Self-Driving Car Engineer Nanodegree

Deep Learning

Project: Build a Traffic Sign Recognition Classifier

In this notebook, a template is provided for you to implement your functionality in stages, which is required to successfully complete this project. If additional code is required that cannot be included in the notebook, be sure that the Python code is successfully imported and included in your submission if necessary.

Note: Once you have completed all of the code implementations, you need to finalize your work by exporting the iPython Notebook as an HTML document. Before exporting the notebook to html, all of the code cells need to have been run so that reviewers can see the final implementation and output. You can then export the notebook by using the menu above and navigating to \n", "File -> Download as -> HTML (.html). Include the finished document along with this notebook as your submission.

In addition to implementing code, there is a writeup to complete. The writeup should be completed in a separate file, which can be either a markdown file or a pdf document. There is a write up template that can be used to guide the writing process. Completing the code template and writeup template will cover all of the rubric points for this project.

The rubric contains "Stand Out Suggestions" for enhancing the project beyond the minimum requirements. The stand out suggestions are optional. If you decide to pursue the "stand out suggestions", you can include the code in this Ipython notebook and also discuss the results in the writeup file.

Note: Code and Markdown cells can be executed using the Shift + Enter keyboard shortcut. In addition, Markdown cells can be edited by typically double-clicking the cell to enter edit mode.


Step 0: Load The Data


In [1]:
# Load pickled data
import pickle

training_file = '../data/train.p'
validation_file = '../data/valid.p'
testing_file = '../data/test.p'

with open(training_file, mode='rb') as f:
    train = pickle.load(f)
with open(validation_file, mode='rb') as f:
    valid = pickle.load(f)
with open(testing_file, mode='rb') as f:
    test = pickle.load(f)
    
X_train, y_train = train['features'], train['labels']
X_valid, y_valid = valid['features'], valid['labels']
X_test, y_test = test['features'], test['labels']

Step 1: Dataset Summary & Exploration

The pickled data is a dictionary with 4 key/value pairs:

  • 'features' is a 4D array containing raw pixel data of the traffic sign images, (num examples, width, height, channels).
  • 'labels' is a 1D array containing the label/class id of the traffic sign. The file signnames.csv contains id -> name mappings for each id.
  • 'sizes' is a list containing tuples, (width, height) representing the original width and height the image.
  • 'coords' is a list containing tuples, (x1, y1, x2, y2) representing coordinates of a bounding box around the sign in the image. THESE COORDINATES ASSUME THE ORIGINAL IMAGE. THE PICKLED DATA CONTAINS RESIZED VERSIONS (32 by 32) OF THESE IMAGES

Complete the basic data summary below. Use python, numpy and/or pandas methods to calculate the data summary rather than hard coding the results. For example, the pandas shape method might be useful for calculating some of the summary results.

Provide a Basic Summary of the Data Set Using Python, Numpy and/or Pandas


In [2]:
### Use python, pandas or numpy methods rather than hard coding the results

import numpy as np

n_train = X_train.shape[0]

n_validation = X_valid.shape[0]

n_test = X_test.shape[0]

image_shape = X_train.shape[1:]

n_classes = np.unique(y_train).size

print("Number of training examples =", n_train)
print("Number of validation examples =", n_validation)
print("Number of testing examples =", n_test)
print("Image data shape =", image_shape)
print("Number of classes =", n_classes)


Number of training examples = 34799
Number of validation examples = 4410
Number of testing examples = 12630
Image data shape = (32, 32, 3)
Number of classes = 43

Include an exploratory visualization of the dataset

Visualize the German Traffic Signs Dataset using the pickled file(s). This is open ended, suggestions include: plotting traffic sign images, plotting the count of each sign, etc.

The Matplotlib examples and gallery pages are a great resource for doing visualizations in Python.

NOTE: It's recommended you start with something simple first. If you wish to do more, come back to it after you've completed the rest of the sections. It can be interesting to look at the distribution of classes in the training, validation and test set. Is the distribution the same? Are there more examples of some classes than others?


