RANSAC Iteration Count

easyPRORANSAC for AlignmentRANSACCV: Image Alignment and Stitching

You are given the estimated inlier ratio and need to calculate how many RANSAC iterations are required for a given success probability.

The formula for required iterations is:

$k = \frac{\log(1 - p)}{\log(1 - w^n)}$

Where:

$k$ = number of iterations needed
$p$ = desired probability of success (e.g., 0.99)
$w$ = inlier ratio (proportion of good correspondences)
$n$ = sample size (points needed for model, e.g., 4 for homography)

This formula comes from the probability that at least one sample contains all inliers after k iterations.

Example

Input

inlier_ratio = 0.5
sample_size = 4
success_prob = 0.99

Output

Reasoning

Probability of all-inlier sample: w^n = 0.5^4 = 0.0625
Probability of at least one outlier: 1 - w^n = 0.9375
Probability of k failures: (1 - w^n)^k
For 99% success: 1 - (1 - w^n)^k >= 0.99 → (1 - w^n)^k <= 0.01 → k * log(1 - w^n) <= log(0.01) → k >= log(0.01) / log(0.9375) → k >= log(1 - 0.99) / log(1 - 0.0625) → k >= -4.605 / -0.0645 ≈ 71.35

Ceiling: k = 72 iterations needed

Constraints

inlier_ratio: proportion of inliers (0 < w < 1)
sample_size: number of points per sample (positive integer)
success_prob: desired probability of finding good model (default 0.99)
Return number of iterations (ceiling of computed value)
Handle edge cases: w=1 returns 1, w=0 returns infinity

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Background Knowledge

RANSAC (RANdom SAmple Consensus) is a robust estimation algorithm widely used in computer vision for model fitting in the presence of outliers, such as in image alignment and stitching where feature matches between images often include mismatches due to noise, occlusions, or repetitive patterns. In the context of image alignment, RANSAC repeatedly samples minimal subsets of correspondences (e.g., n points needed to estimate a homography or fundamental matrix), fits a model, and evaluates how many data points (inliers) support it, selecting the model with the largest inlier set to handle outlier ratios up to 50-90%.

The formula $k =$ \frac{\log(1 - p)}{\log(1 - w^n)} derives from RANSAC's probabilistic foundation: it estimates the number of iterations k required so that, with desired success probability p (typically 0.99), at least one iteration samples an all-inlier set. Here, w is the inlier ratio (fraction of good matches), and n is the sample size (minimal points for the model, e.g., 4 for homography). This ensures reliability despite outliers, balancing computation with confidence—higher w or lower n reduces k, while low w demands more iterations.

Algorithm/Approach

The general pattern is a direct implementation of the RANSAC iteration formula as a standalone calculator, avoiding full RANSAC simulation. Input parameters p, w, n; compute the probability that a single random sample is all-inliers ( $w^n$ ), then determine iterations needed for cumulative success probability p using logarithmic approximation of the geometric series for failure probability $(1 - w^n)^k$ .

Step-by-Step Strategy

Parse inputs: Read floating-point values for p (0 < p ≤ 1), w (0 < w ≤ 1), and integer n ≥ 1. Validate ranges to prevent invalid logs (e.g., ensure $w^n > 0$ ).

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