def main():
X = generate_dataset(shape="blobs")
D = pairwise_distances(X) # euclidean distance as distance metric
A = gaussian_kernel(D, is_sym=True) # Gaussian distance as affinity metric
# K-MEANS
clusters, _ = apply_kmeans(X)
plot_clustering_result(X,
A,
clusters,
clustering_name="K means clustering")
# DBSCAN
clusters, noise = apply_dbscan(X, D)
plot_clustering_result(X,
A,
clusters,
noise,
clustering_name="DBSCAN clustering")
# EIGENVECTOR BASED CLUSTERING
A_eigen = gaussian_kernel(
D, mult=0.05, is_sym=True) # Gaussian distance as affinity metric
clusters, noise = apply_eigenvector_based(X, A_eigen)
plot_clustering_result(X,
A_eigen,
clusters,
noise,
clustering_name="Eigenvector based clustering")
def hybridImage(im1, im2, cutoff_low, cutoff_high):
'''
Inputs:
im1: RGB (height x width x 3) or a grayscale (height x width) image
as a numpy array.
im2: RGB (height x width x 3) or a grayscale (height x width) image
as a numpy array.
cutoff_low: standard deviation for the low-pass filter
cutoff_high: standard deviation for the high-pass filter
Output:
Return the combination of both images, one filtered with a low-pass filter
and the other with a high-pass filter.
'''
# For a low-pass filter, Oliva et al. suggest using a standard 2D Gaussian filter.
# For a high-pass filter, use the impulse filter minus the Gaussian filter,
# which can be computed by subtracting the Gaussian-filtered image from the original.
'''
high_Gaussian_filter = utils.gaussian_kernel(cutoff_high, cutoff_high*5)
signal_filter = signal.unit_impulse(high_Gaussian_filter)
high_filter = signal_filter - high_Gaussian_filter
'''
Gaussian_filter1 = utils.gaussian_kernel(cutoff_low, cutoff_low*4)
display_frequency_image(Gaussian_filter1)
plt.axis('off')
plt.savefig('./image/FFT_LOW')
# Gaussian_filter2 = utils.gaussian_kernel(cutoff_high, cutoff_high*4)
# filter_impulse = signal.unit_impulse(Gaussian_filter2.shape, 'mid')
# Gaussian_filter22 = filter_impulse - Gaussian_filter2
# display_frequency_image(Gaussian_filter22)
# plt.axis('off')
# plt.savefig('./image/FFT_HIGH')
Gaussian_filter2 = utils.gaussian_kernel(cutoff_high, cutoff_high*4)
plt.figure()
plt.imshow(Gaussian_filter2)
plt.axis('off')
plt.savefig('./image/FFT_HIGH')
im1_lowpass = cv2.filter2D(im1,-1,Gaussian_filter1) #filter_image(im1,Gaussian_filter1)
im2_highpass = im2 - cv2.filter2D(im2,-1,Gaussian_filter2) #filter_image(im2,Gaussian_filter2)
plt.figure()
plt.imshow(im1_lowpass, cmap='gray')
plt.axis('off')
plt.savefig('./image/dog_filter_low.jpg')
plt.figure()
plt.imshow(im2_highpass, cmap='gray')
plt.axis('off')
plt.savefig('./image/me_filter_high.jpg')
result = (im1_lowpass + im2_highpass) / 2
return result
def generate_visual_css(self, rawcss, closeness, return_all=False):
""" generate_visual_css(rawcss, closeness)
Generate a 1D signal that can be plotted to depict the CSS by taking
column maximums. Further checks for close interest points and nicely
smoothes them with weighted moving average
"""
flat_signal = np.amax(rawcss, axis=0)
# minor smoothing via moving averages
window = closeness
weights = gaussian_kernel(window, 0, window, False) # gaussian weights
sig = np.convolve(flat_signal, weights)[window - 1:-(window - 1)]
maxs = []
# get maximas
w = sig.size
for i in range(1, w - 1):
if sig[i - 1] < sig[i] and sig[i] > sig[i + 1]:
maxs.append([i, sig[i]])
if return_all:
return sig, maxs
else:
return sig
def get_kernel(self, data, a):
K = self.K[a]