In [40]:
### Data exploration visualization code goes here.
### Feel free to use as many code cells as needed.
import random
import matplotlib.pyplot as plt
# Visualizations will be shown in the notebook.
%matplotlib inline

def plot_image(data, labels):
    fig, axs = plt.subplots(1, 3, figsize=(10, 5))
    axs = axs.ravel()
    for i in range(3):
        index = random.randint(0, len(data) - 1)
        image = data[index].squeeze()
        axs[i].axis('off')
        axs[i].imshow(image)
        axs[i].set_title(labels[index])

In [4]:
print('Random images from training Data')
plot_image(
    X_train,
    y_train
)


Random images from training Data

In [5]:
print('Random images from validation Data')
plot_image(
    X_valid,
    y_valid
)


Random images from validation Data

In [6]:
print('Random Images from testing data')
plot_image(
    X_test,
    y_test
)


Random Images from testing data

In [7]:
def hist(data, title):
    fig, ax = plt.subplots()
    n, bins, patches = ax.hist(data, n_classes, rwidth=0.7)

    ax.plot(bins)
    ax.set_xlabel('Classes')
    ax.set_ylabel('Members per class')
    ax.set_title(title)

    # Tweak spacing to prevent clipping of ylabel
    fig.tight_layout()
    plt.show()

In [8]:
hist(y_train, 'Distribution of classes in training data')



In [9]:
hist(y_valid, 'Distribution of classes in validation data')



In [10]:
hist(y_test, 'Distribution of classes in test data')



Step 2: Design and Test a Model Architecture

Design and implement a deep learning model that learns to recognize traffic signs. Train and test your model on the German Traffic Sign Dataset.

The LeNet-5 implementation shown in the classroom at the end of the CNN lesson is a solid starting point. You'll have to change the number of classes and possibly the preprocessing, but aside from that it's plug and play!

With the LeNet-5 solution from the lecture, you should expect a validation set accuracy of about 0.89. To meet specifications, the validation set accuracy will need to be at least 0.93. It is possible to get an even higher accuracy, but 0.93 is the minimum for a successful project submission.

There are various aspects to consider when thinking about this problem:

  • Neural network architecture (is the network over or underfitting?)
  • Play around preprocessing techniques (normalization, rgb to grayscale, etc)
  • Number of examples per label (some have more than others).
  • Generate fake data.

Here is an example of a published baseline model on this problem. It's not required to be familiar with the approach used in the paper but, it's good practice to try to read papers like these.

Pre-process the Data Set (normalization, grayscale, etc.)

Minimally, the image data should be normalized so that the data has mean zero and equal variance. For image data, (pixel - 128)/ 128 is a quick way to approximately normalize the data and can be used in this project.

Other pre-processing steps are optional. You can try different techniques to see if it improves performance.

Use the code cell (or multiple code cells, if necessary) to implement the first step of your project.


In [11]:
### Preprocess the data here.
def normalize(data):
    if (len(data.shape) != 4):
        print('Expect a 4D array to normalize, refusing to normalize')
        return None;
    
    return  (data - data.mean()) / data.std()

def greyscale(data):
    # return np.sum(data/3, axis=3, keepdims=True)
    return np.dot(data[...,:3], [0.299, 0.587, 0.114])

# Convert to shape 32,32, 1
def expand(arr):
    return np.expand_dims(arr, axis=3)

In [12]:
X_train_grey = expand(greyscale(X_train))
X_train_norm_grey = normalize(X_train_grey)
X_valid_grey = expand(greyscale(X_valid))
X_test_grey = expand(greyscale(X_test))

Augmentation operations (rotation, scale, shear, translate etc.)

As seen in the histograms above, the training data is not distributed evenly. Running my initial model on this data pins the accuracy at ~0.91. Also the accuracy changes everytime I run the model because of the uneven data. After doing some reading online on how to augment image training data, I came accross this article that showed how to use sklearn package to perform operations like rotation, shearing etc and generate more data from limited training data.

In this section I'm going to use some of the techniques in the article to define augmentation operations for data in the training set.


In [13]:
from skimage import transform

def generate_augmented_image(image):
    '''
    Rotate images randomly between -10 and 10 degrees
    Translate between -10 and 10 pixels in all directions
    Zoom between 1 and 1.3
    Shear between -25 and 25 degrees
    '''
    rotation_angle = random.randint(-10, 10)
    
    translation_1 = random.randint(-10, 10)
    translation_2 = random.randint(-10, 10)
    
    zoom = random.uniform(1, 1.3)
    
    shearing_degree = random.uniform(-25, 25)
    
    # Shift image to center and then shift back after transformation otherwise
    # rotations will make image go out of frame
    center_shift = (np.array(image.shape) / 2.) - 0.5
    xform_center   = transform.SimilarityTransform(translation=-center_shift)
    xform_uncenter = transform.SimilarityTransform(translation=center_shift)
    
    xform_augment = transform.AffineTransform(
        rotation = np.deg2rad(rotation_angle),
        scale =(1/zoom, 1/zoom),
        shear = np.deg2rad(shearing_degree),
        translation = (translation_1, translation_2)
    )
    
