今年肝 paper 实在太忙，只做了一题和自己研究相关的（ 顺便膜各位师傅 orz # 证验码 注意到题目给的是 BMP 格式，显然是为了保存图片的一些统计特征。继续审代码，发现随机数均为真随机，故这个方向没有价值。众所周知字体渲染是有 Anti-aliasing 的，所以每个字都有独特的灰度分布。 故我们可以计算每张图片的灰度分布，再加上预计算每个单独字符的灰度分布，得到直方图，在直方图上做优化即可得到验证码。 注意此处应当使用 L1 而不是 L2 (最小二乘）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) ``` ![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)