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Practical Work2

1. The document provides instructions for exercises in a Python programming assignment involving curve fitting, orbit parameter estimation, and the RANSAC algorithm. 2. The first exercise involves fitting linear and quadratic curves to noisy data and estimating the model parameters. 3. The second exercise estimates parameters for an orbit model given observational angle and value data. 4. The third exercise implements a simplified RANSAC algorithm to deal with outliers in a linear dataset by iteratively selecting random models and keeping the model with the most inliers.

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Assimi Dembélé
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10 views2 pages

Practical Work2

1. The document provides instructions for exercises in a Python programming assignment involving curve fitting, orbit parameter estimation, and the RANSAC algorithm. 2. The first exercise involves fitting linear and quadratic curves to noisy data and estimating the model parameters. 3. The second exercise estimates parameters for an orbit model given observational angle and value data. 4. The third exercise implements a simplified RANSAC algorithm to deal with outliers in a linear dataset by iteratively selecting random models and keeping the model with the most inliers.

Uploaded by

Assimi Dembélé
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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MA324 : TP2

You may use TP2.py using your favorite Python IDE (e.g. spyder). Some parts are the same
as in TP1, so you may gain time if you saved your work.
Exercice 1 (Fitting curves)

1. Using the numpy/linspace create an 1D array x that contains 100 samples uniformly distri-
buted on [0, 1]
2. Simulate and plot the model
y = 10 + 2x + 8x2 + ε
where ε are centered normal iid with variance 2
3. Form the matrix X, the vector Y and apply the formula seen during the lecture 2 to estimate
the model parameters. You can compute the matrix inverse with np.linalg.inv
4. Plot the obtained model and the data
5. Do the same as in questions 1-4 for the model

y = 10 + 2x + 8x2 + 10 sin(πx) + ε

1
Exercice 2 (Orbit parameter)

p
1. We observe the following data We assume that the model is f (θ) = 1−e cos(θ) , as in EX1 of

Angles in degrees 43 45 52 93 108 126


Observed values 4.7126 4.5542 4.0419 2.2187 1.8910 1.7599

TD2. Estimate the parameters p and e from this data

Exercice 3 (Dealing with outliers : (simplified) ransac algorithm)

1. Using the numpy/linspace create an 1D array x that contains 100 samples uniformly distri-
buted on [0, 1] and build the model y = 10 + 2x.
2. Modify at random (uniformly) say 10 values of y and replace these values by realizations of
iid centered Gaussian random variable of unit variance and plot the result
3. Write a function that given two models decide 1 if a model has more inliers than the other.
We say that (x, y) is an inlier if for model parameter β1 , β2 we have |β1 x+β2 −y| < T reshold.
Where T reshold is a given value. Hint : compare the number of inliers for both models.
4. Write a function that pick 2 samples at random (uniformly) and compute the associated
model using these 2 samples and return the computed parameters
5. Set T hreshold = 1, and iterate say 10 times : computing a model at random ; compare it
with new one and keep the new one if the new model has more inliers
6. Compare both strategies : the naive one done in TP1 where we performed the estimation
keeping the outliers and the model estimated via ransac.

1. that is return a boolean that indicates if a model is more suitable than the other

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