    # Shift, augment, unshift operations
    xform = xform_center + xform_augment + xform_uncenter
    
    return transform._warps_cy._warp_fast(
        image,
        xform.params,
        output_shape=image.shape
    )

Visualize augmentation


In [41]:
def plot_transformations(images):
    fig, axs = plt.subplots(2, 5, figsize=(10, 5))
    axs = axs.ravel()

    for i in range(5):
        index = random.randint(0, len(images) - 1)
        image = images[index].squeeze()
        axs[i].axis('off')
        axs[i].imshow(image)
        
        axs[i+5].axis('off')
        axs[i+5].imshow(generate_augmented_image(image))

plot_transformations(X_train_grey)


Test dimensionality changes


In [42]:
index = random.randint(0, len(X_train) - 1)
random_image = X_train[index]
print("Original shape: " + str(random_image.shape))
augmented_image = generate_augmented_image(X_train_grey[index].squeeze())
print("Augmented shape: " + str(augmented_image.shape))


Original shape: (32, 32, 3)
Augmented shape: (32, 32)

In [46]:
def plot_images(images):
    fig, axs = plt.subplots(1, len(images), figsize=(10, 5))
    axs = axs.ravel()

    for i in range(len(images)):
        axs[i].axis('off')
        axs[i].imshow(images[i].squeeze())
        
plot_images([random_image, augmented_image])


Augment data for classes with less examples


In [17]:
def plot_examples(data, title):
    _, ax = plt.subplots(1)
    ax.bar(np.arange(n_classes), data, width=0.7)
    ax.set_xlabel('Classes')
    ax.set_ylabel('Examples Per Class')
    ax.set_title(title)
    plt.show()

examples_per_class = np.bincount(y_train)
plot_examples(examples_per_class, 'Before')



In [18]:
print("Mean examples per class: " + str(examples_per_class.mean()))


Mean examples per class: 809.279069767

In [19]:
limit = 800
labels_to_be_augmented = np.where(examples_per_class < limit)[0]
print(str(len(labels_to_be_augmented)) + " labels need more examples")

total_examples = 0
for label in labels_to_be_augmented:
    indices = np.where(y_train == label)[0]
    examples_needed = limit - examples_per_class[label]
    print("Adding " + str(examples_needed) + " examples for label: " + str(label))
    total_examples += examples_needed
    
print("Total number of images that would be added: " + str(total_examples))

X_train_aug = np.copy(X_train_grey)
X_train_aug.resize(n_train+total_examples, image_shape[0], image_shape[1], 1)
y_train_aug = np.copy(y_train)
y_train_aug.resize(n_train+total_examples)

current = n_train
for label in labels_to_be_augmented:
    indices = np.where(y_train == label)[0]
    examples_needed = limit - examples_per_class[label]
    for i in range(examples_needed):
        index = random.randint(0, len(indices) - 1)
        X_train_aug[current] = expand(generate_augmented_image(X_train_aug[index].squeeze()))
        y_train_aug[current] = label
        current += 1

X_train_aug_norm = normalize(X_train_aug)
print(X_train_aug_norm.shape)


26 labels need more examples
Adding 620 examples for label: 0
Adding 440 examples for label: 6
Adding 110 examples for label: 14
Adding 260 examples for label: 15
Adding 440 examples for label: 16
Adding 620 examples for label: 19
Adding 500 examples for label: 20
Adding 530 examples for label: 21
Adding 470 examples for label: 22
Adding 350 examples for label: 23
Adding 560 examples for label: 24
Adding 260 examples for label: 26
Adding 590 examples for label: 27
Adding 320 examples for label: 28
Adding 560 examples for label: 29
Adding 410 examples for label: 30
Adding 110 examples for label: 31
Adding 590 examples for label: 32
Adding 201 examples for label: 33
Adding 440 examples for label: 34
Adding 470 examples for label: 36
Adding 620 examples for label: 37
Adding 530 examples for label: 39
Adding 500 examples for label: 40
Adding 590 examples for label: 41
Adding 590 examples for label: 42
Total number of images that would be added: 11681
(46480, 32, 32, 1)

In [20]:
plot_examples(
    np.bincount(y_train_aug),
    'After'
)



In [21]:
print("Mean examples per class: " + str(np.bincount(y_train_aug).mean()))


Mean examples per class: 1080.93023256

Model Architecture


In [22]:
import tensorflow as tf

EPOCHS = 35
BATCH_SIZE = 135

In [23]:
from tensorflow.contrib.layers import flatten

def LeNet(x):
    # Arguments used for tf.truncated_normal, randomly defines variables for the weights and biases for each layer
    mu = 0
    sigma = 0.1
    
