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#![no_std]
extern crate alloc;
use core::cmp::Reverse;
use alloc::{vec, vec::Vec};
use rand_core::RngCore;
use sample_consensus::{Consensus, Estimator, Model};
/// The ARRSAC algorithm for sample consensus.
///
/// Don't forget to shuffle your input data points to avoid bias before
/// using this consensus process. It will not shuffle your data for you.
/// If you do not shuffle, the output will be biased towards data at the beginning
/// of the inputs.
pub struct Arrsac<R> {
initialization_hypotheses: usize,
initialization_blocks: usize,
max_candidate_hypotheses: usize,
estimations_per_block: usize,
block_size: usize,
likelihood_ratio_threshold: f32,
inlier_threshold: f64,
rng: R,
random_samples: Vec<u32>,
}
impl<R> Arrsac<R>
where
R: RngCore,
{
/// `rng` should have the same properties you would want for a Monte Carlo simulation.
/// It should generate random numbers quickly without having any discernable patterns.
///
/// The `inlier_threshold` is the one parameter that is always specific to your dataset.
/// This must be set to the threshold in which a data point's residual is considered an inlier.
/// Some of the other parameters may need to be configured based on the amount of data,
/// such as `block_size`, `likelihood_ratio_threshold`, and `block_size`. However,
/// `inlier_threshold` has to be set based on the residual function used with the model.
///
/// `initial_epsilon` must be higher than `initial_delta`. If you modify these values,
/// you need to make sure that within one `block_size` the `likelihood_ratio_threshold`
/// can be reached and a model can be rejected. Basically, make sure that
/// `((1.0 - delta) / (1.0 - epsilon))^block_size >>> likelihood_ratio_threshold`.
/// This must be done to ensure outlier models are rejected during the initial generation
/// phase, which only processes `block_size` datapoints.
///
/// `initial_epsilon` should also be as large as you can set it where it is still relatively
/// pessimistic. This is so that we can more easily reject a model early in the process
/// to compute an updated value for delta during the adaptive process. This may not be possible
/// and will depend on your data.
pub fn new(inlier_threshold: f64, rng: R) -> Self {
Self {
initialization_hypotheses: 256,
initialization_blocks: 4,
max_candidate_hypotheses: 64,
estimations_per_block: 64,
block_size: 64,
likelihood_ratio_threshold: 1e3,
inlier_threshold,
rng,
random_samples: vec![],
}
}
/// Number of models generated in the initial step when epsilon and delta are being estimated.
///
/// Default: `256`
#[must_use]
pub fn initialization_hypotheses(self, initialization_hypotheses: usize) -> Self {
Self {
initialization_hypotheses,
..self
}
}
/// Number of data blocks used to compute the initial estimate of delta and epsilon
/// before proceeding with regular block processing. This is used instead of
/// an initial epsilon and delta, which were suggested by the paper.
///
/// Default: `4`
#[must_use]
pub fn initialization_blocks(self, initialization_blocks: usize) -> Self {
Self {
initialization_blocks,
..self
}
}
/// Maximum number of best hypotheses to retain during block processing
///
/// This number is halved on each block such that on block `n` the number of
/// hypotheses retained is `max_candidate_hypotheses >> n`.
///
/// Default: `64`
#[must_use]
pub fn max_candidate_hypotheses(self, max_candidate_hypotheses: usize) -> Self {
Self {
max_candidate_hypotheses,
..self
}
}
/// Number of estmations (may generate multiple hypotheses) that will be ran
/// for each block of data evaluated
///
/// Default: `64`
#[must_use]
pub fn estimations_per_block(self, estimations_per_block: usize) -> Self {
Self {
estimations_per_block,
..self
}
}
/// Number of data points evaluated before more hypotheses are generated
///
/// Default: `64`
#[must_use]
pub fn block_size(self, block_size: usize) -> Self {
Self { block_size, ..self }
}
/// Once a model reaches this level of unlikelihood, it is rejected. Set this
/// higher to make it less restrictive, usually at the cost of more execution time.
///
/// Increasing this will make it more likely to find a good result.
///
/// Decreasing this will speed up execution.