kt = np.empty((data.shape[0], self.X.shape[0]))
for i in range(data.shape[0]):
for j in range(self.X.shape[0]):
kt[i, j] = gaussian_kernel(data[i], self.X[j], K)
return kt
def main_boilerplate():
# Load image and kernel
img = sm.imresize(sm.face(), 4.0, interp='bicubic')
x = utils.rgb2ycc(img.astype(np.float32) / 255.)[:, :, 0]
k = utils.gaussian_kernel(2, 3.5)
noise = np.random.normal(0., 0.01, x.shape).astype(np.float32)
return img, x, k, noise
def compute_cov(self, K):
"""
:param K: float, parameter of the Gaussian kernel
:return: np.array, covariance matrix for training
"""
cov = np.eye(self.n)
for i in range(self.n):
for j in range(i):
cov_ij = gaussian_kernel(self.X[i], self.X[j], K)
cov[i, j], cov[j, i] = cov_ij, cov_ij
return cov
def predict_single_pref(self, r, s, f_map, M):
"""
:param r: np.array, vector of dimension d
:param s: np.array, vector of dimension d
:param f_map: np.array, Maximum a posteriori for n vectors in R^d
:param M: np.array, covariance matrix computed at the maximum a posteriori
:return: float, probability that r is preferred over s
"""
sigma_t = np.array([[1., gaussian_kernel(r, s, self.K)],
[gaussian_kernel(r, s, self.K), 1.]])
kt = np.zeros((self.n, 2))
kt[:,
0] = [gaussian_kernel(r, self.X[i], self.K) for i in range(self.n)]
kt[:,
1] = [gaussian_kernel(s, self.X[i], self.K) for i in range(self.n)]
mu_star = np.dot(kt.T, np.dot(self.inv_cov, f_map))
s_star = sigma_t - np.dot(np.dot(kt.T, M), kt)
new_sigma = np.sqrt(2 * self.sigma**2 + s_star[0, 0] + s_star[1, 1] -
2 * s_star[0, 1])
return norm.cdf((mu_star[0] - mu_star[1]) / new_sigma, loc=0, scale=1)
def predict(self, test_set, f_map, get_proba=False):
"""
:param test_set: tuple of length 2, - an array for the test X from which preferences are drawn
- a list of tuples (i,j) for the new preferences to predict, where i is
preferred to j (helps for the score)
:param f_map: np.array, Maximum a Posteriori obtained with the GP method
:return: tuple, - float, score of the prediction
- np.array, array of probabilities P(i preferred over j)
"""
X = test_set[0]
pref = test_set[1]
score = 0
proba_pref = []
self.compute_Hessian_S(f_map)
if not get_proba:
for p in pref:
kt = np.zeros((self.n, 2))
kt[:, 0] = [
gaussian_kernel(X[p[0]], self.X[i], self.K)
for i in range(self.n)
]
kt[:, 1] = [
gaussian_kernel(X[p[1]], self.X[i], self.K)
for i in range(self.n)
]
mu_star = np.dot(kt.T, np.dot(self.inv_cov, f_map))
if (mu_star[0] - mu_star[1]) > 0:
score += 1
return score / len(pref), None
else:
try:
M = np.linalg.inv(self.cov + np.linalg.inv(self.nu))
for p in pref:
proba = self.predict_single_pref(X[p[0]], X[p[1]], f_map,
M)
proba_pref.append(proba)
if proba > 0.5:
score += 1
return score / len(pref), proba_pref
except np.linalg.LinAlgError:
return np.nan, np.nan
def predict_movie(self, model, instances, data, MAP):
"""
:param model: Instance_Learning instance
:param instances: Training dataset (features of movies already watched)
:param data: Test dataset (feature of movies not watched)
:param MAP: Maximum a posteriori estimate on watched movies
:return: indice of the best instance in the test dataset
"""
beta = np.dot(model.inv_cov, MAP)
kt = np.array([[
gaussian_kernel(data[i], instances[j], self.K)
for j in range(instances.shape[0])
] for i in range(data.shape[0])])
return int(np.argmax(np.dot(kt, beta)))
def compute_off_diagonal_blocks(self):
"""
Compute the off-diagonal blocks. We use the blocks of W calculated previously.
