Spatial Pyramid Pooling (SPP) is a technique which allows Convolutional Neural Networks (CNNs) to use input images of any size, not only $224\text{px} \times 224\text{px}$ as most architectures do. (However, there is a lower bound for the size of the input image).

## Idea

* Convolutional layers operate on any size, but fully connected layers need fixed-size inputs
* Solution:
  * Add a new SPP layer on top of the last convolutional layer, before the fully connected layer
  * Use an approach similar to bag of words (BoW), but maintain the spatial information. The BoW approach is used for text classification, where the order of the words is discarded and only the number of occurences is kept.
  * The SPP layer operates on each feature map independently.
  * The output of the SPP layer is of dimension $k \cdot M$, where $k$ is the number of feature maps the SPP layer got as input and $M$ is the number of bins.

Example: We could use spatial pyramid pooling with 21 bins:

* 1 bin which is the max of the complete feature map
* 4 bins which divide the image into 4 regions of equal size (depending on the input size) and rectangular shape. Each bin gets the max of its region.
* 16 bins which divide the image into 4 regions of equal size (depending on the input size) and rectangular shape. Each bin gets the max of its region.

## Evaluation

* Pascal VOC 2007, Caltech101: state-of-the-art, without finetuning
* ImageNet 2012: Boosts accuracy for various CNN architectures
* ImageNet Large Scale Visual Recognition Challenge (ILSVRC) 2014: Rank #2


## Code

The paper claims that the code is [here](http://research.microsoft.com/en-us/um/people/kahe/), but this seems not to be the case any more.

People have tried to implement it with Tensorflow ([1](http://stackoverflow.com/q/40913794/562769), [2](https://github.com/fchollet/keras/issues/2080), [3](https://github.com/tensorflow/tensorflow/issues/6011)), but by now no public working implementation is available.


## Related papers

* [Atrous Convolution](https://arxiv.org/abs/1606.00915)

Generates abstractive summaries from news articles. Also see [blog](https://metamind.io/research/your-tldr-by-an-ai-a-deep-reinforced-model-for-abstractive-summarization)
* Input:
 * vocab size 150K
 * start with $W_\text{emb}$ Glove 100
* Seq2Seq:
  * bidirectional LSTM, `size=200` in each direction. Final hidden states are concatenated and feed as initial hidden state of the decoder an LSTM of `size=400`. surprising it's only one layer.
* Attention:
  * Add standard attention mechanism between each new hidden state of the decoder and all the hidden states of the encoder
  * A new kind of attention mechanism is done between the new hidden state of the decoder and all previous hidden states of the decoder
  * the new hidden state is concatenated with the two attention outputs and feed to dense+softmax to model next word in summary (output vocab size 50K). The weight matrix $W_h$ is reduced to $W_h = \tanh \left( W_\text{emb} W_\text{proj} \right) $ resulting in faster converges, see [1](arXiv:1611.01462) and [2](https://arxiv.org/abs/1608.05859)
* Pointer mechanism:
  * The concatenated values are also feed to logistic classifier to decide if the softmax output should be used or one of the words in the article should be copied to the output. The article word to be copied is selected using same weights computed in the attention mechanism
* Loss
  * $L_\text{ml}$: NLL of the example summary $y^*$. If only $L_\text{ml}$ is used then 25% of the times use generated instead of given sample as input to next step. 
  * $L_\text{rl}$: sample an entire summary from the model $y^s$ (temperature=1) and the loss is the NLL of the sample multiplied by a reward. The reward is $r(y^s)-r(\hat{y})$ where $r$ is ROUGE-L and $\hat{y}$ is a generated greedy sequences
 * $L=\gamma L_\text{rl} + (1-\gamma)L_\text{ml}$ where $\gamma=0.9984$
* Training
  * `batch=50`, Adam,  `LR=1e-4` for RL/ML+RL training
  * The training labels are summary examples and an indication if copy was used in the pointer mechanism and which word was copied. This is indicated when the summary word is OOV or if it appears in the article and its NER is one of PERSON, LOCATION, ORGANIZATION or MISC
* Generation
  * 5 beams
  * force trigrams not to appear twice in the same beam

3D Image Classification is one of the utmost important requirements in healthcare. But due to huge size of such images and less amount of data, it has become difficult to train traditional end-to-end models of classification such as AlexNet, Resnet, VGG. Major approaches considered for 3D images use slices of the image and not the image as whole. This approach at times leads to loss of information across third axis. 