///
/// This ratio is not exposed as a parameter in the original paper, but is instead computed
/// recursively for a few iterations. It is roughly equivalent to the **reciprocal** of the
/// **probability of rejecting a good model**. You can use that to control the probability
/// that a good model is rejected.
///
/// Default: `1e3`
#[must_use]
pub fn likelihood_ratio_threshold(self, likelihood_ratio_threshold: f32) -> Self {
Self {
likelihood_ratio_threshold,
..self
}
}
/// Residual threshold for determining if a data point is an inlier or an outlier of a model
#[must_use]
pub fn inlier_threshold(self, inlier_threshold: f64) -> Self {
Self {
inlier_threshold,
..self
}
}
/// Adapted from algorithm 3 from "A Comparative Analysis of RANSAC Techniques Leading to Adaptive
/// Real-Time Random Sample Consensus", but it was effectively rewritten to avoid the need for
/// initial epsilon and delta.
///
/// Returns the initial models (and their num inliers) sorted by decreasing inliers
/// and `delta` in that order.
fn initial_hypotheses<E, Data>(
&mut self,
estimator: &E,
data: impl Iterator<Item = Data> + Clone,
) -> (Vec<(E::Model, usize)>, f32)
where
E: Estimator<Data>,
{
assert!(
self.initialization_blocks > 0,
"ARRSAC must have at least 1 initialization block"
);
// NOTE: This whole function is different than that specified in the ARRSAC paper.
// The reason is that you needed to provide a good initial guess for epsilon and delta
// otherwise it could lead to delta exceeding epsilon or situations where models could no
// longer be rejected or were almost always rejected. This solution is an imperfect compomise
// that assumes that delta will be roughly equal to the inlier ratio of the worst model generated,
// which both assumes that the worst model is an outlier and that it is actually representative of the
// population. The assumption of epsilon also assumes that the best model is an inlier, but is an
// otherwise good initial guess. The other caveat with this approach is that a sufficiently large
// set of initial datapoints is required to be able to accurately determine epsilon and delta.
// Therefore a new paremeter is added to separate the normal blocks from the initial generation set.
let mut hypotheses = vec![];
// We don't want more than `block_size` data points to be used to evaluate models initially.
let initial_datapoints = core::cmp::min(
self.initialization_blocks * self.block_size,
data.clone().count(),
);
// Generate the initial batch of random hypotheses and count their inliers and outliers.
for _ in 0..self.initialization_hypotheses {
for model in self.generate_random_hypotheses(estimator, data.clone()) {
let inliers = self.count_inliers(data.clone().take(initial_datapoints), &model);
hypotheses.push((model, inliers));
}
}
// Bail early when no hypothesis was found.
// This will cause execution to terminate.
if hypotheses.is_empty() {
return (hypotheses, 0.0);
}
// Sort the hypotheses by their inliers.
hypotheses.sort_unstable_by_key(|&(_, inliers)| Reverse(inliers));
// Compute epsilon and delta using the best and worst model generated.
let epsilon = hypotheses
.first()
.map(|&(_, inliers)| inliers as f32 / initial_datapoints as f32)
.unwrap_or_default();
let delta = hypotheses
.last()
.map(|&(_, inliers)| if inliers < E::MIN_SAMPLES {E::MIN_SAMPLES} else {inliers} as f32 / initial_datapoints as f32)
.unwrap_or_default();
if epsilon < delta {
// If epsilon is less than delta, then better hypotheses will get rejected and worse accepted,
// which is counter to what we want. In this case, we had a bad initialization, so clear the hypotheses.
// This will cause execution to terminate.
hypotheses.clear();
return (hypotheses, delta);
}
// Populate hypotheses with hypotheses generated from the inliers of the best hypothesis.