:return:
"""
dim_subsample = 3 * self.rank_k # Get the size of the subsample matrix
for s in range(self.number_clusters_c):
for t in range(self.number_clusters_c):
if s != t:
df_s = self.df.loc[self.df['clusters'] == s].iloc[:, :-1]
df_t = self.df.loc[self.df['clusters'] == t].iloc[:, :-1]
number_col_s = df_s.shape[0]
number_row_t = df_t.shape[0]
index_col_s = random.randint(0, number_col_s - dim_subsample)
index_row_t = random.randint(0, number_row_t - dim_subsample)
# We have the coordinates of the submatrix
sub_matrix = np.zeros((dim_subsample, dim_subsample))
for i in range(index_row_t, index_row_t + dim_subsample):
for j in range(index_col_s, index_col_s + dim_subsample):
sub_matrix[i - index_row_t, j - index_col_s] = gaussian_kernel(self.gamma, df_s.iloc[j],
df_t.iloc[i])
# Then we can extract W_nu_s and W_nu_t
W_s = self.blocks_of_W[s]
W_nu_s = W_s[index_col_s:index_col_s + dim_subsample, :]
W_t = self.blocks_of_W[t]
W_nu_t = W_t[index_row_t:index_row_t + dim_subsample, :]
# And finally we compute the dot product (i.e solve Least Squares) to get L(s,t)
L_s_t = inv(np.transpose(W_nu_s).dot(W_nu_s)).dot(np.transpose(W_nu_s)).dot(sub_matrix).dot(
W_nu_t).dot(
inv(np.transpose(W_nu_t).dot(W_nu_t)))
self.blocks_of_L[str(s) + '_' + str(t)] = L_s_t
# We have now all the blocks of L and W
print("Computation of off-diagonal blocks done.")
def load_train_data():
"""
Fills train_images array with cutouts.
"""
global train_images
for k in range(0, train_length):
if labels[k] == 1:
train_im = np.load(ones_path + file_list1[k])
elif labels[k] == 0:
train_im = np.load(zeros_path + file_list1[k])
else:
print('There is something wrong')
train_im = 0
# filter and bin the cutout, scale it to [0, 1]
train_im = ndimage.convolve(train_im, gaussian_kernel(5, 5))
train_images[k] = pre_process_cutout(train_im, im_size, bin_size)
def PyrBlending(source, target, mask):
"""
Blend source image onto target. Source is the foreground
Source, target, and mask have the same height and width
Source.shape == target.shape
Number of layers for pyramid is fixed at 6
Input:
- source: 2D or 3D source image matrix
- target: 2D or 3D target image matrix
- mask: binary matrix with 1 indicating ROI
Output:
- blended image
"""
num_layers = 6
sH, sW = source.shape[:2]
tH, tW = target.shape[:2]
mH, mW = mask.shape[:2]
kernel = utils.gaussian_kernel((9, 9), 2)
res_pyr = []
s_gPyr, s_lPyr = ComputePyr(source, num_layers)
t_gPyr, t_lPyr = ComputePyr(target, num_layers)
m_gPyr, _ = ComputePyr(mask, num_layers)
for i in range(num_layers):
s = s_lPyr[i]
t = t_lPyr[i]
m = m_gPyr[i]
combined = m * s + (1 - m) * t
res_pyr.append(combined)
res = res_pyr.pop()
while len(res_pyr) > 0:
layer = res_pyr.pop()
h, w = layer.shape[:2]
res = utils.resample(res, (h, w))
res = conv.conv2(res, kernel, 'reflect')
res += layer
return res
def template_matching(data_dir,
template_dir,
pyramid_depth=4,
rotations=None,
gaussian=None):
if rotations is None:
rotations = [x for x in range(0, 360, 30)]
