ANMS

ANMS

Adaptive Non-Maximal Suppression (ANMS) selects a spatially well-distributed subset of keypoints from a raw detector response. Standard non-maximal suppression enforces a fixed minimum spacing $r$ between keypoints, which wastes the detector’s ranking information. ANMS instead assigns each keypoint a suppression radius that depends on its response strength — strong keypoints suppress a large neighborhood, weak ones suppress only nearby weaker keypoints — then keeps the top-$n$ points by radius.

For each keypoint $x_i$ with detector response $f(x_i)$, define its suppression radius as the distance to the nearest stronger keypoint:
$r_i={\min }_j\{\Vert x_i-x_j\Vert :f(x_j)>c\cdot f(x_i)\},$
where $c\in (0,1)$ (typically $c=0.9$) is a robustness factor that prevents nearly-equal responses from mutually eliminating each other.

Keypoints are sorted by $r_i$ in decreasing order and the top $n$ are kept.

Intuition

A Harris response map has both a ranking (stronger corners rate higher) and a geometry (corners are spatially distributed). Plain NMS throws away the ranking by treating all keypoints equally once they pass a fixed threshold. Plain top-$n$ by response throws away the geometry, producing a clump of keypoints at the strongest feature.

ANMS threads the needle: the strongest corner in the image gets infinite suppression radius (it cannot be suppressed by anything), the second-strongest gets a radius equal to its distance to the strongest, and so on down the list. Each keypoint’s radius is, by construction, the size of the region it dominates. Picking the top-$n$ by radius keeps one keypoint per “region of dominance,” giving spatial coverage automatically.

Properties

(Radius definition) $r_i$ is the distance to the nearest strictly-stronger keypoint.

With the robustness factor $c<1$, the comparison is $f(x_j)>c\cdot f(x_i)$, which tolerates small response differences and prevents two nearly-equal keypoints in close proximity from canceling each other out.

(Top-n by radius) After sorting by radius, the top $n$ points are spatially well-distributed.

Large radii correspond to keypoints that are both strong and isolated — exactly what downstream matching wants. The user specifies $n$ directly (e.g., 500 keypoints per image).

(Efficiency) Naive implementation is $O(N^2)$ in the number of raw keypoints; KD-tree variants reduce this to $O(N\log N)$.

For typical $N\approx 10^4$ raw Harris corners, the naive version already runs in tens of milliseconds and is rarely a bottleneck.

Examples

ANMS on a Textured Scene

Suppose Harris returns 10,000 corners on a city skyline. Plain top-500 picks 500 corners clustered on the most textured building. ANMS:

1. For each corner, compute $r_i$ as defined above.
2. Sort by $r_i$; keep the 500 largest.

The result is 500 corners spread across the entire skyline — buildings, skyline silhouette, distant objects — giving RANSAC-based homography estimation much better geometric conditioning.

See Also

• 4.1.1. Harris Corner Detection — the standard detector paired with ANMS
• 4.2. Feature Selection — the broader family of selection strategies
• 4.4.1. RANSAC — the downstream estimator that benefits from well-distributed keypoints