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The input data can be downloaded from submission system: the image `daliborka_01.jpg`

and the set of seven 2D points `u2`

.

- Load
`daliborka_01.jpg`

bitmap image into a 3D matrix/array (rows x cols x 3). - Display the array as image.
- Manually acquire coordinates of the set of seven points in the image corresponding to the tops of the five chimneys and the two towers. The points must be ordered
**from left to right**. Store the point coordinates in a 2×7 matrix, i.e. the point coordinates are**column**vectors. - In the bitmap image, colorize the pixels that are nearest to the acquired points (use rounding, not flooring/ceiling). Use the following colors in the following order:
**red = [255, 0, 0], green = [0, 255, 0], blue = [0, 0, 255], magenta = [255, 0, 255], cyan = [0, 255, 255], yellow = [255, 255, 0], white = [255, 255, 255]**to colorize the respective seven points. The colors are defined by their R, G, B values:**color = [R, G, B]**. The order of colors must correspond to the order of points`u`

. Store the modified bitmap image as a file`01_daliborka_points.png`

. - Create function
`A = estimate_A( u2, u )`

for estimation of the affine transformation`A`

(2×3 matrix)**from**n given points`u2`

**to**image points`u`

. The inputs`u2`

, and`u`

are 2xn matrices, e.g., point coordinates are columns.- Perform all possible selections of 3 point correspondences from all n correspondences.
- For each triple compute the affine transformation
`Ai`

(exactly). - Compute transfer errors of the particular transformation for every correspondence, i.e., the euclidean distances between points
`u`

and`ux`

; the points`ux`

are the points`u2`

transformed by`A`

. Find the maximum error over the correspondences. - From the all computed transformations
`Ai`

select the one`A`

that has the maximum transfer error minimal. - Assume general number of points, though we have only 7 points and 35 different triplets.

- Display the image, the set of points
`u`

using the same colors as above, and 100× magnified transfer errors for the best`A`

as red lines. - Export the graph as a pdf file
`01_daliborka_errs.pdf`

. - Store the points
`u`

and the matrix`A`

in the file`01_points.mat`

(Matlab format).

Please note when there is a matrix required as an output data, we mean matrix implemented as `np.array`

, not as `np.matrix`

or any other types. If you are using different type than `np.array`

, convert your result.

Implement the solution in a single file `hw01.py`

. The file must contain the `estimate_A`

function, such that it can be imported (by automatic evaluation) as

import hw01 A = hw01.estimate_A( u2, u )

In addition, when run as main python script, it should do the task described above. Use the `if __name__ == "__main__"`

test for separating code that should not run during import.

Upload an archive containing the following files:

`01_points.mat`

`01_daliborka_points.png`

`01_daliborka_errs.pdf`

`hw01.py`

- your implementation

Note: All files must be in the same directory. Do not use any subdirectories.

The following packages should be used:

import numpy as np # for matrix computation and linear algebra import matplotlib.pyplot as plt # for drawing and image I/O import scipy.io as sio # for matlab file format output import itertools # for generating all combinations

Image reading/writing as numpy array:

img = plt.imread( 'daliborka_01.jpg' ) # note that img is read-only, so a copy must be made to allow pixel modifications img = img.copy() img[0,0] = [ 255, 255, 255 ] # put white to upper left corner plt.imsave( 'out.png', img )

Showing the image:

plt.imshow( img ) plt.show()

Manual input of 7 points:

u = plt.ginput( 7 )

Draw errors, export graph as pdf:

# ux ... points u2 transformed by A e = 100 * ( ux - u ) # error displacements magnified by 100 fig = plt.figure() # figure handle to be used later fig.clf() plt.imshow( img ) # draw all points (in proper color) and errors ... plt.plot( u[3,0], u[3,1], 'o', color=[1,0,1], fillstyle='none' ) # the 4-th point in magenta color plt.plot( (u[3,0 ],u[3,0]+e[3,0]), (u[3,1],u[3,1]+e[3,1]), 'r-') # the 4-th displacement ... plt.show() fig.savefig( '01_daliborka_errs.pdf' )

Generator of all triplets:

n = u.shape[1] iter = itertools.combinations( range( 0, n ), 3 ) # three of n # iterate all combinations for inx in iter: u_i = u[ :, inx] u_2i = u_2[ :, inx ] # do the processing for a single triplet ...

Save results in MATLAB format:

sio.savemat('01_points.mat', {'u': u, 'A': A})

Implement your solution in a main script `hw01.m`

, in the file `estimate_A.m`

containing the function, and optionally in additional files for needed functions.

Upload an archive containing the following files:

`01_points.mat`

`01_daliborka_points.png`

`01_daliborka_errs.pdf`

`estimate_A.m`

`hw01.m`

- your Matlab implementation. It makes all required figures, output files and prints.- any other files required by hw01.m, such that the task is fully runnable

Note: All files must be in the same directory. Do not use any subdirectories.

Image read, display, write:

img = imread( 'daliborka_01.jpg' ); % load the image figure; % create a new figure image( img ); % display the image, keep axes visible axis image % display it with square pixels img(1,1,:) = [255, 255, 255]; % put white to the upper left corner imwrite( img, 'out.png' ); % write the image to a file

Manual input of 7 points:

[x,y] = ginput(7);

Draw errors, export graph as pdf:

% ux .. points u2 transformed by A e = 100 * ( ux - u ); % magnified error displacements ... hold on % to plot over the image ... plot( u(1,4), u(2,4), 'o', 'linewidth', 2, 'color', 'magenta' ) % the 4-th point plot( [ u(1,4) u(1,4)+e(1,4) ], [ u(2,4) u(2,4)+e(2,4) ], 'r-', 'linewidth', 2 ); % the 4-th error ... hold off fig2pdf( gcf, '01_daliborka_errs.pdf' ) % function provided in 'tools'

Save results in MAT file:

save( '01_points.mat', 'u', 'A' )

courses/gvg/labs/hw-01.txt · Last modified: 2021/02/26 21:10 by xmatousm