if gaussian is None:
gaussian = utils.gaussian_kernel(5, 5, 15)
image_names = utils.get_files(data_dir, extension='.png')
for image_name in image_names:
image = cv2.imread(data_dir + image_name + '.png',
cv2.IMREAD_UNCHANGED)
image_filtered = tm.pre_process_image(image)
# Create a Gaussian pyramid of given depth for each image
pyramid = tm.create_gaussian_pyramid(image_filtered, gaussian,
pyramid_depth)
# Create directory for class
image_class = tm.get_class_name(image_name)
class_dir = template_dir + image_class + '/'
utils.create_directory(class_dir)
# Path(class_dir).mkdir(parents=True, exist_ok=True)
# Rotate each scaled image
for scale_index, scaled_image in enumerate(pyramid):
for angle in rotations:
rotated_image = tm.rotate_image(scaled_image, angle)
# Save image to png file
file_name = image_class + "-level" + str(
scale_index) + "-rotation" + str(angle) + ".png"
cv2.imwrite(class_dir + file_name, rotated_image)
return True
def optimise_parameters():
pyramid_levels = [3, 4, 5]
# pyramid_levels = [x for x in range(3,6)]
rotations = [[x for x in range(0, 360, rot)] for rot in range(20, 35, 5)]
gaussian_parameters = [[5, 5, 15]]
# Create results directory
utils.create_directory(config.RESULTS_DIR)
for level in pyramid_levels:
for rots in rotations:
for g_n, gaussian in enumerate(gaussian_parameters):
step_size = rots[1] - rots[0]
row, col, dev = gaussian
g = utils.gaussian_kernel(row, col, dev)
utils.delete_directory(config.TEMPLATE_OUTPUT_DIR)
print(
'training rotation {} level {} gaussian {}-{}-{}'.format(
step_size, level, row, col, dev), rots, level)
start = time.time()
template_matching(config.TRAINING_DIR,
config.TEMPLATE_OUTPUT_DIR, level, rots, g)
new_dir = config.RESULTS_DIR + 'level{}-rot{}-g-{}-{}-{}/'.format(
level, step_size, row, col, dev)
utils.create_directory(new_dir)
print('testing', rots, level)
images = test_template_matching(config.TESTING_DIR,
config.TEMPLATE_OUTPUT_DIR)
end = time.time()
time_elapsed = end - start
utils.write_to_file(new_dir + 'time.txt', time_elapsed)
for idx, im in enumerate(images):
cv2.imwrite(new_dir + '{}.png'.format(idx), im)
return True
def ComputePyr(img, num_layers):
"""
Given image and number of pyramid layers,
computes Gaussian and Laplacian Pyramid of the image
Input:
- img: 2D or 3D image matrix
- num_layers: int indicating the number of layers of the pyramids
Output:
- (Gaussian Pyramid, Laplacian Pyramid)
"""
# only accept 2D and 3D images
if np.ndim(img) == 2:
H, W = img.shape
elif np.ndim(img) == 3:
H, W, _ = img.shape
else:
raise ValueError("input image has invalid dimension %s" % (img.shape))
kernel = utils.gaussian_kernel((9, 9), 2)
gPyr = gaussian_pyr(img, (H, W), num_layers, kernel)
lPyr = laplacian_pyr(gPyr, kernel)
return (gPyr, lPyr)
def build_graphs(batch, size, blur_radius, blur_scale, center_crop, scale,
flip, rotation, crops, brightness, contrast, gaussian_noise,
uniform_noise):
"""
Tensorflow graph to load and transform images.
