图像处理中的经典机器学习方法

import numpy as npimport matplotlib.pyplot as pltfrom sklearn.cluster import KMeansfrom sklearn.metrics import pairwise_distances_argminfrom skimage.io import imreadfrom sklearn.utils import shufflefrom skimage import img_as_floatfrom time import time
pepper = imread("../images/pepper.jpg")
# Display the original imageplt.figure(1), plt.clf()ax = plt.axes([0, 0, 1, 1])plt.axis('off'), plt.title('Original image (%d colors)'%(len(np.unique(pepper)))), plt.imshow(pepper)

n_colors = 64
# Convert to floats instead of the default 8 bits integer coding. Dividingby# 255 is important so that plt.imshow behaves works well on float data# (need tobe in the range [0-1])pepper = np.array(pepper, dtype=np.float64) / 255
# Load Image and transform to a 2D numpy array.w, h, d = original_shape = tuple(pepper.shape)assert d == 3image_array = np.reshape(pepper, (w * h, d))
def recreate_image(codebook, labels, w, h):    """Recreate the (compressed) image from the code book & labels"""    d = codebook.shape[1]    image = np.zeros((w, h, d))    label_idx = 0    for i in range(w):        for j in range(h):              image[i][j] = codebook[labels[label_idx]]              label_idx += 1return image
# Display all results, alongside original imageplt.figure(1)plt.clf()ax = plt.axes([0, 0, 1, 1])plt.axis('off')plt.title('Original image (96,615 colors)')plt.imshow(pepper)
plt.figure(2, figsize=(10,10))plt.clf()i = 1for k in [64, 32, 16, 4]:    t0 = time()    plt.subplot(2,2,i)    plt.axis('off')    image_array_sample = shuffle(image_array, random_state=0)[:1000]    kmeans = KMeans(n_clusters=k, random_state=0).fit(image_array_sample)    print("done in %0.3fs." % (time() - t0))    # Get labels for all points    print("Predicting color indices on the full image (k-means)")    t0 = time()    labels = kmeans.predict(image_array)    print("done in %0.3fs." % (time() - t0))    plt.title('Quantized image (' + str(k) + ' colors, K-Means)')    plt.imshow(recreate_image(kmeans.cluster_centers_, labels, w, h))    i += 1plt.show()plt.figure(3, figsize=(10,10))plt.clf()i = 1for k in [64, 32, 16, 4]:    t0 = time()    plt.subplot(2,2,i)    plt.axis('off')    codebook_random = shuffle(image_array, random_state=0)[:k + 1]    print("Predicting color indices on the full image (random)")    t0 = time()    labels_random = pairwise_distances_argmin(codebook_random,image_array,axis=0)
     print("done in %0.3fs." % (time() - t0))     plt.title('Quantized image (' + str(k) + ' colors, Random)')     plt.imshow(recreate_image(codebook_random, labels_random, w, h))     i += 1plt.show()

from sklearn import clusterfrom skimage.io import imreadfrom skimage.color import rgb2grayfrom scipy.misc import imresizeimport matplotlib.pylab as pylabim = imresize(imread('../images/me14.jpg'), (100,100,3))img = rgb2gray(im)k = 2 # binary segmentation, with 2 output clusters / segmentsX = np.reshape(im, (-1, im.shape[-1]))two_means = cluster.MiniBatchKMeans(n_clusters=k, random_state=10)two_means.fit(X)y_pred = two_means.predict(X)labels = np.reshape(y_pred, im.shape[:2])pylab.figure(figsize=(20,20))pylab.subplot(221), pylab.imshow(np.reshape(y_pred, im.shape[:2])),pylab.title('k-means segmentation (k=2)', size=30)pylab.subplot(222), pylab.imshow(im), pylab.contour(labels == 0,contours=1, colors='red'), pylab.axis('off')pylab.title('k-means contour (k=2)', size=30)spectral = cluster.SpectralClustering(n_clusters=k, eigen_solver='arpack',affinity="nearest_neighbors", n_neighbors=100, random_state=10)spectral.fit(X)y_pred = spectral.labels_.astype(np.int)labels = np.reshape(y_pred, im.shape[:2])pylab.subplot(223), pylab.imshow(np.reshape(y_pred, im.shape[:2])),pylab.title('spectral segmentation (k=2)', size=30)pylab.subplot(224), pylab.imshow(im), pylab.contour(labels == 0,contours=1, colors='red'), pylab.axis('off'), pylab.title('spectral contour(k=2)', size=30), pylab.tight_layout()pylab.show()

