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Fan Jiang
2020-11-06 23:41:45 -05:00
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players/ProfFan/writeup.md
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今年实在太忙，只做了一题
今年实在太忙，只做了一题orz
# 证验码
@@ -7,3 +7,470 @@
注意此处应当使用 L1 而不是 L2 优化，因为16个字符远少于 26*2+10，结果应当是稀疏的。本题用 L2 也可以得到解，但是如果增加干扰线条的密度，L2 应该会失败。
# 代码
```python
%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np
import random, string
```
```python
import shuffle
```
```python
# !wget https://github.com/adobe-fonts/source-code-pro/raw/release/TTF/SourceCodePro-Light.ttf
```
```python
alphabet = sorted(string.digits + string.ascii_letters)
#code = "".join([random.choice(alphabet) for _ in range(16)])
code = "01234567890ABcde"
print("Code:", code)
```
Code: 01234567890ABcde
```python
original = shuffle.generate_captcha(code, shuffle_mode=False)
shuffled = shuffle.generate_captcha(code, shuffle_mode=True)
```
```python
plt.subplot(211)
plt.imshow(original)
plt.subplot(212)
plt.imshow(shuffled)
```
<matplotlib.image.AxesImage at 0x7f8312f56970>
![svg](solver_files/solver_5_1.svg)
```python
fig, axs = plt.subplots(2, 10, figsize=(20,6))
for i in range(10):
test_onealpha = np.array(shuffle.img_generate("{}".format(i)))
axs[0][i].imshow(test_onealpha)
counts = np.bincount(test_onealpha[:, :, 0].flatten(),minlength=255)
axs[1][i].plot(counts)
axs[1][i].set_yscale('log')
```
![svg](solver_files/solver_6_0.svg)
```python
counts_full = []
for k in range(3):
counts = np.bincount(np.array(shuffled)[:, :, 0].flatten(),minlength=256)
counts[255] = 0
counts_full.append(counts)
counts_full = np.hstack(counts_full)
print(counts_full.shape)
```
(768,)
```python
# %pip install cvxpy
```
```python
import cvxpy as cvx
```
```python
bases = []
for i in range(len(alphabet)):
bases_rgb = []
for k in range(3):
test_onealpha = np.array(shuffle.img_generate("{}".format(alphabet[i])))
counts = np.bincount(test_onealpha[:, :, k].flatten(),minlength=256)
counts[255] = 0
bases_rgb.append(counts)
bases.append(np.hstack(bases_rgb))
A = np.vstack(bases).T
print(A.shape)
print(A.T)
```
(768, 62)
[[224 5 2 ... 3 5 0]
[134 1 1 ... 0 2 0]
[171 2 1 ... 3 4 0]
...
[ 94 1 2 ... 2 6 0]
[118 4 3 ... 2 6 0]
[195 2 2 ... 1 3 0]]
/usr/lib/python3.8/site-packages/ipykernel/ipkernel.py:287: DeprecationWarning: `should_run_async` will not call `transform_cell` automatically in the future. Please pass the result to `transformed_cell` argument and any exception that happen during thetransform in `preprocessing_exc_tuple` in IPython 7.17 and above.
and should_run_async(code)
```python
import PIL
shuffled = PIL.Image.open("./captcha_shuffled.bmp")
# Solve actual problem
counts_full = []
for k in range(3):
counts = np.bincount(np.array(shuffled)[:, :, 0].flatten(),minlength=256)
counts[255] = 0
counts_full.append(counts)
counts_full = np.hstack(counts_full)
print(counts_full.shape)
```
(768,)
/usr/lib/python3.8/site-packages/ipykernel/ipkernel.py:287: DeprecationWarning: `should_run_async` will not call `transform_cell` automatically in the future. Please pass the result to `transformed_cell` argument and any exception that happen during thetransform in `preprocessing_exc_tuple` in IPython 7.17 and above.
