CIO LEVEL SUMMARY:

1. Convolutional Neural Networks (CNN) expand the principles of Feed Forward Neural Networks in order to preserve spatial relationships between input data.

2. CNNs are especially useful for image data, since pixels often have strong relationships with their surrounding pixels.

3. Spatial relationships are preserved by sliding a filter matrix (or kernel) across the matrix and performing the convolution operation. Using the same weights for the filter at each location allows CNNs to recognize features no matter where they are in the image.

4. Convolution filters often help detect features such as edges or curves which can help the CNN classify the image.

5. Pooling is used to reduce the dimensions of the convolved image in order to make it more manageable to use.

6. The output of the convolutional and pooling layers is fed into at least one Feed Forward layer in order to classify the image as desired.

WHAT ARE CONVOLUTIONAL NEURAL NETS?

Neural Networks are incredibly useful models that can learn complex relationships between inputs and an output or prediction--like using a patient’s vital signs to predict risk of heart disease. However, plain Feed Forward Neural Networks aren’t equipped to handle situations in which the input data has spatial relationships. Simple Feed Forward Neural Networks take in one dimensional vectors as input, which discounts any spatial relationships between these inputs.

If you wanted to feed a small black and white image--like a handwritten digit from the MNIST dataset--into a simple Feed Forward Neural Network, you could take a matrix of the pixels and flatten it so that instead of a 28x28 pixel square, you get a single, one dimensional vector that is 784 pixels long. Below, a 3x3 matrix of pixels is shown flattened into a one dimensional vector of 9 pixels.

And for smaller, simpler problems like classifying the MNIST digits, transforming a 2D matrix of pixels into a 1D vector of pixels can be surprisingly effective.

MNIST digits from Wikipedia

But often, the images that we want to work with are much more complicated.

When we flatten an image into a 1D vector, we lose information about the spatial relationships between the pixels. A pixel in one area most likely has strong relationships with the pixels surrounding it. If we want to look at an MRI to recognize things like tumors, lesions, or hippocampal volume, the spatial relationship between pixels is incredibly important.

Convolutional Neural Networks (CNNs) allow us to take advantage of the spatial relationships of numbers--whether they’re pixel values or not--in our neural network architecture. There are three new “steps” that we can use in a CNN that we didn’t have when we built a Feed Forward Neural Network in the last article. Convolution, Detection, and Pooling.

CONVOLUTION

First, we’ll consider a simple black and white fluorescent microscopy image. This is a mitochondrion from a HeLa cell.

We also have images (courtesy of the National Institute on Aging), of 9 other types of organelles.

We can use a Convolutional Neural Network in order to classify new images as one of the 10 types of organelles in this dataset (Nuclei, Endoplasmic reticulum, cis/medial Golgi, cis Golgi, Lysosomes, Mitochondria, Nucleoli, Actin, Endosomes, and Microtubules).

We can represent an image as a matrix of pixels. On the left is the numeric version our our matrix, on the right is the same matrix, but with the corresponding color for each pixel. 0’s are black, 1’s are white, and anything in between is a shade of gray.

To preserve the spatial relationships between the pixels in these images, we create matrices called filters (or kernels) which we can slide over the matrix of pixels in the image.

A filter that looks for edges might look like this.

The convolution operation takes the dot product of the filter, and the matrix of pixels it is on top of. This particular filter is useful, because the scalar output of the dot product will be LARGE if there is a big difference between the center pixel and surrounding pixels (i.e. an edge), and small if there’s a small difference between the center pixel and those around it (i.e. not an edge).

When we multiply each element of the filter with the value of the pixel under it, and add all these up, we get a single number, in this case, -1.41.

In general, if we call the filter F, and the submatrix M, then convolution is

We then slide the filter to the next position, take the dot product, and repeat. To decide the next position, we have to define the stride, which tells us how far to move the filter for the next calculation. Here we have a stride of 1 since we’re moving the filter by one pixel each time.

In this case, our matrix of pixels is 10x10, and our filter is 3x3, so with a stride of 1, our output will be 8x8. In general, the dimensions with matrix Width W, Stride S and Filter width F will be $((W-F)/S) + 1$ But often, we want our output to be the same size as our input. So we surround our image with a “padding” of 0’s. Our original matrix looks like this:

To pad it, we add a row of 0’s at the top and bottom, and a column of 0’s at either side.

This allows our output to have the same dimensions as our original input, which is often useful when working with images.

Using our filter and our padded matrix, we get this output.

At the (2,2) location, you can see the -1.41 that we calculated above.

Plotting a rescaled version of this matrix (so that each value is between 0 and 1), we can see that this filter does detect edges relatively well.

Now, we’ve completed the convolution step. But, just like with Feed Forward Neural Networks, we often want to use some kind of activation function to scale our output and introduce some non-linearity.

