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Table of contents
1.
Introduction
2.
The Need for RANSAC Algorithm?
3.
RANSAC Algorithm
4.
Frequently Asked Questions
4.1.
I would like to figure out what my model's parameters are. What am I supposed to do?
4.2.
Why can't RANSAC's behavior be replicated?
4.3.
What is the "best suitable" value for σ?
4.4.
Is RANSAC only for linear models?
5.
Conclusion
Last Updated: Mar 27, 2024

RANSAC Algorithm

Author Anju Jaiswal
0 upvote
Master Python: Predicting weather forecasts
Speaker
Ashwin Goyal
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Introduction

Fischler and Bolles created the RANdom SAmple Consensus (RANSAC) algorithm, a general parameter estimation approach designed to deal with a high proportion of outliers in the input data. By removing outliers in the training dataset, the RANSAC (RANdom SAmple Consensus) technique takes the linear regression process to the next level. Outliers in the training dataset impact the coefficients/parameters learned during training. 

As a result, outliers should be discovered and deleted during the exploratory data analysis phase. Outliers from the training data set should be removed, use Statistical approaches such as Z-scores, Box plots, other types of plots, hypothesis tests, and many others.

The Need for RANSAC Algorithm?

The concept underlying traditional linear regression is straightforward: create a "best-fit" line across the data points that minimizes mean squared errors. It appears to be in good condition. However, we do not often obtain such clean, well-behaved data.

The Classic example of linear regression

You have been given a dataset and want to use it to fit a mathematical model. We can now presume that there are some inliers and outliers in this data. Outliers are data points that any plausible mathematical model cannot describe. Inliers are data points that a mathematical model can explain. 

Data points

The quality of the mathematical model we can fit the data is usually harmed by their presence in the dataset. While estimating the parameters of our mathematical model, we should disregard these outliers for optimum outcomes. RANSAC assists us in finding these locations in order to provide a better fit for the inliers.

Even the inliers may not completely match the mathematical model owing to noise. However, the outliers either have an unusually significant quantity of noise or are produced due to measurement errors or sensor difficulties.

Let us discuss the algorithm now.

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RANSAC Algorithm

Basic idea: Try on a few different fits and choose the best one!

The following stages will be followed. The method will be terminated if the model performance passes a user-defined threshold or a set number of iterations has been achieved.

for n in range(numTrials): # num of trials we opt for or iterations
Pick a random set of points
Solve the model using those parameters
Divide the original dataset into inliers and outliers based on the fit.
The model-fitting points become part of the consensus set. The model is good if a certain number of points have been classified as part of the consensus set.
count number of inliers,
pick the model with the most inliers

Trying different fits

So, what appears to be a reasonable compromise? We must define a maximum distance threshold possible inlier can have while using RANSAC. The absolute value for each activity must be chosen separately based on the problem we attempt to solve.

Another critical question is how many times we must perform this process to discover a solution. We must admit that RANSAC does not always provide a decent answer. It is a non-deterministic system. To develop a model for our data, we choose points at random. That implies that depending on how data is distributed, and we can develop a decent model with a certain probability.

Also read, Sampling and Quantization

Frequently Asked Questions

I would like to figure out what my model's parameters are. What am I supposed to do?

The model parametrization should be essential because the parameters should not be interdependent. It should be simple to generate a relation that maps the MSS input data to the model parameters.

Why can't RANSAC's behavior be replicated?

Because of the algorithm's inherent characteristics, RANSAC randomly selects the MSS elements from the total dataset (with or without a bias). As a result, the behavior may vary from run to run.

What is the "best suitable" value for σ?

The above question does not have any universal answer. If the noise impacting the inliers is Gaussian, the value is used to calculate the threshold that distinguishes between inliers and outliers. As a result, the "correct" answer depends on the type of data you are working with.

Is RANSAC only for linear models?

Not in the least! For example, you might have a point cloud that needs to be modeled as a circle. Multiple circles may be concealed in the point cloud, and RANSAC will produce the circle model that best fits the most observations.

Conclusion

In this blog we got an overview of the RANSAC's algorithm. We saw that even when the data set contains many outliers, it can estimate the parameters with high accuracy. We learnt about why we need the algorithm and where it can be used. Finally we looked at the pseudocode of the Algorithm. To get a complete understanding of various machine learning and computer vision algorithms, check out our Machine learning course.

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