In [ ]:
#hide
from fastai2.vision.all import *
from utils import *
matplotlib.rc('image', cmap='Greys')
Convolutional neural networks¶
The magic of convolutions¶
In [ ]:
path = untar_data(URLs.MNIST_SAMPLE)
In [ ]:
#hide
Path.BASE_PATH = path
In [ ]:
top_edge = tensor([[-1,-1,-1],
[ 0, 0, 0],
[ 1, 1, 1]]).float()
In [ ]:
im3 = Image.open(path/'train'/'3'/'12.png')
show_image(im3);
In [ ]:
im3_t = tensor(im3)
im3_t[0:3,0:3] * top_edge
Out[ ]:
tensor([[-0., -0., -0.],
[0., 0., 0.],
[0., 0., 0.]])
In [ ]:
(im3_t[0:3,0:3] * top_edge).sum()
Out[ ]:
tensor(0.)
In [ ]:
df = pd.DataFrame(im3_t[:10,:20])
df.style.set_properties(**{'font-size':'6pt'}).background_gradient('Greys')
Out[ ]:
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 5 | 0 | 0 | 0 | 12 | 99 | 91 | 142 | 155 | 246 | 182 | 155 | 155 | 155 | 155 | 131 | 52 | 0 | 0 | 0 | 0 |
| 6 | 0 | 0 | 0 | 138 | 254 | 254 | 254 | 254 | 254 | 254 | 254 | 254 | 254 | 254 | 254 | 252 | 210 | 122 | 33 | 0 |
| 7 | 0 | 0 | 0 | 220 | 254 | 254 | 254 | 235 | 189 | 189 | 189 | 189 | 150 | 189 | 205 | 254 | 254 | 254 | 75 | 0 |
| 8 | 0 | 0 | 0 | 35 | 74 | 35 | 35 | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 13 | 224 | 254 | 254 | 153 | 0 |
| 9 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 90 | 254 | 254 | 247 | 53 | 0 |
In [ ]:
(im3_t[4:7,6:9] * top_edge).sum()
Out[ ]:
tensor(762.)
In [ ]:
(im3_t[7:10,17:20] * top_edge).sum()
Out[ ]:
tensor(-29.)
In [ ]:
def apply_kernel(row, col, kernel):
return (im3_t[row-1:row+2,col-1:col+2] * kernel).sum()
In [ ]:
apply_kernel(5,7,top_edge)
Out[ ]:
tensor(762.)
In [ ]:
[[(i,j) for j in range(1,5)] for i in range(1,5)]
Out[ ]:
[[(1, 1), (1, 2), (1, 3), (1, 4)], [(2, 1), (2, 2), (2, 3), (2, 4)], [(3, 1), (3, 2), (3, 3), (3, 4)], [(4, 1), (4, 2), (4, 3), (4, 4)]]
In [ ]:
rng = range(1,27)
top_edge3 = tensor([[apply_kernel(i,j,top_edge) for j in rng] for i in rng])
show_image(top_edge3);
In [ ]:
left_edge = tensor([[-1,1,0],
[-1,1,0],
[-1,1,0]]).float()
left_edge3 = tensor([[apply_kernel(i,j,left_edge) for j in rng] for i in rng])
show_image(left_edge3);
Convolutions in PyTorch¶
In [ ]:
diag1_edge = tensor([[ 0,-1, 1],
[-1, 1, 0],
[ 1, 0, 0]]).float()
diag2_edge = tensor([[ 1,-1, 0],
[ 0, 1,-1],
[ 0, 0, 1]]).float()
edge_kernels = torch.stack([left_edge, top_edge, diag1_edge, diag2_edge])
edge_kernels.shape
Out[ ]:
torch.Size([4, 3, 3])
In [ ]:
mnist = DataBlock(blockernel_size=(ImageBlock(cls=PILImageBW), CategoryBlock),
get_items=get_image_files,
splitter=GrandparentSplitter(),
get_y=parent_label)
dls = mnist.dataloaders(path)
xb,yb = first(dls.valid)
xb.shape
Out[ ]:
torch.Size([64, 1, 28, 28])
In [ ]:
xb,yb = to_cpu(xb),to_cpu(yb)
In [ ]:
edge_kernels.shape,edge_kernels.unsqueeze(1).shape
Out[ ]:
(torch.Size([4, 3, 3]), torch.Size([4, 1, 3, 3]))
In [ ]:
edge_kernels = edge_kernels.unsqueeze(1)
In [ ]:
batch_features = F.conv2d(xb, edge_kernels)
batch_features.shape
Out[ ]:
torch.Size([64, 4, 26, 26])
In [ ]:
show_image(batch_features[0,0]);
