CS231A

My own solutions for CS231A_1718fall problem sets

The course is CS231A: Computer Vision, From 3D Reconstruction to Recognition
The repository contains my solutions for problem sets
All the material can be downloaded from class syllabus on stanford
There are some detailed comments in the codes which I hope will help you understand the program

Reference solutions

Here are some solutions which are easy to check, in case someone needs them.
If you find some mistakes, feel free to tell me.

Problem set 0

• Problem 2

(a^T b)Ma: 
 [ 3  9 15  2]
multiply each row of M element-wise by a: 
 [[1 2 0]
 [4 5 0]
 [7 8 0]
 [0 2 0]]
sorted M: 
 [0 0 0 0 0 1 2 2 4 5 7 8]

• Problem 3

Problem3_1	Problem3_2	Problem3_3

Problem3_4	Problem3_5

• Problem 4

Problem4_1	Problem4_2	Problem4_3

Problem set 1

• Problem 2

Camera Matrix:
[[ 5.31276507e-01 -1.80886074e-02  1.20509667e-01  1.29720641e+02]
[ 4.84975447e-02  5.36366401e-01 -1.02675222e-01  4.43879607e+01]
[-1.40079365e-18  4.77048956e-18  1.40946282e-18  1.00000000e+00]]
RMS Error:  1.4054885481541644

• Problem 3

Intrinsic Matrix:
[[ 2.87873596e+03 -0.00000000e+00  8.58115141e+02]
[-0.00000000e+00  2.87873596e+03  1.08694938e+03]
[-0.00000000e+00 -0.00000000e+00  1.10969448e+00]]

Actual Matrix:
[[2.448e+03 0.000e+00 1.253e+03]
[0.000e+00 2.438e+03 9.860e+02]
[0.000e+00 0.000e+00 1.000e+00]]

Angle between floor and box: 90.027361241031

Rotation between two cameras:
[[ 8.19551249e-01  1.35836471e-01 -3.69928448e-01]
[ 9.09898356e-02  1.16646489e+00  1.42060135e-01]
[-7.67565342e-16 -1.22124533e-15  1.01061171e+00]]
Angle around z-axis (pointing out of camera): -9.410931 degrees
Angle around y-axis (pointing vertically): -19.924588 degrees
Angle around x-axis (pointing horizontally): -8.001552 degrees

Problem set 2

• Problem 1

--------------------------------------------------------------------------------
Set: data/set2
--------------------------------------------------------------------------------
Fundamental Matrix from LLS  8-point algorithm:
[[-5.63087200e-06  2.74976583e-05 -6.42650411e-03]
[-2.77622828e-05 -6.74748522e-06  1.52182033e-02]
[ 1.07623595e-02 -1.22519240e-02 -9.99730547e-01]]
Distance to lines in image 1 for LLS: 9.701438829436539
Distance to lines in image 2 for LLS: 14.568227190498169
p'^T F p = 0.033136691062293
Fundamental Matrix from normalized 8-point algorithm:
[[-1.51007608e-07  2.51618737e-06 -1.56134009e-04]
[ 3.63462620e-06  3.22311660e-07  7.02588719e-03]
[ 2.36155133e-04 -8.53003408e-03 -2.45880925e-03]]
Distance to lines in image 1 for normalized: 0.8895134540568762
Distance to lines in image 2 for normalized: 0.8917343723800133

Problem1_1	Problem1_2

Problem1_3	Problem1_4

• Problem 2

e1 [-1.30071143e+03 -1.42448272e+02  1.00000000e+00]
e2 [1.65412463e+03 4.53021078e+01 1.00000000e+00]
H1:
[[-1.20006316e+01 -4.15501447e+00 -1.23476881e+02]
[ 1.41006481e+00 -1.48704147e+01 -2.84177469e+02]
[-9.21889298e-03 -2.19184511e-03 -1.23033440e+01]]
H2:
[[ 8.09798131e-01 -1.22036874e-01  7.99331183e+01]
[-3.00186699e-02  1.01581538e+00  3.63604348e+00]
[-6.99360915e-04  1.05393946e-04  1.15205554e+00]]