The paper uses the complete 3D image for training, and since the number of images are less we use unsupervised techniques for weights initialization and fine tune the fully connected layers using supervised learning for classification. The major contribution of the paper is the extension of 2D Convolutional Auto-encoders to 3D Domain and taking it further for MRI Classification which can be useful in numerous other applications.

**Algorithm**

1. Train 3D Convolution Auto-encoders using [CADDementia dataset](https://grand-challenge.org/site/caddementia/home/) 
2. Extract the encoder layer from the trained auto-encoders and add fully connected layers to it, followed by softmax
3. Train and test the classification model using [ADNI data](http://adni.loni.usc.edu/)

**3D CAN Model**

This model is 3D extension of [2D Convolutional Auto-encoders](http://people.idsia.ch/~ciresan/data/icann2011.pdf) (2D CAN)

![3D Convolutional Auto-encoders](http://i.imgur.com/66y52uQ.png)

Each convolution in encoder is a 3D Convolution followed by ReLU and maxpool, while in decoder, each convolution is a maxunpool followed by 3D Full Convolution and ReLU. In the last decoder block, instead of ReLU, Sigmoid will be used.

Here the weights were shared in the decoder and encoder as specified in [2D CAN](http://people.idsia.ch/~ciresan/data/icann2011.pdf)

**3D Classification model**

![Classification of MRIs using 3D Convolutional Auto-encoders](http://i.imgur.com/3hOeR8o.png)

The weights of the classification model are initialized using the trained 3D-CAN model as mentioned in algorithm.

**Loss Function**

Weighted negative log likelihood for Classification and Mean Squared Error for Unsupervised learning

**Training algorithm**

[Adadelta](https://arxiv.org/abs/1212.5701)

**Results**

Obtained 89.1% on 10-fold cross validation on dataset of 270 patients for classification of MRI into Mild Cognitive Impairment (MCI), Normal Control (NC) and Alzheimer's disease (AD)

**Image Source**

All images are taken from the [paper](https://arxiv.org/abs/1607.00455) itself.

Facebook has [released a series of papers](https://research.facebook.com/blog/learning-to-segment/) for object segmentation and detection. This paper is the first in that series.

This is how modern object detection works (think [RCNN](https://arxiv.org/abs/1311.2524), [Fast RCNN](http://arxiv.org/abs/1504.08083)):

1.  A rich set of object proposals (i.e., a set of image regions which are likely to contain an object) is generated using a fast (but possibly imprecise) algorithm.
2.  A CNN classifier is applied on each of the proposals.

The current paper improves the step 1, i.e., region/object proposals.

Most object proposals approaches fall into three categories: 
* Objectness scoring
* Seed Segmentation
* Superpixel Merging

Current method is different from these three. 
It share similarities with [Faster R-CNN](https://arxiv.org/abs/1506.01497) in that proposals are generated using a CNN.
The method predicts a segmentation mask given an input *patch* and assigns a score corresponding to how likely the patch is to contain an object.


## Model and Training

Both mask and score predictions are achieved with a single convolutional network but with multiple outputs. All the convolutional layers except the last few are from VGG-A pretrained model.

Each training sample is a triplet of RGB input patch, the binary mask corresponding to the input patch, a label which specifies whether the patch contains an object. A patch is given label 1 only if it satisfies the following constraints:
* the patch contains an object roughly centered in the input patch
* the object is fully contained in the patch and in a given scale range

Note that the network must output a mask for a single object at the center even when multiple objects are present.

Figure 1 shows the architecture and sampling for training.
![figure1](https://i.imgur.com/zSyP0ij.png)

Model is then jointly trained for segmentation and objectness. Negative samples are not used for segmentation.

## Inference

During full image inference, model is applied densely at multiple locations and scales.
This can be done efficiently since all computations are convolutional like in a fully convolutional network (FCN). 

![figure2](https://i.imgur.com/dQWfy8R.png)

This approach surpasses the previous state of the art by a large margin in both box and segmentation proposal generation. 

  * The paper describes a method to separate content and style from each other in an image.
  * The style can then be transfered to a new image.
  * Examples:
    * Let a photograph look like a painting of van Gogh.
    * Improve a dark beach photo by taking the style from a sunny beach photo.