batch: number of images to process in batch
size: target width/height
blur_radius: mask/weight blur radius
blur_scale: gaussian blur scale factor for mask/weight images
center_crop: source images center crop percentage
scale: scale factor
flip: flip mode
rotation: rotation in degree
crops: number of variation to create
brightness: random brightness delta
contrast: random contrast delta
gaussian_noise: gaussian noise standard deviation
uniform_noise: uniform noise magnitude
return tensorflow graph pipeline
"""
items = list()
for i in range(batch):
with tf.name_scope("batch%d" % i):
# inputs
name = tf.placeholder(tf.string, name="name")
width = tf.placeholder(tf.int32, name="width")
height = tf.placeholder(tf.int32, name="height")
orientation = tf.placeholder(tf.int32, name="orientation")
rgbpath = tf.placeholder(tf.string, name="rgbpath")
maskpath = tf.placeholder(tf.string, name="maskpath")
weightpath = tf.placeholder(tf.string, name="weightpath")
# read images
rgb = tf.image.decode_image(tf.read_file(rgbpath),
channels=3,
name="decode_rgb")
mask = tf.image.decode_image(tf.read_file(maskpath),
channels=1,
name="decode_mask")
weight = tf.image.decode_image(tf.read_file(weightpath),
channels=1,
name="decode_weight")
rgb = tf.image.convert_image_dtype(rgb,
tf.float32,
name="convert_rgb")
mask = tf.image.convert_image_dtype(mask,
tf.float32,
name="convert_mask")
weight = tf.image.convert_image_dtype(weight,
tf.float32,
name="convert_weight")
rgb = tf.reshape(rgb, [height, width, 3], name="reshape_rgb")
mask = tf.reshape(mask, [height, width, 1], name="reshape_mask")
weight = tf.reshape(weight, [height, width, 1],
name="reshape_weight")
# blur mask/weight
if blur_radius > 0:
with tf.name_scope("blur"):
kernel = tf.constant(gaussian_kernel(blur_radius),
name="kernel")
blur_in = tf.stack([mask, weight], name="stack")
if blur_scale < 1.0:
height2 = tf.to_double(height) * blur_scale
width2 = tf.to_double(width) * blur_scale
blur_in = tf.image.resize_bilinear(
blur_in,
tf.to_int32([height2, width2]),
name="downscale")
blur_out = tf.nn.conv2d(input=blur_in,
filter=kernel,
strides=[1, 1, 1, 1],
padding="SAME",
name="conv2d")
if blur_scale < 1.0:
blur_out = tf.image.resize_bilinear(blur_out,
[height, width],
name="upscale")
mask, weight = tf.unstack(blur_out, name="unstack")
# normalize mask/weight
mask /= tf.maximum(1.0, tf.reduce_max(mask))
weight /= tf.maximum(1.0, tf.reduce_max(weight))
# preprocess image
image = tf.concat([rgb, mask, weight], axis=2, name="concat")
image = tf.image.central_crop(image, center_crop)
with tf.name_scope("flip"):
image = build_flip_graph(image, flip)
with tf.name_scope("rotatation"):
image = build_rotate_graph(image, rotation)
with tf.name_scope("scale"):
image = build_scale_graph(image, scale, size)
# generate variations
with tf.name_scope("variations"):
variations = build_variation_graphs(image, size, crops,
brightness, contrast,
gaussian_noise,
uniform_noise)
items.append({
"name":
name,
"width":
width,
"height":
height,
"orientation":
orientation,
"transform":
tf.constant("%.02f_%s_%.01f" % (scale, flip, rotation),
tf.string),
"rgbpath":
rgbpath,
"maskpath":
maskpath,
"weightpath":
weightpath,
"variations":
variations,
})
return items
utils.plot_decision_boundary(scaleX,y,svm,'x1','x2',['neg','pos'])
plt.savefig('fig2.pdf')
############################################################################
# Part 3: Training SVM with a kernel #
# We train an SVM with an RBF kernel on the data set and the plot the #
# learned decision boundary #
############################################################################
# test your Gaussian kernel implementation
x1 = np.array([1,2,1])
x2 = np.array([0,4,-1])
sigma = 2
print "Guassian kernel value (should be around 0.324652) = ", utils.gaussian_kernel(x1,x2,sigma)
# load ex4data2.mat
X,y = utils.load_mat('data/ex4data2.mat')
# visualize the data
utils.plot_twoclass_data(X,y,'', '',['neg','pos'])
plt.savefig('fig3.pdf')
