Follow-Me Project

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Scholar: Christopher Ohara

Program: Udacity Robotics Nanodegree

Introduction

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This project consists of programming and training a Fully Convolutional Network (FCN) for a drone. The implemented hyperparameters allow the drone to track a target (the "hero') in a populated urban area. These types of problems are common in robotics and artificial intelligence, especially for autonomous navigation (self-driving cars, drones) and human-machine interaction (shop-floor robots).

The target has specific characteristics that are distinguishable from environment and other people (wearing a vibrantly red shirt). This project utilizes Python, Unity, Tensorflow and Keras.

Using the simulator, data is collected for three different conditions:

1. Navigate the empty map to record ambient environment
2. Spawn only the target in an otherwise unpopulated environment
3. Follow the target through the populated map

Network Architecture

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Since spatial information is required for a moving target, a fully convolutional network (FNC) is required. The amount of layers is dependent on a few factors described by the algorithms and layers below, but specifically, considerations need to be given to depth (increases with layers), number of hyperparameters (influenced by separable convolutions) and methods to retain spatial information.

The image below shows the chosen network architecture for this application.

FCN Layer Definitions

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Below are some useful definitions for functions used in different layers that constitute a fully convolutional network (FCN), needed to build a semantic segmentation model.

• The encoders in this project utilize separable convolution and batch normalization. By having separable convolution (additional layers) allow for the number of hyperparameters to be reduced at an added cost of "depth." Batch normalization allows for the minimization of the batch by adjusting for the "mean" value. This is a very common technique for neural networks in order to improve training rates and network training speed. Encoders create a set of feature maps from a filter bank by using convolutions. After batch normalization, an ReLU is applied with max pooling to achieve translation invariance. Since the boundary data must be stored, there can be issues if convolutions are called in an incorrect order. One thing to note is, by storing this data (memory) the overall accuracy decreases and the cost of the system increases. Encoders project the input to the hidden layer. The hidden layer then learns a set of latent factors or features. In short, encoders map input data to a different compressed feature representation, which is beneficial for images since they use (relatively) a lot of memory. This is advantageous since compression saves memory, but again, features can be lost during data reduction.

• Decoder blocks have a different tasks. The selection for this project is to include an upsampler (bilinear) layer and a concatenation step. The upsampler takes a "weighted average" of pixel data from the adjacent pixels to return a more useful value (average). The concatenation layer chains the upsample and large input layers together. Finally, the output layer performs another separable convolution to retain the spatial information. The bilinear upsampler does interpolation in one direction and then in another (similar to a forward/backward propagation). This allows for a relatively realistic image to be produced, since the information is represented. Also, with respect to data, some information is technically "lost" since it is a weighted average. This can be problematic if there is an application (military, noise) in which the entire dataset (analog for instance) needs to be preserved. Decoders re-project the hidden layer to the output, in order to reconstruct the input back into the input space (e.g. image compression and decompression to reform the image). Note: Upsampling by a factor of 2 is generally recommended, but different factors can be used as well. Upsampling is used in the decoder block of the FCN. Note: A layer concatenation step is similar to skip connections. Note: Separable convolution layers (1 or 2 additional) are used to extract some more spatial information from prior layers.

• 1x1 convolutions are useful for the reduction of dimensionality while retaining data. Essentially, the 1x1 convolution layer behaves as a linear coordinate-dependent transformation in the filter space. It should be noted that its usage is a function of kernel size and results in less over-fitting (especially when using stochastic gradient descent). 1x1 convolutions, while mathematically equivalent to Fully Connected Layers (FCL), are more flexible. FCLs require a fixed size, where as the 1x1 can accept various values. 1x1 convolutions help increase model accuracy while allowing new parameters and non-linearity. Since the FCL will constrain the network to its specifications, using a 1x1 is more beneficial for dimensionality reduction. The 1x1 convolution condenses all of the input pixels into one pixel. For example, if there are initially 256 channels (color pixels) for input, 64 1x1 convolutions will collapse these pixels into a single output pixel, effectively mapping the inputs to the outputs. In the case mentioned here, using 1x1 convolutions is nearly 4x faster than working with 256 inputs to 256 outputs. Instead of taking the product of all of the inputs, the 1x1 convolution allows for the neural network to specify which inputs (colors) to select. These lower dimensional embeddings retain a large portion of information and also include an ReLU. In practice, 1x1 convolutions are essentially (1x1xnumber_of_channels) with zero padding and a stride of one. 1x1s are the similar to a FCL based on the total number of parameters. Basically, this is very advantageous for computational speed at the cost of potentially losing some important features (a very specific color, an interested section of noise, etc.).

• Skip connections work to improve the gradient flow through the network. This effectively increases the capacity without increasing the number of parameters. Skip connections are not often used in networks that are smaller than ten layers, due to the benefits appearing from traversing the gradient in many layers. This is similar to taking many samples (or integral slices in calculus) to gain very small gains over a large number of processes to result in a large summation of gains.