    # Layer 1: Convolutional. Input = 32x32x1. Output = 28x28x6.
    wc1 = tf.Variable(tf.truncated_normal([5, 5, 1, 6], mean=mu, stddev=sigma))
    bc1 = tf.Variable(tf.truncated_normal([6], mean=mu, stddev=sigma))
    conv1 = tf.nn.conv2d(x, wc1, strides=[1, 1, 1, 1], padding='VALID')
    conv1 = tf.nn.bias_add(conv1, bc1)

    # Activation.
    conv1 = tf.nn.relu(conv1)

    # Pooling. Input = 28x28x6. Output = 14x14x6.
    p1 = tf.nn.max_pool(conv1, ksize=[1, 2, 2, 1], strides=[1, 2, 2, 1], padding='VALID')

    # Layer 2: Convolutional. Output = 10x10x16.
    wc2 = tf.Variable(tf.truncated_normal([5, 5, 6, 16], mean=mu, stddev=sigma))
    bc2 = tf.Variable(tf.truncated_normal([16], mean=mu, stddev=sigma))
    conv2 = tf.nn.conv2d(p1, wc2, strides=[1, 1, 1, 1], padding='VALID')
    conv2 = tf.nn.bias_add(conv2, bc2)
    
    # Activation.
    conv2 = tf.nn.relu(conv2)

    # Pooling. Input = 10x10x16. Output = 5x5x16.
    p2 = tf.nn.max_pool(conv2, ksize=[1, 2, 2, 1], strides=[1, 2, 2, 1], padding='VALID')

    # Layer 3: Convolutional. Output = 2x2x100.
    wc3 = tf.Variable(tf.truncated_normal([4, 4, 16, 100], mean=mu, stddev=sigma))
    bc3 = tf.Variable(tf.truncated_normal([100], mean=mu, stddev=sigma))
    conv3 = tf.nn.conv2d(p2, wc3, strides=[1, 1, 1, 1], padding='VALID')
    conv3 = tf.nn.bias_add(conv3, bc3)
    
    # Activation.
    p3 = tf.nn.relu(conv3)

    # Flatten. Input = 2x2x100. Output = 400.
    flat = flatten(p3)
    
    # Layer 3: Fully Connected. Input = 400. Output = 120.
    wfc1 = tf.Variable(tf.truncated_normal([400, 120], mean=mu, stddev=sigma))
    bfc1 = tf.Variable(tf.truncated_normal([120], mean=mu, stddev=sigma))
    fc1 = tf.add(tf.matmul(flat, wfc1), bfc1)
    
    # Activation.
    fc1 = tf.nn.relu(fc1)
    
    # Dropout
    fc1 = tf.nn.dropout(fc1, keep_prob)

#     # Layer 4: Fully Connected. Input = 120. Output = 84.
#     wfc2 = tf.Variable(tf.truncated_normal([120, 84], mean=mu, stddev=sigma))
#     bfc2 = tf.Variable(tf.truncated_normal([84], mean=mu, stddev=sigma))
#     fc2 = tf.add(tf.matmul(fc1, wfc2), bfc2)
    
#     # Activation.
#     fc2 = tf.nn.relu(fc2)
    
#     # Dropout
#     fc2 = tf.nn.dropout(fc2, keep_prob)

#     # Layer 5: Fully Connected. Input = 84. Output = 43.
#     wout = tf.Variable(tf.truncated_normal([84, 43], mean=mu, stddev=sigma))
#     bout = tf.Variable(tf.truncated_normal([43], mean=mu, stddev=sigma))
#     logits = tf.add(tf.matmul(fc2, wout), bout)

    # Layer 5: Fully Connected. Input = 120. Output = 43.
    wout = tf.Variable(tf.truncated_normal([120, 43], mean=mu, stddev=sigma))
    bout = tf.Variable(tf.truncated_normal([43], mean=mu, stddev=sigma))
    logits = tf.add(tf.matmul(fc1, wout), bout)
    
    return logits

Train, Validate and Test the Model

A validation set can be used to assess how well the model is performing. A low accuracy on the training and validation sets imply underfitting. A high accuracy on the training set but low accuracy on the validation set implies overfitting.