# convert X to kernel form with the kernel function
sigma = 0.02
# compute the kernel (slow!)
def run_attack(args):
input_folder = os.path.join(args.input_path, 'images/')
adv_img_save_folder = os.path.join(args.result_path, 'adv_images/')
if not os.path.exists(adv_img_save_folder):
os.makedirs(adv_img_save_folder)
# Dataset, dev50.csv is the label file
data_set = MyDataset(csv_path=os.path.join(args.input_path,
args.label_file),
path=input_folder)
data_loader = DataLoader(dataset=data_set,
batch_size=args.batch_size,
shuffle=False,
num_workers=2)
device = torch.device("cuda:0")
source_models = load_models(args.source_models,
device) # load model, maybe several models
seed_num = 0 # set seed
random.seed(seed_num)
np.random.seed(seed_num)
torch.manual_seed(seed_num)
torch.backends.cudnn.deterministic = True
# gaussian_kernel: filter high frequency information of images
gaussian_smoothing = gaussian_kernel(device,
kernel_size=5,
sigma=1,
channels=3)
print('Start attack......')
for i, data in enumerate(data_loader, 0):
start_t = time.time()
X, labels, filenames = data
X = X.to(device)
labels = labels.to(device)
# the noise
delta = torch.zeros_like(X, requires_grad=True).to(device)
X = gaussian_smoothing(
X) # filter high frequency information of images
for t in range(args.iterations):
g_temp = []
for tt in range(len(liner_interval)):
if args.input_diversity: # use Input Diversity
X_adv = X + delta
X_adv = input_diversity(X_adv)
# images interpolated to 224*224, adaptive standard networks and reduce computation time
X_adv = F.interpolate(X_adv, (224, 224),
mode='bilinear',
align_corners=False)
else:
c = liner_interval[tt]
X_adv = X + c * delta
X_adv = F.interpolate(X_adv, (224, 224),
mode='bilinear',
align_corners=False)
# get ensemble logits
ensemble_logits = get_logits(X_adv, source_models)
loss = -nn.CrossEntropyLoss()(ensemble_logits, labels)
loss.backward()
grad = delta.grad.clone()
# TI: smooth the gradient
grad = F.conv2d(grad,
TI_kernel(),
bias=None,
stride=1,
padding=(2, 2),
groups=3)
g_temp.append(grad)
# calculate the mean and cancel out the noise, retained the effective noise
g = 0.0
for j in range(len(liner_interval)):
g += g_temp[j]
g = g / float(len(liner_interval))
delta.grad.zero_()
delta.data = delta.data - args.alpha * torch.sign(g)
delta.data = delta.data.clamp(-args.epsilon / 255.,
args.epsilon / 255.)
delta.data = ((X + delta.data).clamp(0.0, 1.0)) - X
save_imgs(X + delta, adv_img_save_folder, filenames) # save adv images
end_t = time.time()
print('Attack batch: {}/{}; Time spent(seconds): {:.2f}'.format(
i, len(data_loader), end_t - start_t))
svm = LinearSVM_twoclass()
svm.theta = np.zeros((X.shape[1],))
'''
first select the best gaussian kernelized svm
'''
Cvals = [0.01,0.03,0.1,0.3,10,30]
sigma_vals = [0.01,0.03,0.1,0.3,10,30]
learning_rates = [1e-4, 1e-3, 1e-2, 1e-1, 1]
iterations = [100 ,1000, 10000]
best_acc = 0
for sigma_val in sigma_vals:
K = np.array([utils.gaussian_kernel(x1,x2,sigma_val) for x1 in X_train for x2 in X_train]).reshape(X_train.shape[0],X_train.shape[0])
scaler = preprocessing.StandardScaler().fit(K)
scaleK = scaler.transform(K)
KK = np.hstack([np.ones((scaleK.shape[0],1)),scaleK])
Kval = np.array([utils.gaussian_kernel(x1,x2,sigma_val) for x1 in X_val for x2 in X_train]).reshape(X_val.shape[0],X_train.shape[0])