### How
  * They use the pretrained 19-layer VGG net as their base network.
  * They assume that two images are provided: One with the *content*, one with the desired *style*.
  * They feed the content image through the VGG net and extract the activations of the last convolutional layer. These activations are called the *content representation*.
  * They feed the style image through the VGG net and extract the activations of all convolutional layers. They transform each layer to a *Gram Matrix* representation. These Gram Matrices are called the *style representation*.
  * How to calculate a *Gram Matrix*:
    * Take the activations of a layer. That layer will contain some convolution filters (e.g. 128), each one having its own activations.
    * Convert each filter's activations to a (1-dimensional) vector.
    * Pick all pairs of filters. Calculate the scalar product of both filter's vectors.
    * Add the scalar product result as an entry to a matrix of size `#filters x #filters` (e.g. 128x128).
    * Repeat that for every pair to get the Gram Matrix.
    * The Gram Matrix roughly represents the *texture* of the image.
  * Now you have the content representation (activations of a layer) and the style representation (Gram Matrices).
  * Create a new image of the size of the content image. Fill it with random white noise.
  * Feed that image through VGG to get its content representation and style representation. (This step will be repeated many times during the image creation.)
  * Make changes to the new image using gradient descent to optimize a loss function.
    * The loss function has two components:
      * The mean squared error between the new image's content representation and the previously extracted content representation.
      * The mean squared error between the new image's style representation and the previously extracted style representation.
    * Add up both components to get the total loss.
    * Give both components a weight to alter for more/less style matching (at the expense of content matching).


![Examples](https://raw.githubusercontent.com/aleju/papers/master/neural-nets/images/A_Neural_Algorithm_for_Artistic_Style__examples.jpg?raw=true "Examples")

*One example input image with different styles added to it.*

-------------------------

### Rough chapter-wise notes

* Page 1
  * A painted image can be decomposed in its content and its artistic style.
  * Here they use a neural network to separate content and style from each other (and to apply that style to an existing image).

* Page 2
  * Representations get more abstract as you go deeper in networks, hence they should more resemble the actual content (as opposed to the artistic style).
  * They call the feature responses in higher layers *content representation*.
  * To capture style information, they use a method that was originally designed to capture texture information.
  * They somehow build a feature space on top of the existing one, that is somehow dependent on correlations of features. That leads to a "stationary" (?) and multi-scale representation of the style.

* Page 3
  * They use VGG as their base CNN.

* Page 4
  * Based on the extracted style features, they can generate a new image, which has equal activations in these style features.
  * The new image should match the style (texture, color, localized structures) of the artistic image.
  * The style features become more and more abtstract with higher layers. They call that multi-scale the *style representation*.
  * The key contribution of the paper is a method to separate style and content representation from each other.
  * These representations can then be used to change the style of an existing image (by changing it so that its content representation stays the same, but its style representation matches the artwork).

* Page 6
  * The generated images look most appealing if all features from the style representation are used. (The lower layers tend to reflect small features, the higher layers tend to reflect larger features.)
  * Content and style can't be separated perfectly.
  * Their loss function has two terms, one for content matching and one for style matching.
  * The terms can be increased/decreased to match content or style more.

* Page 8
  * Previous techniques work only on limited or simple domains or used non-parametric approaches (see non-photorealistic rendering).
  * Previously neural networks have been used to classify the time period of paintings (based on their style).
  * They argue that separating content from style might be useful and many other domains (other than transfering style of paintings to images).

* Page 9
  * The style representation is gathered by measuring correlations between activations of neurons.
  * They argue that this is somehow similar to what "complex cells" in the primary visual system (V1) do.
  * They note that deep convnets seem to automatically learn to separate content from style, probably because it is helpful for style-invariant classification.

* Page 9, Methods
  * They use the 19 layer VGG net as their basis.
  * They use only its convolutional layers, not the linear ones.
  * They use average pooling instead of max pooling, as that produced slightly better results.

* Page 10, Methods
  * The information about the image that is contained in layers can be visualized. To do that, extract the features of a layer as the labels, then start with a white noise image and change it via gradient descent until the generated features have minimal distance (MSE) to the extracted features.
  * The build a style representation by calculating Gram Matrices for each layer.

* Page 11, Methods
  * The Gram Matrix is generated in the following way:
    * Convert each filter of a convolutional layer to a 1-dimensional vector.
    * For a pair of filters i, j calculate the value in the Gram Matrix by calculating the scalar product of the two vectors of the filters.
    * Do that for every pair of filters, generating a matrix of size #filters x #filters. That is the Gram Matrix.
  * Again, a white noise image can be changed with gradient descent to match the style of a given image (i.e. minimize MSE between two Gram Matrices).
  * That can be extended to match the style of several layers by measuring the MSE of the Gram Matrices of each layer and giving each layer a weighting.

* Page 12, Methods
  * To transfer the style of a painting to an existing image, proceed as follows:
    * Start with a white noise image.
    * Optimize that image with gradient descent so that it minimizes both the content loss (relative to the image) and the style loss (relative to the painting).
    * Each distance (content, style) can be weighted to have more or less influence on the loss function.