Define placeholder tensors


In [24]:
x = tf.placeholder(tf.float32, (None, 32, 32, 1))
y = tf.placeholder(tf.int32, (None))
keep_prob = tf.placeholder(tf.float32)
one_hot_y = tf.one_hot(y, 43)

Define operations


In [25]:
rate = 0.001

logits = LeNet(x)
cross_entropy = tf.nn.softmax_cross_entropy_with_logits(labels=one_hot_y, logits=logits)
loss_operation = tf.reduce_mean(cross_entropy)
optimizer = tf.train.AdamOptimizer(learning_rate = rate)
training_operation = optimizer.minimize(loss_operation)

Evaluation pipeline


In [57]:
correct_prediction = tf.equal(tf.argmax(logits, 1), tf.argmax(one_hot_y, 1))
accuracy_operation = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))
saver = tf.train.Saver()

def evaluate(X_data, y_data):
    num_examples = len(X_data)
    total_loss = 0
    total_accuracy = 0
    sess = tf.get_default_session()
    for offset in range(0, num_examples, BATCH_SIZE):
        batch_x, batch_y = X_data[offset:offset+BATCH_SIZE], y_data[offset:offset+BATCH_SIZE]
        loss, accuracy = sess.run([loss_operation, accuracy_operation], feed_dict={x: batch_x, y: batch_y, keep_prob: 1.0})
        total_loss += (loss * len(batch_x))
        total_accuracy += (accuracy * len(batch_x))
    return (total_loss / num_examples, total_accuracy / num_examples)

def evaluate_without_loss(X_data, y_data):
    num_examples = len(X_data)
    total_accuracy = 0
    sess = tf.get_default_session()
    for offset in range(0, num_examples, BATCH_SIZE):
        batch_x, batch_y = X_data[offset:offset+BATCH_SIZE], y_data[offset:offset+BATCH_SIZE]
        accuracy = sess.run(accuracy_operation, feed_dict={x: batch_x, y: batch_y, keep_prob: 1.0})
        total_accuracy += (accuracy * len(batch_x))
    return total_accuracy / num_examples

Training and Validation pipeline


In [27]:
### Train your model here.
### Calculate and report the accuracy on the training and validation set.
### Once a final model architecture is selected, 
### the accuracy on the test set should be calculated and reported as well.
### Feel free to use as many code cells as needed.
from sklearn.utils import shuffle

def train(training_data, training_labels, validation_data, validation_labels):
    
    with tf.Session() as sess:
        sess.run(tf.global_variables_initializer())
        num_examples = len(X_train)

        print("Training...")
        print()

        for i in range(EPOCHS):
            shuffled_x, shuffled_y = shuffle(training_data, training_labels)
            for offset in range(0, num_examples, BATCH_SIZE):
                end = offset + BATCH_SIZE
                batch_x, batch_y = shuffled_x[offset:end], shuffled_y[offset:end]
                sess.run(training_operation, feed_dict={x: batch_x, y: batch_y, keep_prob: 0.5})

            validation_loss, validation_accuracy = evaluate(validation_data, validation_labels)
            print("EPOCH {} ...".format(i+1))
            print("Validation Loss = {:.3f}".format(validation_loss))
            print("Validation Accuracy = {:.3f}".format(validation_accuracy))
            print()

        saver.save(sess, './lenet')
        print("Model saved")
    
# train(X_train_norm_grey, y_train, X_valid_grey, y_valid)
train(X_train_aug_norm, y_train_aug, X_valid_grey, y_valid)


Training...