import numpy as npimport matplotlib.pylab as pltfrom sklearn.datasets import load_digitsfrom sklearn.preprocessing import StandardScalerfrom sklearn.decomposition import PCAfrom sklearn.pipeline import Pipeline
digits = load_digits()#print(digits.keys())print(digits.data.shape)j = 1np.random.seed(1)fig = plt.figure(figsize=(3,3))fig.subplots_adjust(left=0, right=1, bottom=0, top=1, hspace=0.05,wspace=0.05)for i in np.random.choice(digits.data.shape[0], 25):    plt.subplot(5,5,j), plt.imshow(np.reshape(digits.data[i,:], (8,8)),cmap='binary'),   plt.axis('off')    j += 1plt.show()

pca_digits=PCA(2)digits.data_proj = pca_digits.fit_transform(digits.data)print(np.sum(pca_digits.explained_variance_ratio_))# 0.28509364823696987plt.figure(figsize=(15,10))plt.scatter(digits.data_proj[:, 0], digits.data_proj[:, 1], lw=0.25,c=digits.target, edgecolor='k', s=100, cmap=plt.cm.get_cmap('cubehelix',10))plt.xlabel('PC1', size=20), plt.ylabel('PC2', size=20), plt.title('2DProjection of handwritten digits with PCA', size=25)plt.colorbar(ticks=range(10), label='digit value')plt.clim(-0.5, 9.5)

from sklearn.datasets import fetch_olivetti_facesfaces = fetch_olivetti_faces().dataprint(faces.shape) # there are 400 faces each of them is of 64x64=4096 pixelsfig = plt.figure(figsize=(5,5))fig.subplots_adjust(left=0, right=1, bottom=0, top=1, hspace=0.05, wspace=0.05)# plot 25 random facesj = 1np.random.seed(0)for i in np.random.choice(range(faces.shape[0]), 25):    ax = fig.add_subplot(5, 5, j, xticks=[], yticks=[])    ax.imshow(np.reshape(faces[i,:],(64,64)), cmap=plt.cm.bone,interpolation='nearest')    j += 1plt.show()

from sklearn.preprocessing import StandardScalerfrom sklearn.decomposition import PCAfrom sklearn.pipeline import Pipelinen_comp =64pipeline = Pipeline([('scaling', StandardScaler()), ('pca',PCA(n_components=n_comp))])faces_proj = pipeline.fit_transform(faces)print(faces_proj.shape)# (400, 64)mean_face = np.reshape(pipeline.named_steps['scaling'].mean_, (64,64))sd_face = np.reshape(np.sqrt(pipeline.named_steps['scaling'].var_),(64,64))pylab.figure(figsize=(8, 6))pylab.plot(np.cumsum(pipeline.named_steps['pca'].explained_variance_ratio_), linewidth=2)pylab.grid(), pylab.axis('tight'), pylab.xlabel('n_components'),pylab.ylabel('cumulative explained_variance_ratio_')pylab.show()pylab.figure(figsize=(10,5))pylab.subplot(121), pylab.imshow(mean_face, cmap=pylab.cm.bone),pylab.axis('off'), pylab.title('Mean face')pylab.subplot(122), pylab.imshow(sd_face, cmap=pylab.cm.bone),pylab.axis('off'), pylab.title('SD face')pylab.show()

fig = plt.figure(figsize=(5,2))fig.subplots_adjust(left=0, right=1, bottom=0, top=1, hspace=0.05,wspace=0.05)# plot the first 10 eigenfacesfor i in range(10):    ax = fig.add_subplot(2, 5, i+1, xticks=[], yticks=[])    ax.imshow(np.reshape(pipeline.named_steps['pca'].components_[i,:],    (64,64)), cmap=plt.cm.bone, interpolation='nearest')