Sigmoid activations like the logistic and tanh activations are often useful, as well as the ever popular Rectified Linear Unit (ReLu). Applying these functions elementwise to our output matrix is often referred to as the Detector Step of a Convolutional Layer.

Edge detection filters are usually simple and easy to understand. But in a CNN, the filters aren’t explicitly chosen, they’re learned by the network through training.

The values of the filter matrix are often referred to as weights. And these weights are often randomly initialized and then tweaked through backpropagation or similar training methods.

The weights of the filter are tied, or shared. This means that they don’t change as the filter slides over the image, which results in a phenomenon called spatial invariance. This is really useful, since it allows the CNN to recognize patterns or objects no matter where they are in the image, because it’s using the same filter everywhere. It also reduces the amount of weights (or parameters) that need to be optimized. Less calculations means that the CNN can be trained both faster, and often with less data.

In our organelle classification example, we want to recognize a mitochondrion no matter if it’s in the center, or slightly offset.

POOLING

Convolution helps extract useful features from images. But when we’re working with large complex images, we often want to reduce the amount of features we have. To do this, we use Pooling. Pooling reduces the dimensions of our output matrices so that we can work with smaller sets of features.

Two popular forms of pooling are max pooling, and average pooling.

Similarly to the Convolution Step, in the Pooling Step we need to specify the size of the filter that we want to use, and the stride. For example, here, we’ll look at 2x2 sections of our matrix, and our stride will be 2.

In max pooling, we take the maximum value of each 2x2 section, and create a new, smaller matrix.

In average pooling, we take the average of each value in the 2x2 section to create our new matrix.

Like with the Convolution step, the output of pooling on a Matrix with width W, with Filter width F, and Stride S will be $((W-F)/S) + 1$ or 2x2 in this case.

In practice, we often use more than one convolution and one pooling layer in our network. We can layer convolution, detection (activation), and pooling layers to create Deep Convolutional architectures.

In many cases, we want to use Convolutional layers to generate “features” that we can then feed into one or more Feed Forward Layers that produce an output, like a decision about which of 10 organelles is in an unseen image. So the last few layers of a CNN look similar to the last few layers of a Feed Forward Neural Network.

APPLICATIONS

Let’s build a Convolutional Neural Network in Python to classify our organelle data.

First, the necessary import statements.

import keras
from keras.models import Sequential
from keras.preprocessing.image import img_to_array, ImageDataGenerator
from keras.utils import to_categorical
from keras.layers import Dense, Conv2D, MaxPooling2D, Dropout, Flatten
from keras.layers.core import Activation, Dense, Flatten
from keras import backend as K
from keras.optimizers import SGD

from sklearn.model_selection import train_test_split

import numpy as np
import glob
import cv2
import random


We need a few packages and functions to build a Convolutional Neural Network, each one will be explained as needed.

Before we start, we’ll define variables and a few useful functions that will help us to load our organelle images into Python.

# variable definitions------------------------------
nclass = 10

#fun definitions------------------------------------
image = cv2.resize(image, (50,50))
image = img_to_array(image)

return image
d2 = {}
random.seed(42) #set seed in order to create reproducibility
for k in d: #for each key in the dictionary
random.shuffle(d[k]) #randomize image order
imagesList = []
for item in d[k]: #list
d2[k] = imagesList
return d2


Next, we will find our images and load them into Python using the functions we just created.

# get images ---------------------------------------
foldNames = glob.glob("hela/*")
d = {}
for folder in foldNames:
# get folder names
labelNames = glob.glob(folder+"/*.TIF") + glob.glob(folder+"/*.tif")
d[folder[5:]] = labelNames

images = ims["dna"] +\
ims["mitochondria"] +\
ims["actin"] +\
ims["endosome"] +\
ims["er"] +\
ims["golgia"] +\
ims["golgpp"] +\
ims["lysosome"] +\
ims["microtubules"] +\
ims["nucleolus"]

labels = [1 for i in ims["dna"]] +\
[0 for i in ims["mitochondria"]] +\
[2 for i in ims["actin"]] +\
[3 for i in ims["endosome"]] +\
[4 for i in ims["er"]] +\
[5 for i in ims["golgia"]] +\
[6 for i in ims["golgpp"]] +\
[7 for i in ims["lysosome"]] +\
[8 for i in ims["microtubules"]] +\
[9 for i in ims["nucleolus"]]

data = np.array(images, dtype = 'float') / 255.0 #for color ims
labels = np.array(labels)


Now that our images our loaded into the array data and our labels (a number indicating which organelle the picture contains) in the array labels, we’re ready to start preparing to build a model.

First, we’ll need to create a training set and a testing set. We’ll use the training set in order to train our CNN, and the testing set in order to check how accurately our model performs on data it had never seen before.