EPOCH 1 ...
Validation Loss = 14.589
Validation Accuracy = 0.692

EPOCH 2 ...
Validation Loss = 12.500
Validation Accuracy = 0.801

EPOCH 3 ...
Validation Loss = 7.236
Validation Accuracy = 0.878

EPOCH 4 ...
Validation Loss = 7.984
Validation Accuracy = 0.887

EPOCH 5 ...
Validation Loss = 6.095
Validation Accuracy = 0.919

EPOCH 6 ...
Validation Loss = 6.058
Validation Accuracy = 0.916

EPOCH 7 ...
Validation Loss = 5.576
Validation Accuracy = 0.913

EPOCH 8 ...
Validation Loss = 7.274
Validation Accuracy = 0.931

EPOCH 9 ...
Validation Loss = 4.826
Validation Accuracy = 0.937

EPOCH 10 ...
Validation Loss = 6.672
Validation Accuracy = 0.933

EPOCH 11 ...
Validation Loss = 6.877
Validation Accuracy = 0.944

EPOCH 12 ...
Validation Loss = 6.954
Validation Accuracy = 0.934

EPOCH 13 ...
Validation Loss = 6.456
Validation Accuracy = 0.943

EPOCH 14 ...
Validation Loss = 7.448
Validation Accuracy = 0.921

EPOCH 15 ...
Validation Loss = 7.081
Validation Accuracy = 0.938

EPOCH 16 ...
Validation Loss = 6.686
Validation Accuracy = 0.943

EPOCH 17 ...
Validation Loss = 8.625
Validation Accuracy = 0.941

EPOCH 18 ...
Validation Loss = 10.300
Validation Accuracy = 0.936

EPOCH 19 ...
Validation Loss = 7.552
Validation Accuracy = 0.935

EPOCH 20 ...
Validation Loss = 6.613
Validation Accuracy = 0.942

EPOCH 21 ...
Validation Loss = 8.336
Validation Accuracy = 0.950

EPOCH 22 ...
Validation Loss = 7.455
Validation Accuracy = 0.949

EPOCH 23 ...
Validation Loss = 6.756
Validation Accuracy = 0.941

EPOCH 24 ...
Validation Loss = 7.286
Validation Accuracy = 0.946

EPOCH 25 ...
Validation Loss = 6.901
Validation Accuracy = 0.940

EPOCH 26 ...
Validation Loss = 8.466
Validation Accuracy = 0.951

EPOCH 27 ...
Validation Loss = 8.777
Validation Accuracy = 0.947

EPOCH 28 ...
Validation Loss = 7.948
Validation Accuracy = 0.946

EPOCH 29 ...
Validation Loss = 9.090
Validation Accuracy = 0.950

EPOCH 30 ...
Validation Loss = 10.121
Validation Accuracy = 0.938

EPOCH 31 ...
Validation Loss = 8.368
Validation Accuracy = 0.948

EPOCH 32 ...
Validation Loss = 9.606
Validation Accuracy = 0.952

EPOCH 33 ...
Validation Loss = 9.457
Validation Accuracy = 0.953

EPOCH 34 ...
Validation Loss = 10.657
Validation Accuracy = 0.947

EPOCH 35 ...
Validation Loss = 10.347
Validation Accuracy = 0.954

Model saved

Evaluation on Test data


In [59]:
with tf.Session() as sess:
    saver.restore(sess, './lenet')

    test_accuracy = evaluate_without_loss(X_test_grey, y_test)
    print("Test Accuracy = {:.3f}".format(test_accuracy))


Test Accuracy = 0.931

Step 3: Test a Model on New Images

To give yourself more insight into how your model is working, download at least five pictures of German traffic signs from the web and use your model to predict the traffic sign type.

You may find signnames.csv useful as it contains mappings from the class id (integer) to the actual sign name.

Load and Output the Images


In [74]:
### Load the images and plot them here.
### Feel free to use as many code cells as needed.
from scipy import misc
import glob

real_test_images = []

for _, file in enumerate(glob.glob('./internet_images/*')):
    img = misc.imread(file)
    real_test_images.append(img)
    
X_real_test = np.asarray(real_test_images)
y_real_test = [4, 13, 14, 25, 36, 33, 11]

plot_image(X_real_test, y_real_test)


Predict the Sign Type for Each Image


In [93]:
### Run the predictions here and use the model to output the prediction for each image.
### Make sure to pre-process the images with the same pre-processing pipeline used earlier.
### Feel free to use as many code cells as needed.
X_real_test_grey = greyscale(X_real_test)
X_real_test_norm_grey = normalize(expand(X_real_test_grey))

softmax = tf.nn.softmax(logits)
top_1 = tf.nn.top_k(softmax, k=1)

with tf.Session() as sess:
    saver.restore(sess, './lenet')
    
    predictions = sess.run(top_1, feed_dict={x: X_real_test_norm_grey, y: y_real_test, keep_prob: 1.0})

    for i in range(len(y_real_test)):
        print('Actual label:' + str(y_real_test[i]) + ' Prediction:' + str(predictions[1][i][0]))


Actual label:4 Prediction:4
Actual label:13 Prediction:13
Actual label:14 Prediction:14
Actual label:25 Prediction:25
Actual label:36 Prediction:25
Actual label:33 Prediction:33
Actual label:11 Prediction:11

Analyze Performance


In [76]:
### Calculate the accuracy for these 5 new images. 
### For example, if the model predicted 1 out of 5 signs correctly, it's 20% accurate on these new images.
with tf.Session() as sess:
    saver.restore(sess, './lenet')
    
    real_test_accuracy = sess.run(accuracy_operation, feed_dict={x: X_real_test_norm_grey, y: y_real_test, keep_prob: 1.0})
    print("Real test Accuracy = {:.3f}".format(real_test_accuracy))


Real test Accuracy = 0.857

Output Top 5 Softmax Probabilities For Each Image Found on the Web

For each of the new images, print out the model's softmax probabilities to show the certainty of the model's predictions (limit the output to the top 5 probabilities for each image). tf.nn.top_k could prove helpful here.