  • http://iamaaditya.github.io/2016/03/one-by-one-convolution/

  • https://datascience.stackexchange.com/questions/12830/how-are-1x1-convolutions-the-same-as-a-fully-connected-layer

  • https://stackoverflow.com/questions/39366271/for-what-reason-convolution-1x1-is-used-in-deep-neural-networks

  • https://stats.stackexchange.com/questions/194142/what-does-1x1-convolution-mean-in-a-neural-network

Building the Model

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There are three steps to building the model:

• Add encoder blocks to build the encoder layers.
• Add a 1x1 Convolution layer using the conv2d_batchnorm() function. Remember that 1x1 Convolutions require a kernel and stride of 1.
• Add decoder blocks for the decoder layers.

An example is given in python, since is readable and demonstrates a written version of the network architecture:

def fcn_model(inputs, num_classes):

    # Add Encoder Blocks.
    # Remember that with each encoder layer, the depth of your model (the number of filters) increases.
    additional_layer = conv2d_batchnorm(inputs, 16, 1, 1)
    encoding_layer1 = encoder_block(additional_layer, 32, 2)           
    encoding_layer2 = encoder_block(encoding_layer1, 64, 2)
    encoding_layer3 = encoder_block(encoding_layer2, 128, 2)

    # Add 1x1 Convolution layer using conv2d_batchnorm().
    convolution_layer = conv2d_batchnorm(encoding_layer3, 256, 1, 1)

    # Add the same number of Decoder Blocks as the number of Encoder Blocks
    decoding_layer1 = decoder_block(convolution_layer, encoding_layer2, 128)     # note default kernel_size=3
    decoding_layer2 = decoder_block(decoding_layer1, encoding_layer1, 64)
    decoding_layer3 = decoder_block(decoding_layer2, additional_layer, 32)

    x = decoding_layer3

    # The function returns the output layer of your model. "x" is the final layer obtained from the last decoder_block()
    return layers.Conv2D(num_classes, 1, activation='softmax', padding='same')(x)

Hyperparameters

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Hyperparameters must be defined and implemented to train the network.

Note: The hyperparameters were chosen based on previous instruction, intuition and ultimately trial-and-error. The training rate was chosen to be slightly below .5, as it resulted in a closer fit to the model. A relatively high number (40) of epochs was chosen, to have the training set propagated more times to attempt at convergence between the training and validation sets. Likewise, a higher amount of steps (based on the number of available images) resulted in better results, as to be expected. The changes did increase the computational time (which can be mitigated in the cloud). Since there was not time requirement (let's plan for this drone to not attempt computation in real-time), it was justifiable to allow a higher time allowance for a better score.

• Learning Rate - Usually understood as how quickly the network learns how to identify the chosen object, though this depends on overfitting and underfitting. A good learning rate is a higher value than the low learning rate. Yet it is more accurate (credit: Udacity mentor and image below) A lower learning rate is more accurate as the machine does not change its mind as quickly, at a nonlinear (maybe O(2^n)) increase in time below a certain value (approaching zero). A good learning rate will have a nice, smooth negative exponential (e^-t) characteristic when graphed.

• Number of Epochs - Number of propagations. Imagine washing your clothes 20 times to get them really clean. There is a point in which they will not become more clean, and the ideal number (amount of times) can be arrived at by trial and error or knowing the impacts of the other hyperparameters on the overall network or system.

• Steps per Epoch - The number of batches sent through in each epoch. The total number of training images sent through each epoch = (num of batches) * (num of steps) (Credit: Udacity mentor). Imagine washing ten socks in a load of laundry. From the Keras documentation: "Total number of steps (batches of samples) to yield from generator before declaring one epoch finished and starting the next epoch. It should typically be equal to the number of unique samples of your dataset divided by the batch size."

• Validation Steps - Like the steps per epoch, except it is specifically for the validation set.

• Workers - How many processes to work on the problem. More processes is better (AWS uses 4 for Large p2 clusters) but using only 2 might be more feasible on a personal computer (note: this will take a very long time depending on epoch number and learning rate, easily more than 24 hours below .5 learning rate and more than 20 epochs).

• Batch Size - Example: if you have 1000 images and a batch size of 100, the algorithm will send 100 images through the training process at a time. Larger batch sizes process more data at a time, but at a higher computational cost trade-off to decreased amount of memory required.

  • https://keras.io/models/sequential/

  • https://stats.stackexchange.com/questions/153531/what-is-batch-size-in-neural-network

  • https://www.quora.com/What-is-the-learning-rate-in-neural-networks

Image for Learning rates:

The final hyperparameter selections are:

learning_rate = 0.004
batch_size = 32
num_epochs = 40
steps_per_epoch = 200
validation_steps = 50
workers = 4

Hyperparameter Testing

Initially, the standard 0.01 value for the learning rate was used. However, this resulted in large spikes (similar to the impulses from a Dirac function) in the negative exponential curve. Next, a .005 learning rate was implemented, and while having more appealing characteristics, still resulted in spikes in the curve. Following this, 0.004 was used and the training curve and validation curve quickly began to converge (noticeable after only 4 epochs). Finally, 0.003 was attempted, but would have resulted in more than 48 hours (locally, 12 hours in the cloud) to train the network, which was deemed unrealistic and impractical.

The batch size was chosen relative to the processing power and memory allocation available. A higher batch size (usually 2^n power, but actually not required) would have a better performance, at the risk of full memory utilization.

40 epochs were chosen initially, due to familiarity with another project. After analyzing the performance with the other hyperparameters (specifically the training rate), it appeared the training results (final score) would be just as good at 20 epochs instead, but this was not true with respect to the differences in training and validation loss. In a decision to maintain a high final score, 40 epochs proved to have a lower loss factor and this value was chosen.

The validation steps and steps per epoch are usually determined based on total number of batches (images). The more images in the dataset results in a higher number of steps.

The images below show the comparisons between the epoch(3) and epoch(40). It can be seen that these hyperparameters allow a relatively close following of the curves for the training and validation sets, with respect to the error loss.

Prediction & Results

Now that the model is trained and saved, it can be used to make predictions on the validation dataset. These predictions can be compared to the mask images, which are the ground truth labels, to evaluate how well your model is doing under different conditions.

There are three different predictions available from the helper code provided:

• patrol_with_targ: Test how well the network can detect the hero from a distance.
• patrol_non_targ: Test how often the network makes a mistake and identifies the wrong person as the target.
• following_images: Test how well the network can identify the target while following them.

Compare the predictions, and compare them to the ground truth labels and original images.

Images while following the target

Scores for while the quad is following behind the target:

number of validation samples intersection over the union evaulated on 542
average intersection over union for background is 0.9957179100643849
average intersection over union for other people is 0.39279620415847066
average intersection over union for the hero is 0.9063536271767668
number true positives: 539, number false positives: 0, number false negatives: 0

Images while at patrol without target:

Scores for images while the quad is on patrol and the target is not visible:

number of validation samples intersection over the union evaulated on 270
average intersection over union for background is 0.9901814911147127
average intersection over union for other people is 0.8145893794238864
average intersection over union for the hero is 0.0
number true positives: 0, number false positives: 36, number false negatives: 0

Images while at patrol with target at a distance:

This score measures how well the neural network can detect the target from far away:

number of validation samples intersection over the union evaluated on 322
average intersection over union for background is 0.9971254607964568
average intersection over union for other people is 0.5102308567179387
average intersection over union for the hero is 0.42784565743401926
number true positives: 197, number false positives: 3, number false negatives: 104

Evaluation

Now, we can calculate the score based on the true/false positives and negatives

Sum all the true positives, etc. from the three datasets to get a weight for the score:

true_pos = true_pos1 + true_pos2 + true_pos3
false_pos = false_pos1 + false_pos2 + false_pos3
false_neg = false_neg1 + false_neg2 + false_neg3

weight = true_pos/(true_pos+false_neg+false_pos)
= 0.8373151308304891

The IoU for the dataset that never includes the hero is excluded from grading:

final_IoU = (iou1 + iou3)/2
= 0.667099642305

The final score is given by:

final_score = final_IoU * weight

• Final Score = 0.558572624274

Discussion & Future Improvements

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Now that the expected performance can be seen (and tested in the simulation) further applications should be considered. There is the question of "would this work for a dog, car or some other object?" The answer, like in my robotic applications is, "it depends." In order for the program and algorithms to work for another object would require a new dataset from an image stream. However, most of the core code can be used as-is or with some minor modifications. Similarly, the hyperparameter selection we used can give us some intuition when applying this information to the future object of interest.

There are a few suggestions for improvements. The primary consideration should be given to speed of computation. While this project is very beneficial as a learning exercise and for tracking a dedicated object, it will have major issues in a real-time environment. Consider, in this project, if a new target was requested or the current target changed clothing in the street. This particular drone is "not intelligent" so it will just report that the target was lost.

Another issue is feasibility. To acquire nominal results, many pictures of the target were taken for training. This makes training a neural network with very limited or non-precise images unreliable. Likewise, if there is poor visibility (like fog working as a light diffuser) the results will not be nominal. This is a very common issue for military tracking applications and robotics. Other sensors need to be implemented (IR, Ultrasonic, GPS, IMU) and with a combination of onboard processing (MCUs, FPGAs) and cloud computation. This shows that there will be a strong relationship between robotics, AI, real-time OS for embedded systems, and IoT for the optimization of tasks in the future.

Finally, not too much time was spent in the construction of the hyperparameters. They could be derived with a more theoretical (or compared with previous work) to find the best learning rate, batch size, and step size. Collecting more images for training might have been beneficial too, up until a point (recall: trade-off between training speed and accuracy). In short, the score could be optimized greatly at the expense of a deeper investigation.