// This will use the initialization datapoints and filter with SPRT.
self.populate_hypotheses_sprt(
estimator,
&mut hypotheses,
delta,
data,
initial_datapoints,
self.initialization_hypotheses,
);
// Sort the hypotheses by their inliers.
hypotheses.sort_unstable_by_key(|&(_, inliers)| Reverse(inliers));
// Filter down the hypotheses to just the best ones.
hypotheses.truncate(self.max_candidate_hypotheses >> (self.initialization_blocks - 1));
(hypotheses, delta)
}
/// Populates `self.random_samples` using a len.
fn populate_samples(&mut self, num: usize, len: usize) {
// We can generate no hypotheses if the amout of data is too low.
if len < num {
panic!("cannot use arrsac without having enough samples");
}
let len = len as u32;
// Threshold generation below adapted from randomize::RandRangeU32.
let threshold = len.wrapping_neg() % len;
self.random_samples.clear();
for _ in 0..num {
loop {
let mul = u64::from(self.rng.next_u32()).wrapping_mul(u64::from(len));
if mul as u32 >= threshold {
let s = (mul >> 32) as u32;
if !self.random_samples.contains(&s) {
self.random_samples.push(s);
break;
}
}
}
}
}
fn populate_hypotheses_sprt<E, Data>(
&mut self,
estimator: &E,
hypotheses: &mut Vec<(E::Model, usize)>,
delta: f32,
data: impl Iterator<Item = Data> + Clone,
num_checked: usize,
num_hypotheses: usize,
) where
E: Estimator<Data>,
{
// Update epsilon using the best model.
// Since epsilon can only increase and delta is fixed, we can be sure that these ratios
// will still be valid (epsilon > delta).
let epsilon = hypotheses[0].1 as f32 / num_checked as f32;
// Create the likelihood ratios for inliers and outliers.
let positive_likelihood_ratio = delta / epsilon;
let negative_likelihood_ratio = (1.0 - delta) / (1.0 - epsilon);
// Generate the list of inliers for the best model.
let mut inliers = self.inliers(data.clone().take(num_checked), &hypotheses[0].0);
if inliers.len() <= E::MIN_SAMPLES {
// If we don't have enough samples to generate more models, then we should expand the inliers to
// the entire dataset.
inliers = self.inliers(data.clone().take(num_checked), &hypotheses[0].0);
}
// We generate hypotheses until we reach the initial num hypotheses.
// We can't count the number generated because it could generate 0 hypotheses
// and then the loop would continue indefinitely.
let mut random_hypotheses = Vec::new();
for _ in 0..num_hypotheses {
random_hypotheses.extend(self.generate_random_hypotheses_subset(
estimator,
data.clone(),
&inliers,
));
for model in random_hypotheses.drain(..) {
if let Some(inliers) = self.asprt(
data.clone().take(num_checked),
&model,
positive_likelihood_ratio,
negative_likelihood_ratio,
E::MIN_SAMPLES,
) {
hypotheses.push((model, inliers));
}
}
}
}
/// Generates as many hypotheses as one call to `Estimator::estimate()` returns from all data.
fn generate_random_hypotheses<E, Data>(
&mut self,
estimator: &E,
data: impl Iterator<Item = Data> + Clone,
) -> E::ModelIter
where
E: Estimator<Data>,
{
self.populate_samples(E::MIN_SAMPLES, data.clone().count());
estimator.estimate(
self.random_samples
.iter()
.map(|&ix| data.clone().nth(ix as usize).unwrap()),
)
}
/// Generates as many hypotheses as one call to `Estimator::estimate()` returns from a subset of the data.
fn generate_random_hypotheses_subset<E, Data>(
&mut self,
estimator: &E,
data: impl Iterator<Item = Data> + Clone,
subset: &[usize],
) -> E::ModelIter
where
E: Estimator<Data>,
{
self.populate_samples(E::MIN_SAMPLES, subset.len());
estimator.estimate(
core::mem::take(&mut self.random_samples)
.iter()
.map(|&ix| data.clone().nth(subset[ix as usize]).unwrap()),
)
}
/// Algorithm 1 in "Randomized RANSAC with Sequential Probability Ratio Test".
///
/// This tests if a model is accepted. Returns `Some(inliers)` if accepted or `None` if rejected.