The example below demonstrates how tf.nn.top_k can be used to find the top k predictions for each image.

tf.nn.top_k will return the values and indices (class ids) of the top k predictions. So if k=3, for each sign, it'll return the 3 largest probabilities (out of a possible 43) and the correspoding class ids.

Take this numpy array as an example. The values in the array represent predictions. The array contains softmax probabilities for five candidate images with six possible classes. tf.nn.top_k is used to choose the three classes with the highest probability:

# (5, 6) array
a = np.array([[ 0.24879643,  0.07032244,  0.12641572,  0.34763842,  0.07893497,
         0.12789202],
       [ 0.28086119,  0.27569815,  0.08594638,  0.0178669 ,  0.18063401,
         0.15899337],
       [ 0.26076848,  0.23664738,  0.08020603,  0.07001922,  0.1134371 ,
         0.23892179],
       [ 0.11943333,  0.29198961,  0.02605103,  0.26234032,  0.1351348 ,
         0.16505091],
       [ 0.09561176,  0.34396535,  0.0643941 ,  0.16240774,  0.24206137,
         0.09155967]])

Running it through sess.run(tf.nn.top_k(tf.constant(a), k=3)) produces:

TopKV2(values=array([[ 0.34763842,  0.24879643,  0.12789202],
       [ 0.28086119,  0.27569815,  0.18063401],
       [ 0.26076848,  0.23892179,  0.23664738],
       [ 0.29198961,  0.26234032,  0.16505091],
       [ 0.34396535,  0.24206137,  0.16240774]]), indices=array([[3, 0, 5],
       [0, 1, 4],
       [0, 5, 1],
       [1, 3, 5],
       [1, 4, 3]], dtype=int32))

Looking just at the first row we get [ 0.34763842, 0.24879643, 0.12789202], you can confirm these are the 3 largest probabilities in a. You'll also notice [3, 0, 5] are the corresponding indices.


In [106]:
### Print out the top five softmax probabilities for the predictions on the German traffic sign images found on the web. 
### Feel free to use as many code cells as needed.
top_5 = tf.nn.top_k(softmax, k=5)

with tf.Session() as sess:
    saver.restore(sess, './lenet')
    
    top_5_preds = sess.run(top_5, feed_dict={x: X_real_test_norm_grey, keep_prob: 1.0})
    
    for i in range(len(y_real_test)):
        print('Actual label:' + str(y_real_test[i]))
        print('Top Prediction:' + str(top_5_preds[1][i][0]) + ' Confidence:' + str(100*top_5_preds[0][i][0]))
        print('Next Prediction:' + str(top_5_preds[1][i][1]) + ' Confidence:' + str(100*top_5_preds[0][i][1]))
        print('Next Prediction:' + str(top_5_preds[1][i][2]) + ' Confidence:' + str(100*top_5_preds[0][i][2]))
        print('Next Prediction:' + str(top_5_preds[1][i][3]) + ' Confidence:' + str(100*top_5_preds[0][i][3]))
        print('Next Prediction:' + str(top_5_preds[1][i][4]) + ' Confidence:' + str(100*top_5_preds[0][i][4]))
        print('----------')


Actual label:4
Top Prediction:4 Confidence:86.712116003
Next Prediction:0 Confidence:12.9258781672
Next Prediction:1 Confidence:0.361989717931
Next Prediction:24 Confidence:6.64126389438e-06
Next Prediction:31 Confidence:2.44453630671e-06
----------
Actual label:13
Top Prediction:13 Confidence:100.0
Next Prediction:34 Confidence:1.91032525688e-29
Next Prediction:14 Confidence:5.96077786326e-30
Next Prediction:38 Confidence:7.36646952994e-32
Next Prediction:39 Confidence:1.95574917393e-34
----------
Actual label:14
Top Prediction:14 Confidence:99.5147764683
Next Prediction:13 Confidence:0.485222507268
Next Prediction:34 Confidence:1.29102349471e-10
Next Prediction:33 Confidence:8.23958330477e-16
Next Prediction:38 Confidence:4.86847101535e-18
----------
Actual label:25
Top Prediction:25 Confidence:100.0
Next Prediction:31 Confidence:8.51428660914e-30
Next Prediction:0 Confidence:0.0
Next Prediction:1 Confidence:0.0
Next Prediction:2 Confidence:0.0
----------
Actual label:36
Top Prediction:25 Confidence:52.4584889412
Next Prediction:33 Confidence:47.5414991379
Next Prediction:14 Confidence:9.11794302283e-06
Next Prediction:30 Confidence:5.33666277835e-08
Next Prediction:34 Confidence:8.81082231778e-13
----------
Actual label:33
Top Prediction:33 Confidence:99.9725043774
Next Prediction:35 Confidence:0.0162915806868
Next Prediction:3 Confidence:0.00663176761009
Next Prediction:25 Confidence:0.00227772979997
Next Prediction:34 Confidence:0.00225135445362
----------
Actual label:11
Top Prediction:11 Confidence:100.0
Next Prediction:30 Confidence:1.78105366356e-14
Next Prediction:20 Confidence:2.35539637288e-27
Next Prediction:7 Confidence:3.36878725269e-30
Next Prediction:40 Confidence:1.5791166829e-31
----------