# Split data into training and testing sets----------------
train_data, test_data, train_labels, test_labels = train_test_split(data,labels,test_size=0.25) # use 25% of the data for test

trainY = to_categorical(train_labels, num_classes=nclass)
testY = to_categorical(test_labels, num_classes=nclass)


Convolutional Neural Networks often require a large amount of data to train. While we have hundreds of images, it might be helpful to have more to work with.

In order to “create” more data to train our CNN, we’ll use the ImageDataGenerator() function from keras. This function uses our existing data in order to generate new images for us to train our model with. One way that the generator can create new images is by rotating or shifting existing images. This not only provides new data points, but also helps the network to learn to recognize the organelles no matter where they are in the image. Check out the documentation for this function to see a more in depth explanation of how it works.

# Augment Small Dataset--------------------------------------
aug = ImageDataGenerator(rotation_range=30, width_shift_range=0.1,
height_shift_range=0.1, shear_range=0.2, zoom_range=0.2,
horizontal_flip=True, fill_mode="nearest")
aug.fit(train_data)


Once we have our training set, we can specify the architecture of our Convolutional Neural Network. We’ll do this using a function called createModel(). Inside this function, we’ll specify the architecture of our CNN.

def createModel(height, width, depth, n_classes):

model = Sequential()

# CONVOLUTIONAL LAYER 1
# 32 filters, size 4x4

# CONVOLUTIONAL LAYER 1
# 64 filters, size 4x4

#POOLING

# fully connected layer


First, we create a base model using Sequential(), then we keep adding layers to our model. Our first Convolutional layer uses 32 filters, each of size 4x4. Python will pad our images with 0’s so that the output from the convolution is the same size as the original input.

Then, the output of the convolution is fed into a ReLu activation.

Next we add a second convolutional layer. This time with 64 4x4 filters. Again, our images will be padded so that the input and output of the convolution have the same dimensions. We feed this output through a ReLu activation function, and finally we reach our Pooling Step.

Here, we’ll use Max Pooling, with size 2x2, and stride 1.

Now that we’re done with the convolutional parts of the network, we use the function Flatten() in order to turn the output of our convolutional layers into a one dimensional vector. After applying another ReLu activation, we feed this--now one dimensional--vector into a normal feed forward layer in order to get the organelle’s classification. We use a softmax activation at the last layer in order to get probabilities for each class of organelle.

We’ve laid the groundwork for our model, now we need to ask Python to train it.

m = createModel(50,50,1,nclass)
b_size = 32
e = 1000

# train the network
print("Begin Training....\n")
H = m.fit_generator(aug.flow(train_data, trainY, batch_size=b_size),
validation_data=(test_data, testY),
epochs=e, verbose=1)


Since we’re using stochastic gradient descent (which approximates the gradient of the loss function using only a small sample), we need to specify a batch size. Here, we chose 32.

We also need to define the number of epochs to use when training our model. An epoch refers to a full pass of the training data through the network. That means that each image in our training set will be sent through the model.

This model might take a while to train, so if you’re in a rush, you can reduce the number of epochs that your model will use. But don’t reduce it too far. The network needs to see a lot of data in order to generate a well performing model.

Once our model is done running, we’ll be able to see how it performed (in terms of accuracy) on both our training and testing set (in the model, this is also called the validation set).

CONCLUSION

The Convolutional Neural Network is a powerful tool for performing image related tasks. CNNs have been used extensively in the medical and health fields. They have been used to segment tumors1, find brain lesions2, diagnose skin lesions3, and have even been used in computer vision to recognize the location of surgical tools during laparoscopic surgery4. And as these fields increase the amount of image data they collect, the uses for CNNs will grow.

REFRENCES

1. Pereira, S., Pinto, A., Alves, V., & Silva, C. A. (2016). Brain tumor segmentation using convolutional neural networks in MRI images. IEEE transactions on medical imaging, 35(5), 1240-1251.

2. Kamnitsas, K., Chen, L., Ledig, C., Rueckert, D., & Glocker, B. (2015). Multi-scale 3D convolutional neural networks for lesion segmentation in brain MRI. Ischemic stroke lesion segmentation, 13, 46.

3. Kawahara, J., BenTaieb, A., & Hamarneh, G. (2016, April). Deep features to classify skin lesions. In Biomedical Imaging (ISBI), 2016 IEEE 13th International Symposium on (pp. 1397-1400). IEEE.

4. Choi, B., Jo, K., Choi, S., & Choi, J. (2017, July). Surgical-tools detection based on Convolutional Neural Network in laparoscopic robot-assisted surgery. In Engineering in Medicine and Biology Society (EMBC), 2017 39th Annual International Conference of the IEEE (pp. 1756-1759). IEEE.