Lowe's Ratio Test

The ratio test keeps a match only when the best candidate beats the runner up clearly, which drops pairs from repetitive texture.

The ratio test compares first and second neighbor distances and keeps clear winners.

Why Does This Exist?

Nearest neighbor always returns something, even on brick walls where every patch looks alike. Absolute distance thresholds fail because good pairs in hard lighting can sit farther than false pairs in clean texture. Lowe's fix compares each query against itself: how much better is best than second best.

A clear winner means a distinctive patch. A close race means ambiguity, so the pair is dropped before geometry. It sits between feature matching and robust fitting.

Think of It Like This

A photo finish rule

A race winner by a full stride is clear. A blanket finish with three noses together is a guess. Judges demand a margin before paying out.

The ratio $d_1/d_2$ is that margin. Below about $0.75$ pays, above it refuses. Where it stops: sprint margins are fixed, while descriptor margins shift with binary versus float distances.

How It Actually Works

Run knn with $k = 2$ per query to get best distance $d_1$ and runner up $d_2$ . Keep the match when:

$\frac{d_1}{d_2} < \tau$

Lowe's $\tau = 0.75$ suits SIFT floats. Binary ORB often uses $0.75$ to $0.8$ on Hamming distances. Apply before cross check and RANSAC so estimators see cleaner input.

Worked example

A SIFT query with $d_1 = 210$ and $d_2 = 340$ gives $210 / 340 = 0.6176$ , rounded to $0.62$ , and survives. A brick query with $d_1 = 190$ and $d_2 = 205$ gives $190 / 205 = 0.9268$ , rounded to $0.93$ , and is dropped even though its absolute best beats the first query. On $1{,}000$ raw pairs, ratio filtering often keeps $250$ to $400$ , and most drops are correct rejections of repeated texture. Tighten $\tau$ to $0.7$ for cleaner input, loosen to $0.8$ when recall starves.

Code

The point of this snippet is the filter itself: applying $\tau = 0.75$ to the worked example's distance pairs reproduces the keep and drop verdicts with only the standard library.

1pairs = [(210, 340), (190, 205)]2tau = 0.753
4for d1, d2 in pairs:5    ratio = round(d1 / d2, 2)6    print(d1, d2, ratio, "keep" if ratio < tau else "drop")7# -> 210 340 0.62 keep8# -> 190 205 0.93 drop

The first pair keeps at $0.62$ and the second drops at $0.93$ , matching the hand computation.

Watch Out For

One threshold for all descriptors

Float Euclidean gaps and binary Hamming gaps live on different scales. Copying $0.75$ everywhere either starves ORB or floods SIFT. Tune per descriptor family on your own pairs.

Ratio as the only filter

Ratio kills ambiguity, not geometric error. Repeated windows can still pass by chance. Always follow with cross check or a RANSAC vote before estimating pose.

The Quick Version

Needs knn with $k = 2$ distances per query.
Keeps matches with $d_1/d_2$ below threshold, classically $0.75$ .
The fixture keeps $0.62$ and drops $0.93$ despite the dropped query's smaller best distance.
Rejects repetitive texture better than absolute caps.
Tune separately for float and binary descriptors.