Project Writeup

Once you have completed the code implementation, document your results in a project writeup using this template as a guide. The writeup can be in a markdown or pdf file.

Note: Once you have completed all of the code implementations and successfully answered each question above, you may finalize your work by exporting the iPython Notebook as an HTML document. You can do this by using the menu above and navigating to \n", "File -> Download as -> HTML (.html). Include the finished document along with this notebook as your submission.


Step 4 (Optional): Visualize the Neural Network's State with Test Images

This Section is not required to complete but acts as an additional excersise for understaning the output of a neural network's weights. While neural networks can be a great learning device they are often referred to as a black box. We can understand what the weights of a neural network look like better by plotting their feature maps. After successfully training your neural network you can see what it's feature maps look like by plotting the output of the network's weight layers in response to a test stimuli image. From these plotted feature maps, it's possible to see what characteristics of an image the network finds interesting. For a sign, maybe the inner network feature maps react with high activation to the sign's boundary outline or to the contrast in the sign's painted symbol.

Provided for you below is the function code that allows you to get the visualization output of any tensorflow weight layer you want. The inputs to the function should be a stimuli image, one used during training or a new one you provided, and then the tensorflow variable name that represents the layer's state during the training process, for instance if you wanted to see what the LeNet lab's feature maps looked like for it's second convolutional layer you could enter conv2 as the tf_activation variable.

For an example of what feature map outputs look like, check out NVIDIA's results in their paper End-to-End Deep Learning for Self-Driving Cars in the section Visualization of internal CNN State. NVIDIA was able to show that their network's inner weights had high activations to road boundary lines by comparing feature maps from an image with a clear path to one without. Try experimenting with a similar test to show that your trained network's weights are looking for interesting features, whether it's looking at differences in feature maps from images with or without a sign, or even what feature maps look like in a trained network vs a completely untrained one on the same sign image.

Your output should look something like this (above)


In [ ]:
### Visualize your network's feature maps here.
### Feel free to use as many code cells as needed.

# image_input: the test image being fed into the network to produce the feature maps
# tf_activation: should be a tf variable name used during your training procedure that represents the calculated state of a specific weight layer
# activation_min/max: can be used to view the activation contrast in more detail, by default matplot sets min and max to the actual min and max values of the output
# plt_num: used to plot out multiple different weight feature map sets on the same block, just extend the plt number for each new feature map entry

def outputFeatureMap(image_input, tf_activation, activation_min=-1, activation_max=-1 ,plt_num=1):
    # Here make sure to preprocess your image_input in a way your network expects
    # with size, normalization, ect if needed
    # image_input =
    # Note: x should be the same name as your network's tensorflow data placeholder variable
    # If you get an error tf_activation is not defined it may be having trouble accessing the variable from inside a function
    activation = tf_activation.eval(session=sess,feed_dict={x : image_input})
    featuremaps = activation.shape[3]
    plt.figure(plt_num, figsize=(15,15))
    for featuremap in range(featuremaps):
        plt.subplot(6,8, featuremap+1) # sets the number of feature maps to show on each row and column
        plt.title('FeatureMap ' + str(featuremap)) # displays the feature map number
        if activation_min != -1 & activation_max != -1:
            plt.imshow(activation[0,:,:, featuremap], interpolation="nearest", vmin =activation_min, vmax=activation_max, cmap="gray")
        elif activation_max != -1:
            plt.imshow(activation[0,:,:, featuremap], interpolation="nearest", vmax=activation_max, cmap="gray")
        elif activation_min !=-1:
            plt.imshow(activation[0,:,:, featuremap], interpolation="nearest", vmin=activation_min, cmap="gray")
        else:
            plt.imshow(activation[0,:,:, featuremap], interpolation="nearest", cmap="gray")