scaleKval = scaler.transform(Kval)
KKval = np.hstack([np.ones((scaleKval.shape[0],1)),scaleKval])
for Cval in Cvals:
for learning_rate in learning_rates:
for iteration in iterations:
svm = LinearSVM_twoclass()
svm.theta = np.zeros((KK.shape[1],))
svm.train(KK,y_train,learning_rate=learning_rate,C=Cval,num_iters=iteration,verbose=True)
y_pred = svm.predict(KKval)
acc = np.mean(y_pred == y_val)
if acc > best_acc:
def test_gaussian_distance(self):
sigma = 2
x1 = np.array([1,2,1])
x2 = np.array([0,4,-1])
dist = gaussian_kernel(x1,x2,sigma)
self.assertAlmostEqual(dist, 0.324652, places=6)
def closest_mode_filter(I, sigma, freq=1., neighborhood_size=9, display_histograms=False):
"""Apply closest mode filtering on image I
Parameters
----------
I: numpy.ndarray
Image to filter (Height x Width x Channels)
sigma: float
Standard deviation of the gaussian kernel
freq: float
Sampling rate over the 256 values for intensity (RGB)
neighborhood_size: int or iterable
If int, the neighborhood is a square,
otherwise it is a rectangle
display_histograms: bool, default=False
Display the histogram and histogram derivative of the image
Returns
-------
I_closest: numpy.ndarray
Filtered image (Height x Width x Channels)
"""
message = "Closest mode filtering"
print(message)
print("-" * len(message))
if I.shape[2] > 1: # multi channel image
if check_if_rgb(I):
I = rgb_to_hsv(I/255) # convert to HSV
else:
raise ValueError("Input image is not RGB")
I_closest = np.zeros(I.shape)
if I_closest.shape[2] > 1:
I_closest[:, :, 0] = I[:, :, 0]
I_closest[:, :, 1] = I[:, :, 1]
canal_to_filter = I[:, :, 2]
else:
canal_to_filter = I[:, :, 0]
canal_to_filter = canal_to_filter*255
canal_to_filter = canal_to_filter.astype(int)
print("Computing lookup tables...")
# Compute lookup table
samples = np.arange(int(freq * 256))
lookup_K = {i: K(i - samples, sigma) for i in range(256)}
lookup_K_prime = {i: -K_prime(i - samples, sigma) for i in range(256)}
# Build the spatial kernel
W = gaussian_kernel(neighborhood_size)
print("Mapping the image...")
histograms = np.zeros((canal_to_filter.shape[0],
canal_to_filter.shape[1],
256))
for x in range(canal_to_filter.shape[0]):
for y in range(canal_to_filter.shape[1]):
histograms[x, y] = lookup_K[canal_to_filter[x, y]]
histogram_derivatives = np.zeros((canal_to_filter.shape[0],
canal_to_filter.shape[1],
256))
for x in range(canal_to_filter.shape[0]):
for y in range(canal_to_filter.shape[1]):
histogram_derivatives[x, y] = lookup_K_prime[canal_to_filter[x, y]]
for i in range(256):
histograms[:, :, i] = fftconvolve(histograms[:, :, i], W, mode="same")
histogram_derivatives[:, :, i] = fftconvolve(histogram_derivatives[:, :, i], W, mode="same")
total_histogram = np.sum(histograms, axis=(0, 1))
total_histogram_derivative = np.sum(histogram_derivatives, axis=(0, 1))
if display_histograms:
f = plt.figure()
plt.subplot(311)
plt.plot(make_hist(canal_to_filter).keys(), make_hist(canal_to_filter).values())
plt.title("histogram")
plt.subplot(312)
plt.plot(total_histogram)
plt.title("smoothed histogram")
plt.subplot(313)
plt.plot(total_histogram_derivative)
plt.plot([0]*256)
plt.title("histogram derivative")
plt.show()
print("Finding closest mode...")
