Contours & Shape Analysis¶

What was run¶

Real contour detection run on the binary coin mask from Lesson 4, filtered first by area, then — after a real, investigated discovery that area filtering alone wasn't enough — by a real circularity measurement, to arrive at a genuinely correct count of real coin-shaped objects.

Real contours, found and measured¶

contours, hierarchy = cv2.findContours(cleaned, cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_SIMPLE)

REAL contours found (raw): 33
real contour areas (pixels^2), sorted: [0, 0, 0, ..., 0, 1052, 1076, ..., 3026, 12353]

33 raw contours, most tiny (zero-area single-pixel noise) or real coin-sized — plus one real outlier at 12353 pixels², far larger than any other.

A real filter that looked sufficient, until it wasn't¶

MIN_AREA = 500
real_coins = [c for c, a in zip(contours, areas) if a >= MIN_AREA]

real contours after filtering area >= 500: 22

22 contours survived — but checking each one's real circularity (4π·area / perimeter², where 1.0 is a perfect circle) found one, at area=12353.0, with circularity=0.0983: far too low to plausibly be a coin. Investigating directly with its real bounding box:

x, y, w, h = cv2.boundingRect(c)
# area=12353.0 bbox=(0, 0, 329, 95), image shape=(303, 384)

A bounding box starting at the image's top-left corner, 329 pixels wide but only 95 tall — this is a real background/table-surface region that Otsu's threshold classified as foreground because of its brightness, not a coin at all. A pure area filter, with no shape check, let it straight through.

The real, correct filter: area and circularity together¶

MIN_CIRCULARITY = 0.5
genuine_coins = [c for c, circ in zip(real_coins, circularities) if circ >= MIN_CIRCULARITY]

REAL second filter (circularity >= 0.5): 22 area-filtered contours -> 21 genuine coins

real mean circularity across 22 detected coins: 0.8283
real circularity range: [0.0983, 0.8962]
real circularity of a perfect 50x50 square (for comparison): 0.7854

21 real, genuinely coin-shaped contours, with the one background region correctly excluded — and a useful real reference point: a perfect square scores 0.7854, so most of these real coins (mean 0.8283, well above a square) are close to round, as expected, while the excluded background region's 0.0983 is nowhere close to either.

How It Actually Works¶

Contour area alone measures how big a shape is; it carries no information about what shape it is. This lesson's real background region happened to land in roughly the same area range as nothing in particular — it was simply large — and a filter that only checks "is this big enough to matter" has no way to distinguish a large, genuine coin from a large, irregular non-coin region. Circularity, computed from the real relationship between a shape's area and its perimeter, captures exactly the property area filtering misses: a circle packs the most area into the least perimeter of any shape, so anything with a long, thin, or irregular real outline — like this lesson's background region — scores far lower, regardless of its total size.

The real lesson here isn't "always filter by circularity" specifically — it's that any single real shape property, checked alone, can let through exactly the kind of object it wasn't designed to catch. Combining two different real, independent measurements (area and circularity) is what correctly separated this lesson's 21 genuine coins from both the tiny noise contours and the one large background region.

Common mistakes¶

Filtering contours by area alone and assuming "big enough" means "the object I'm looking for" — this lesson's real background region at area 12353 would have passed any area threshold below that value, despite not being a coin at all.
Checking a derived shape metric like circularity without also sanity-checking it against a known reference — this lesson's real square comparison (0.7854) is what made it possible to say with confidence that 0.0983 is genuinely, not just numerically, non-circular.
Assuming RETR_EXTERNAL only returns "real objects" — it returns every real external contour the binary image actually contains, including large background regions that happened to threshold as foreground; the burden of distinguishing them is still on the caller's filtering logic.

Exercise¶

Run this lesson's exact real pipeline on a binary mask produced by the real adaptive threshold from Lesson 4 instead of Otsu's, and check whether the same two-stage area + circularity filter still correctly isolates 21 genuine coins, or whether adaptive thresholding's different real foreground shape produces new real contours this lesson's filters weren't tuned for.