margin / (top_margin + bottom_margin)

   bottom_centering_ratio = bottom_margin / (top_margin + bottom_margin)
4. Percentage Conversion: These ratios are converted to percentages (e.g., left_percentage = left_centering_ratio * 100).
5. Balance Score: A balance score (like Left/Right or Top/Bottom centering) is calculated based on how close the ratios are to a perfect 50/50 split (e.g., leftRight_balance = 100 - abs(left_percentage - 50) * 2).

Because homographies preserve ratios along lines, these percentages calculated directly from the potentially distorted image accurately reflect the card's centering as perceived from the angle the photo was taken. This matches how a human grader would assess the card visually from that same perspective.

🟣 When Perspective Correction (Homography) is Needed

While ratio-checking in the distorted image is valid for assessing centering as seen, applying a perspective correction (calculating and applying the inverse homography) is necessary if you need:

1. Real-world Measurements: To determine centering in millimeters or absolute units.
2. Cross-Photo Comparison: To compare centering accurately between cards photographed at different angles.
3. Standardized View: To simulate a top-down, scanner-like view for consistent analysis, independent of the original photo's perspective.

Perspective correction involves mathematically "un-distorting" the selected card corners back into a perfect rectangle (e.g., mapping them to the corners of a 750x1050 pixel canvas). Measurements and ratios calculated after this normalization represent an idealized, top-down view.