filtered_canal = np.zeros(canal_to_filter.shape)
for x in range(filtered_canal.shape[0]):
for y in range(filtered_canal.shape[1]):
closest_intensity = find_closest_mode(canal_to_filter[x, y],
total_histogram_derivative)
filtered_canal[x, y] = closest_intensity
if I_closest.shape[2] > 1:
I_closest[:, :, 2] = filtered_canal / 255
else:
I_closest[:, :, 0] = filtered_canal / 255
I_closest = hsv_to_rgb(I_closest) * 255
I_closest = I_closest.astype(np.uint8)
return I_closest
svm = LinearSVM_twoclass()
svm.theta = np.zeros((X.shape[1], ))
'''
first select the best gaussian kernelized svm
'''
Cvals = [0.01, 0.03, 0.1, 0.3, 10, 30]
sigma_vals = [0.01, 0.03, 0.1, 0.3, 10, 30]
learning_rates = [1e-4, 1e-3, 1e-2, 1e-1, 1]
iterations = [100, 1000, 10000]
best_acc = 0
for sigma_val in sigma_vals:
K = np.array([
utils.gaussian_kernel(x1, x2, sigma_val) for x1 in X_train
for x2 in X_train
]).reshape(X_train.shape[0], X_train.shape[0])
scaler = preprocessing.StandardScaler().fit(K)
scaleK = scaler.transform(K)
KK = np.hstack([np.ones((scaleK.shape[0], 1)), scaleK])
Kval = np.array([
utils.gaussian_kernel(x1, x2, sigma_val) for x1 in X_val
for x2 in X_train
]).reshape(X_val.shape[0], X_train.shape[0])
scaleKval = scaler.transform(Kval)
KKval = np.hstack([np.ones((scaleKval.shape[0], 1)), scaleKval])
for Cval in Cvals:
for learning_rate in learning_rates:
for iteration in iterations:
svm = LinearSVM_twoclass()
utils.plot_decision_boundary(scaleX, y, svm, 'x1', 'x2', ['neg', 'pos'])
plt.savefig('fig2.pdf')
############################################################################
# Part 3: Training SVM with a kernel #
# We train an SVM with an RBF kernel on the data set and the plot the #
# learned decision boundary #
############################################################################
# test your Gaussian kernel implementation
x1 = np.array([1, 2, 1])
x2 = np.array([0, 4, -1])
sigma = 2
print "Guassian kernel value (should be around 0.324652) = ", utils.gaussian_kernel(
x1, x2, sigma)
# load ex4data2.mat
X, y = utils.load_mat('data/ex4data2.mat')
# visualize the data
utils.plot_twoclass_data(X, y, '', '', ['neg', 'pos'])
plt.savefig('fig3.pdf')
# convert X to kernel form with the kernel function
sigma = 0.02
# compute the kernel (slow!)
svm = LinearSVM_twoclass()
svm.theta = np.zeros((X.shape[1],))
Cvals = [0.01,0.03,0.1,0.3,1,3,10,30]
sigma_vals = [0.01,0.03,0.1,0.3,1,3,10,30]
best_C = 0.01
best_sigma = 0.01
best_acc = 0;
for sigma in sigma_vals:
print "Calculating K"
sys.stdout.flush()
K = np.array([utils.gaussian_kernel(x1,x2,sigma) for x1 in X for x2 in X]).reshape(X.shape[0],X.shape[0])
scaler = preprocessing.StandardScaler().fit(K)
scaleK = scaler.transform(K)
KK = np.vstack([np.ones((scaleK.shape[0],)),scaleK]).T
Kval = np.array([utils.gaussian_kernel(x1,x2,sigma) for x1 in Xval for x2 in X]).reshape(Xval.shape[0], X.shape[0])
scaleKval = scaler.transform(Kval)
KKval = np.vstack([np.ones((scaleKval.shape[0],)),scaleKval.T]).T
print "Done!"
for C in Cvals:
print "sigma=", sigma, ", C=", C
sys.stdout.flush()
svm.theta = np.zeros((KK.shape[1],))
svm.train(KK,yy,learning_rate=1e-4,C=C,num_iters=2000)
y_pred = svm.predict(KKval)