and should_run_async(code)
```python
vx = cvx.Variable(len(alphabet))
objective = cvx.Minimize(cvx.norm(A*vx - counts_full, 1))
constraints = [vx >= 0]
prob = cvx.Problem(objective, constraints)
result = prob.solve(verbose=True)
```
ECOS 2.0.7 - (C) embotech GmbH, Zurich Switzerland, 2012-15. Web: www.embotech.com/ECOS
It pcost dcost gap pres dres k/t mu step sigma IR | BT
0 -2.788e-13 +1.258e-12 +5e+05 8e-01 4e-01 1e+00 3e+02 --- --- 1 2 - | - -
1 +4.640e+03 +4.675e+03 +2e+05 3e-01 1e-01 3e+01 1e+02 0.7401 2e-01 1 1 1 | 0 0
2 +5.846e+03 +5.861e+03 +9e+04 1e-01 4e-02 1e+01 6e+01 0.6585 8e-02 1 1 1 | 0 0
3 +5.968e+03 +5.970e+03 +1e+04 1e-02 3e-03 2e+00 6e+00 0.9494 6e-02 1 1 1 | 0 0
4 +6.080e+03 +6.080e+03 +3e+03 4e-03 1e-03 5e-01 2e+00 0.7566 6e-02 1 1 1 | 0 0
5 +6.151e+03 +6.152e+03 +2e+03 2e-03 6e-04 3e-01 1e+00 0.6536 5e-01 1 1 1 | 0 0
6 +6.193e+03 +6.193e+03 +9e+02 1e-03 3e-04 1e-01 5e-01 0.6015 1e-01 1 1 1 | 0 0
7 +6.198e+03 +6.198e+03 +8e+02 1e-03 3e-04 1e-01 5e-01 0.2129 7e-01 1 1 1 | 0 0
8 +6.216e+03 +6.216e+03 +6e+02 9e-04 2e-04 1e-01 3e-01 0.5360 4e-01 1 1 1 | 0 0
9 +6.230e+03 +6.230e+03 +3e+02 6e-04 1e-04 6e-02 2e-01 0.6585 4e-01 1 1 1 | 0 0
10 +6.244e+03 +6.244e+03 +2e+02 3e-04 5e-05 3e-02 1e-01 0.6652 2e-01 1 1 1 | 0 0
11 +6.249e+03 +6.249e+03 +1e+02 2e-04 3e-05 2e-02 7e-02 0.5025 4e-01 1 1 1 | 0 0
12 +6.255e+03 +6.255e+03 +6e+01 1e-04 2e-05 1e-02 4e-02 0.7639 3e-01 1 1 1 | 0 0
13 +6.259e+03 +6.259e+03 +3e+01 5e-05 7e-06 6e-03 2e-02 0.6280 1e-01 1 1 1 | 0 0
14 +6.261e+03 +6.261e+03 +1e+01 2e-05 3e-06 2e-03 7e-03 0.7859 2e-01 1 1 1 | 0 0
15 +6.262e+03 +6.262e+03 +4e+00 8e-06 1e-06 9e-04 2e-03 0.7343 1e-01 1 1 1 | 0 0
16 +6.263e+03 +6.263e+03 +8e-01 2e-06 2e-07 2e-04 5e-04 0.8474 6e-02 1 1 1 | 0 0
17 +6.263e+03 +6.263e+03 +3e-01 7e-07 9e-08 8e-05 2e-04 0.6258 6e-02 1 1 1 | 0 0
18 +6.263e+03 +6.263e+03 +4e-02 7e-08 1e-08 8e-06 2e-05 0.9127 2e-02 1 1 1 | 0 0
19 +6.263e+03 +6.263e+03 +2e-03 3e-09 4e-10 4e-07 1e-06 0.9579 2e-04 2 1 1 | 0 0
20 +6.263e+03 +6.263e+03 +2e-05 3e-11 5e-12 4e-09 1e-08 0.9890 1e-04 2 1 1 | 0 0
OPTIMAL (within feastol=3.4e-11, reltol=2.7e-09, abstol=1.7e-05).
Runtime: 0.048064 seconds.
/home/fan/.local/lib/python3.8/site-packages/cvxpy/expressions/expression.py:550: UserWarning:
This use of ``*`` has resulted in matrix multiplication.
Using ``*`` for matrix multiplication has been deprecated since CVXPY 1.1.
Use ``*`` for matrix-scalar and vector-scalar multiplication.
Use ``@`` for matrix-matrix and matrix-vector multiplication.
Use ``multiply`` for elementwise multiplication.
warnings.warn(__STAR_MATMUL_WARNING__, UserWarning)
```python
print(*zip(alphabet, vx.value.round(0)))
```
('0', 1.0) ('1', 0.0) ('2', -0.0) ('3', 0.0) ('4', -0.0) ('5', 1.0) ('6', 0.0) ('7', -0.0) ('8', 0.0) ('9', -0.0) ('A', 0.0) ('B', -0.0) ('C', -0.0) ('D', -0.0) ('E', 1.0) ('F', 0.0) ('G', -0.0) ('H', 1.0) ('I', -0.0) ('J', -0.0) ('K', 0.0) ('L', 1.0) ('M', -0.0) ('N', -0.0) ('O', 0.0) ('P', 1.0) ('Q', -0.0) ('R', -0.0) ('S', 1.0) ('T', -0.0) ('U', 0.0) ('V', 0.0) ('W', 1.0) ('X', 1.0) ('Y', 0.0) ('Z', 1.0) ('a', -0.0) ('b', 0.0) ('c', 0.0) ('d', 0.0) ('e', -0.0) ('f', -0.0) ('g', -0.0) ('h', -0.0) ('i', -0.0) ('j', -0.0) ('k', -0.0) ('l', 2.0) ('m', -0.0) ('n', -0.0) ('o', -0.0) ('p', -0.0) ('q', 0.0) ('r', -0.0) ('s', 1.0) ('t', -0.0) ('u', 1.0) ('v', 0.0) ('w', 1.0) ('x', 1.0) ('y', -0.0) ('z', -0.0)
```python
print(A @ np.array([[2,2,2,2,2,2, 1,1,1,1]]).T - np.expand_dims(counts_full,axis=1))
```
[[ 159]
[ 2]
[ 2]
[ 0]
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[ 1]
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[ 1]
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[ 1]
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[ 1]
[ 1]
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[ 1]
[ 2]
[ 1]
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[ 0]
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[ 1]
[ 1]
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[ 0]
[ 1]
[ 1]
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[-238]
[ 0]
[ 1]
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[ 0]
[ 1]
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[ 1]
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[-149]
[ 0]
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[ 1]
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[ 1]
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[-323]
[-154]
[ 1]
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[-338]
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[ 0]
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[ -94]
[ 1]
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[ 1]
[ 1]
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[ 1]
[ 0]
[ 4]
[ 0]]
```python
```