///
/// `inlier_threshold` - The model residual error threshold between inliers and outliers
/// `positive_likelihood_ratio` - `δ / ε`
/// `negative_likelihood_ratio` - `(1 - δ) / (1 - ε)`
fn asprt<Data, M: Model<Data>>(
&self,
data: impl Iterator<Item = Data>,
model: &M,
positive_likelihood_ratio: f32,
negative_likelihood_ratio: f32,
minimum_samples: usize,
) -> Option<usize> {
let mut likelihood_ratio = 1.0;
let mut inliers = 0;
for data in data {
likelihood_ratio *= if model.residual(&data) < self.inlier_threshold {
inliers += 1;
positive_likelihood_ratio
} else {
negative_likelihood_ratio
};
if likelihood_ratio > self.likelihood_ratio_threshold || likelihood_ratio.is_nan() {
return None;
}
}
(inliers >= minimum_samples).then(|| inliers)
}
/// Determines the number of inliers a model has.
fn count_inliers<Data, M: Model<Data>>(
&self,
data: impl Iterator<Item = Data>,
model: &M,
) -> usize {
data.filter(|data| model.residual(data) < self.inlier_threshold)
.count()
}
/// Gets indices of inliers for a model.
fn inliers<Data, M: Model<Data>>(
&self,
data: impl Iterator<Item = Data>,
model: &M,
) -> Vec<usize> {
data.enumerate()
.filter(|(_, data)| model.residual(data) < self.inlier_threshold)
.map(|(ix, _)| ix)
.collect()
}
}
impl<E, R, Data> Consensus<E, Data> for Arrsac<R>
where
E: Estimator<Data>,
R: RngCore,
{
type Inliers = Vec<usize>;
fn model<I>(&mut self, estimator: &E, data: I) -> Option<E::Model>
where
I: Iterator<Item = Data> + Clone,
{
self.model_inliers(estimator, data).map(|(model, _)| model)
}
fn model_inliers<I>(&mut self, estimator: &E, data: I) -> Option<(E::Model, Self::Inliers)>
where
I: Iterator<Item = Data> + Clone,
{
// Don't do anything if we don't have enough data.
if data.clone().count() < E::MIN_SAMPLES {
return None;
}
// Generate the initial set of hypotheses. This also gets us an estimate of delta.
let (mut hypotheses, delta) = self.initial_hypotheses(estimator, data.clone());
// If there are no initial hypotheses then initialization failed, so exit early.
if hypotheses.is_empty() {
return None;
}
// Gradually increase how many datapoints we are evaluating until we evaluate them all.
// This starts at the first block that was not evaluated in initial_hypotheses.
'outer: for block in self.initialization_blocks.. {
let samples_up_to_beginning_of_block = block * self.block_size;
let samples_up_to_end_of_block = samples_up_to_beginning_of_block + self.block_size;
// Score hypotheses with samples.
for sample in samples_up_to_beginning_of_block..samples_up_to_end_of_block {
// Score the hypotheses with the new datapoint.
let new_datapoint = if let Some(datapoint) = data.clone().nth(sample) {
datapoint
} else {
// We reached the last datapoint, so break out of the outer loop.
break 'outer;
};
for (hypothesis, inlier_count) in hypotheses.iter_mut() {
if hypothesis.residual(&new_datapoint) < self.inlier_threshold {
*inlier_count += 1;
}
}
}
// Sort the hypotheses by their inliers to find the best.
hypotheses.sort_unstable_by_key(|&(_, inliers)| Reverse(inliers));
// Populate hypotheses with hypotheses that pass SPRT.
self.populate_hypotheses_sprt(
estimator,
&mut hypotheses,
delta,
data.clone(),
samples_up_to_end_of_block,
self.estimations_per_block,
);
// This will retain at least half of the hypotheses each time
// and gradually decrease as the number of samples we are evaluating increases.
// NOTE:
// The paper says to use a peculiar formula that just results in doing
// this basic right shift below, but as written it contained some apparent errors in
// where it was ran. This seems to be the correct location to do this.
hypotheses.sort_unstable_by_key(|&(_, inliers)| Reverse(inliers));
hypotheses.truncate(self.max_candidate_hypotheses >> block);
if hypotheses.len() <= 1 {
break 'outer;
}
}
hypotheses
.into_iter()
.max_by_key(|&(_, inliers)| inliers)
.map(|(model, _)| {
let inliers = self.inliers(data.clone(), &model);
(model, inliers)
})
}
}