• Problem 3

Problem3_1	Problem3_2

• Problem 4

--------------------------------------------------------------------------------
Part A: Check your matrices against the example R,T
--------------------------------------------------------------------------------
Example RT:
 [[ 0.9736 -0.0988 -0.2056  0.9994]
 [ 0.1019  0.9948  0.0045 -0.0089]
 [ 0.2041 -0.0254  0.9786  0.0331]]
Estimated RT:
 [[[ 0.98305251 -0.11787055 -0.14040758  0.99941228]
  [-0.11925737 -0.99286228 -0.00147453 -0.00886961]
  [-0.13923158  0.01819418 -0.99009269  0.03311219]]

 [[ 0.98305251 -0.11787055 -0.14040758 -0.99941228]
  [-0.11925737 -0.99286228 -0.00147453  0.00886961]
  [-0.13923158  0.01819418 -0.99009269 -0.03311219]]

 [[ 0.97364135 -0.09878708 -0.20558119  0.99941228]
  [ 0.10189204  0.99478508  0.00454512 -0.00886961]
  [ 0.2040601  -0.02537241  0.97862951  0.03311219]]

 [[ 0.97364135 -0.09878708 -0.20558119 -0.99941228]
  [ 0.10189204  0.99478508  0.00454512  0.00886961]
  [ 0.2040601  -0.02537241  0.97862951 -0.03311219]]]
--------------------------------------------------------------------------------
Part B: Check that the difference from expected point
is near zero
--------------------------------------------------------------------------------
Difference:  0.0029243053036863698
--------------------------------------------------------------------------------
Part C: Check that the difference from expected error/Jacobian
is near zero
--------------------------------------------------------------------------------
Error Difference:  8.301300130674275e-07
Jacobian Difference:  1.817115702351657e-08
--------------------------------------------------------------------------------
Part D: Check that the reprojection error from nonlinear method
is lower than linear method
--------------------------------------------------------------------------------
Linear method error: 98.73542356894195
Nonlinear method error: 95.59481784846034
--------------------------------------------------------------------------------
Part E: Check your matrix against the example R,T
--------------------------------------------------------------------------------
Example RT:
 [[ 0.9736 -0.0988 -0.2056  0.9994]
 [ 0.1019  0.9948  0.0045 -0.0089]
 [ 0.2041 -0.0254  0.9786  0.0331]]
Estimated RT:
 [[ 0.97364135 -0.09878708 -0.20558119  0.99941228]
 [ 0.10189204  0.99478508  0.00454512 -0.00886961]
 [ 0.2040601  -0.02537241  0.97862951  0.03311219]]

Problem Set 3

• Problem 1

Problem1_1	Problem1_2	Problem1_3

Problem1_4	Problem1_5

• Problem 2

Problem2_1	Problem2_2

Problem2_3	Problem2_4

Problem2_5	Problem2_6

Problem2_7	Problem2_8

Problem2_9	Problem2_10

Problem2_11	Problem2_12

• Problem 3

--------------------------------------------------------------------------------
Part A: Image gradient
--------------------------------------------------------------------------------
Expected angle: 126.339396329
Expected magnitude: 0.423547566786
Checking gradient test case 1: True
Expected angles: 
[[100.30484647  63.43494882 167.47119229]
[ 68.19859051   0.          45.        ]
[ 53.13010235  64.53665494 180.        ]]
Expected magnitudes: 
[[11.18033989 11.18033989  9.21954446]
[ 5.38516481 11.          7.07106781]
[15.         11.62970335  2.        ]]
Checking gradient test case 2: True
--------------------------------------------------------------------------------
Part B: Histogram generation
--------------------------------------------------------------------------------
Checking histogram test case 1: True
Checking histogram test case 2: True
Submit these results: [4.535 2.465 0.95  0.8   0.45  0.9   0.    0.    0.   ]

Problem Set 4

• Problem 1

Problem1_1	Problem1_2

• Problem 2

Problem2_1	Problem2_2

Problem2_3	Problem2_4

Problem2_5	Problem2_6