# face reconstructionfaces_inv_proj = pipeline.named_steps['pca'].inverse_transform(faces_proj)#reshaping as 400 images of 64x64 dimensionfig = plt.figure(figsize=(5,5))fig.subplots_adjust(left=0, right=1, bottom=0, top=1, hspace=0.05,wspace=0.05)# plot the faces, each image is 64 by 64 dimension but 8x8 pixelsj = 1np.random.seed(0)for i in np.random.choice(range(faces.shape[0]), 25):    ax = fig.add_subplot(5, 5, j, xticks=[], yticks=[])    ax.imshow(mean_face + sd_face*np.reshape(faces_inv_proj,(400,64,64))     [i,:], cmap=plt.cm.bone, interpolation='nearest')    j += 1

%matplotlib inlineimport gzip, os, sysimport numpy as npfrom scipy.stats import multivariate_normalfrom urllib.request import urlretrieveimport matplotlib.pyplot as pylab

## Define a function that displays a digit given its vector representationdef show_digit(x, label): pylab.axis('off') pylab.imshow(x.reshape((28,28)), cmap=pylab.cm.gray) pylab.title('Label ' + str(label))
pylab.figure(figsize=(10,10))for i in range(25): pylab.subplot(5, 5, i+1) show_digit(test_data[i,], test_labels[i])pylab.tight_layout()pylab.show()

import timefrom sklearn.neighbors import BallTree
## Build nearest neighbor structure on training datat_before = time.time()ball_tree = BallTree(train_data)t_after = time.time()
## Compute training timet_training = t_after - t_beforeprint("Time to build data structure (seconds): ", t_training)
## Get nearest neighbor predictions on testing datat_before = time.time()test_neighbors = np.squeeze(ball_tree.query(test_data, k=1,return_distance=False))test_predictions = train_labels[test_neighbors]t_after = time.time()
## Compute testing timet_testing = t_after - t_beforeprint("Time to classify test set (seconds): ", t_testing)# Time to build data structure (seconds): 20.65474772453308# Time to classify test set (seconds): 532.3929145336151

# evaluate the classifiert_accuracy = sum(test_predictions == test_labels) / float(len(test_labels))t_accuracy# 0.96909999999999996
import pandas as pdimport seaborn as snfrom sklearn import metrics
cm = metrics.confusion_matrix(test_labels,test_predictions)df_cm = pd.DataFrame(cm, range(10), range(10))sn.set(font_scale=1.2)#for label sizesn.heatmap(df_cm, annot=True,annot_kws={"size": 16}, fmt="g")

def display_char(image):    plt.imshow(np.reshape(image, (28,28)), cmap=plt.cm.gray)    plt.axis('off')，plt.show()
def fit_generative_model(x,y):    k = 10 # labels 0,1,...,k-1    d = (x.shape)[1] # number of features    mu = np.zeros((k,d))    sigma = np.zeros((k,d,d))    pi = np.zeros(k)    c = 3500 #10000 #1000 #100 #10 #0.1 #1e9    for label in range(k):          indices = (y == label)          pi[label] = sum(indices) / float(len(y))          mu[label] = np.mean(x[indices,:], axis=0)          sigma[label] = np.cov(x[indices,:], rowvar=0, bias=1) + c*np.eye(d)return mu, sigma, pi
mu, sigma, pi = fit_generative_model(train_data, train_labels)display_char(mu[0])display_char(mu[1])display_char(mu[2])