Strides and padding¶
CNNs from different viewpoints¶
Our first convolutional neural network¶
Learning kernels¶
Creating the CNN¶
In [ ]:
simple_net = nn.Sequential(
nn.Linear(28*28,30),
nn.ReLU(),
nn.Linear(30,1)
)
In [ ]:
simple_net
Out[ ]:
Sequential( (0): Linear(in_features=784, out_features=30, bias=True) (1): ReLU() (2): Linear(in_features=30, out_features=1, bias=True) )
In [ ]:
broken_cnn = sequential(
nn.Conv2d(1,30, kernel_size=3, padding=1),
nn.ReLU(),
nn.Conv2d(30,1, kernel_size=3, padding=1)
)
In [ ]:
broken_cnn(xb).shape
Out[ ]:
torch.Size([64, 1, 28, 28])
In [ ]:
def conv(ni, nf, ks=3, act=True):
res = nn.Conv2d(ni, nf, stride=2, kernel_size=ks, padding=ks//2)
if act: res = nn.Sequential(res, nn.ReLU())
return res
In [ ]:
simple_cnn = sequential(
conv(1 ,4), #14x14
conv(4 ,8), #7x7
conv(8 ,16), #4x4
conv(16,32), #2x2
conv(32,2, act=False), #1x1
Flatten(),
)
In [ ]:
simple_cnn(xb).shape
Out[ ]:
torch.Size([64, 2])
In [ ]:
learn = Learner(dls, simple_cnn, loss_func=F.cross_entropy, metrics=accuracy)
In [ ]:
learn.summary()
Out[ ]:
Sequential (Input shape: ['64 x 1 x 28 x 28']) ================================================================ Layer (type) Output Shape Param # Trainable ================================================================ Conv2d 64 x 4 x 14 x 14 40 True ________________________________________________________________ ReLU 64 x 4 x 14 x 14 0 False ________________________________________________________________ Conv2d 64 x 8 x 7 x 7 296 True ________________________________________________________________ ReLU 64 x 8 x 7 x 7 0 False ________________________________________________________________ Conv2d 64 x 16 x 4 x 4 1,168 True ________________________________________________________________ ReLU 64 x 16 x 4 x 4 0 False ________________________________________________________________ Conv2d 64 x 32 x 2 x 2 4,640 True ________________________________________________________________ ReLU 64 x 32 x 2 x 2 0 False ________________________________________________________________ Conv2d 64 x 2 x 1 x 1 578 True ________________________________________________________________ Flatten 64 x 2 0 False ________________________________________________________________ Total params: 6,722 Total trainable params: 6,722 Total non-trainable params: 0 Optimizer used: <function Adam at 0x7fbc9c258cb0> Loss function: <function cross_entropy at 0x7fbca9ba0170> Callbacks: - TrainEvalCallback - Recorder - ProgressCallback
In [ ]:
learn.fit_one_cycle(2, 0.01)
| epoch | train_loss | valid_loss | accuracy | time |
|---|---|---|---|---|
| 0 | 0.072684 | 0.045110 | 0.990186 | 00:05 |
| 1 | 0.022580 | 0.030775 | 0.990186 | 00:05 |
Colour images¶
In [ ]:
im = image2tensor(Image.open('images/grizzly.jpg'))
im.shape
Out[ ]:
torch.Size([3, 1000, 846])
In [ ]:
show_image(im);
In [ ]:
_,axs = subplots(1,3)
for bear,ax,color in zip(im,axs,('Reds','Greens','Blues')):
show_image(255-bear, ax=ax, cmap=color)
Conclusions¶
In [ ]: