Programming Assignment 2: Convolutional Neural Networks Solution

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Description

Convolutional Neural Network for Image Processing

In this assignment, we will train a convolutional neural network to solve two classic image processing tasks: image colourization and super-resolution. First, we will focus on image colourization. That is, given a greyscale image, we wish to predict the colour at each pixel. Image colourization is a di cult problem for many reasons, one of which being that it is ill-posed: for a single greyscale image, there can be multiple, equally valid colourings.

Setting Up

We recommend that you use Colab(https://colab.research.google.com/) for the assignment, as all the assignment notebooks have been tested on Colab. Otherwise, if you are working on your own environment, you will need to install Python 2, PyTorch (https://pytorch.org), iPython Notebooks, SciPy, NumPy and scikit-learn. Check out the websites of the course and relevant packages for more details.

From the assignment zip le, you will nd two python notebook les: colour_regression.ipynb, colourization.ipynb. To setup the Colab environment, you will need to upload the two notebook les using the upload tab at https://colab.research.google.com/.

Dataset

We will use the CIFAR-10 data set, which consists of images of size 32×32 pixels. For most of the questions we will use a subset of the dataset. The data loading script is included with the notebooks, and should download automatically the rst time it is loaded. If you have trouble downloading the le, you can also do so manully from:

http://www.cs.toronto.edu/~kriz/cifar-10-python.tar.gz

To make the problem easier, we will only use the \Horse” category from this data set. Now let’s learn to colour some horses!

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Questions

A. Colourization as Regression (2 points)

There are many ways to frame the problem of image colourization as a machine learning problem. One na ve approach is to frame it as a regression problem, where we build a model to predict the RGB intensities at each pixel given the greyscale input. In this case, the outputs are continuous, and so squared error can be used to train the model.

In this section, you will get familar with training neural networks using cloud GPUs. Open the notebook colour_regression.ipynb on Colab and answer the following questions.

    1. Describe the model RegressionCNN. How many convolution layers does it have? What are the lter sizes and number of lters at each layer? Construct a table or draw a diagram.

    1. Run all the notebook cells in colour_regression.ipynb on Colab (No coding involved). You will train a CNN, and generate some images showing validation outputs. How many epochs are we training the CNN model in the given setting?

    1. Re-train a couple of new models using a di erent number of training epochs. You may train each new models in a new code cell by copying and modifying the code from the last notebook cell. Comment on how the results (output images, training loss) change as we increase or decrease the number of epochs.

    1. A colour space3 [1] is a choice of mapping of colours into three-dimensional coordinates. Some colours could be close together in one colour space, but further apart in others. The RGB colour space is probably the most familiar to you, the model used in colour_regression.py computes squared error in RGB colour space. But, most state of the art colourization models do not use RGB colour space. How could using the RGB colour space be problematic? Your answer should relate how human perception of color is di erent than the squared distance. You may use the Wikipedia article on color space to help you answer the question.

    1. How does framing colourization as a classi cation problem alleviate the above problem?

B. Colourization as Classi cation (2 points)

We will select a subset of 24 colours and frame colourization as a pixel-wise classi cation problem, where we label each pixel with one of 24 colours. The 24 colours are selected using k-means clustering4 over colours, and selecting cluster centers. This was already done for you, and cluster centers are provided in http://www.cs.toronto.edu/~jba/kmeans_colour_a2.tar.gz and will be downloaded automatically by the notebook. For simplicy, we still measure distance in RGB space. This is not ideal but reduces the software dependencies for this assignment.

Open the notebook colourization.ipynb on Colab and answer the following questions.

  1. Complete the model CNN in colourization.ipynb. This model should have the same layers and convolutional lters as the RegressionCNN, with the exception of the output layer. Con-tinue to use PyTorch layers like nn.ReLU, nn.BatchNorm2d and nn.MaxPool2d, however we will not use nn.Conv2d. We will use our own convolution layer MyConv2d included in the le to better understand its internals.

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    1. Run main training loop of CNN in colourization.ipynb on Colab. This will train a CNN for a few epochs using the cross-entropy objective. It will generate some images showing the trained result at the end. How do the results compare to the previous regression model?

  1. Skip Connections (3 points)

A skip connection in a neural network is a connection which skips one or more layer and connects to a later layer. We will introduce skip connections.

    1. Add a skip connection from the rst layer to the last, second layer to the second last, etc. That is, the nal convolution should have both the output of the previous layer and the initial greyscale input as input. This type of skip-connection is introduced by [3], and is called a “UNet”. Following the CNN class that you have completed, complete the __init__ and forward methods of the UNet class.

Hint: You will need to use the function torch.cat.

    1. Train the “UNet” model for the same amount of epochs as the previous CNN and plot the training curve using a batch size of 100. How does the result compare to the previous model? Did skip connections improve the validation loss and accuracy? Did the skip connections improve the output qualitatively? How? Give at least two reasons why skip connections might improve the performance of our CNN models.

    1. Re-train a few more “UNet” models using di erent mini batch sizes with a xed number of epochs. Describe the e ect of batch sizes on the training/validation loss, and the nal image output.

  1. Super-Resolution (1 point)

Many classic image processing problems are to transform the input images into an output image via a transformation pipeline, e.g. colourization, denoising, and super-resolution. These image processing tasks share many similarities, where the inputs are lower quality images and the outputs are the restored high-quality images. Instead of hand-design the transformations, one approach is to learn the transformation pipeline from a training dataset using supervised learning. Previously, you have trained conv nets for colourization. In this question, you will use the same conv net models to solve super-resolution tasks. In the super-resolution task, we aim to recover a high-resolution image from a low-resolution input.

  1. Take a look at the data process function process. What is the resolution di erence between the downsized input image and output image?

  1. Bilinear interpolation5 is one of the basic but widely used resampling techniques in image processing. Run super-resolution with both CNN and UNet. Are there any di erence in the model outputs? Also, comment on how the neural network results (images from the third row) di er from the bilinear interpolation results (images from the fourth row). Give at least two reasons why conv nets are better than bilinear interpolation.

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E. Visualizing Intermediate Activations (2 point)

We will visualize the intermediate activations for several inputs. Run the visualization block in the colourization.ipynb that has already been written for you. For each model, a list of images will be generated and be stored in csc421/a2/outputs/model_name/act0/ folder in the Colab environment. You will need to use the left side panel (the “Table of conetents” panel) to nd these images under the Files tab.

    1. Visualize the activations of the CNN for a few test examples. How are the activation in the rst few layers di erent from the later layers? You do not need to attach the output images to your writeup, only descriptions of what you see.

    1. Visualize the activations of the colourization UNet for a few test examples. How do the activations di er from the CNN activations?

    1. Visualize the activations of the super-resolution UNet for a few test examples. Describe how the activations di er from the colourization models?

  1. Conceptional Problems (2 point)

    1. We also did not tune any hyperparameters for this assignment other than the number of epochs and batch size. What are some hyperparameters that could be tuned? List ve.

    1. In the RegressionCNN model, nn.MaxPool2d layers are applied after nn.ReLU activations, comment on how the output of CNN changes if we switch the order of the max-pooling and ReLU?

    1. The loss functions and the evaluation metrics in this assignment are de ned at pixel-level. In general, these pixel-level measures correlate poorly with human assessment of visual quality. How can we improve the evaluation to match with human assessment better? You may nd

      1. useful for answering this question.

    1. In colourization.ipynb, we have trained a few di erent image processing convolutional neural networks on input and output image size of 32×32. In the test time, the desired output size is often di erent than the one used in training. Describe how we can modify the trained models in this assignment to colourize test images that are larger than 32×32.

What To Submit

For reference, here is everything you need to hand in:

A PDF le a2-writeup.pdf containing the following: { Five questions from Part A

{ Question 2 from Part B { Question 2,3 from Part C

{ Both questions from Part D

{ Answers to all three questions from Part E { Answers to all conceptual questions

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{ Optional: Which part of this assignment did you nd the most valuable? The most di cult and/or frustrating?

Your implementation of colourization.ipynb.

This assignment is graded out of 12 points: 2 for Part A, 2 for Part B, 3 for Part C, 3 for Part D and E, and 2 for Part F.

References

  1. https://en.wikipedia.org/wiki/Color_space

  1. Zhang, R., Isola, P., and Efros, A. A. (2016, October). Colorful image colorization. In European Conference on Computer Vision (pp. 649-666). Springer International Publishing.

  1. Ronneberger, O., Fischer, P., and Brox, T. (2015, October). U-net: Convolutional networks for biomedical image segmentation. In International Conference on Medical Image Computing and Computer-Assisted Intervention (pp. 234-241). Springer, Cham.

  1. Johnson, Justin, Alexandre Alahi, and Li Fei-Fei. “Perceptual losses for real-time style trans-fer and super-resolution.” In European conference on computer vision, pp. 694-711. Springer, Cham, 2016.

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