Convolutional Neural Networks IV

In this post, I will deal with back propagation, gradient descent etc. Do check out my previous posts regarding Max Pooling, filters, dropout layers, fully connected layers and CNN. To begin click here.
So

What is Back Propagation?

Backpropagation is done whenever we find some error. After obtaining the probabilities of the images the CNN subtracts the actual answer with the obtained answer. Clearly, this is an error. So our first objective is too reduce this error. While I was working with the probabilities with the image of the letter 'R' (click here to know about the image 'R'), I got the probability of R as 0.911 and the probability of some other is 0.42.

Actual probability of getting a 'R' is 1 thus, the error is |1 - 0.911| = 0.081
The actual probability of not getting a 'R' is 0 thus, the error is   |0 - 0.42| = 0.42.
Thus the total error is 0.501. Now comes the power of weights. These weights are used in the gradient descent optimization algorithm which is used to find the minimum of the function. These weights are kept on adjusting along the gradient descent and each and every time the slope is chosen which produces the minimum error (like here we have 0.501). This slope is then fed in the equation which is evaluated to find the weights and that weight is multiplied with the input coming from every feature of the neuron (values) and then added with the bias to get the final value. This whole operation is performed several times to update the weights with appropriate values and updated within the network.

Consider the following image below

Fig 1- Gradient Descent

The red dot moves across the graph and tries to find the minimum error with the weight axis. This is performed for every neuron pair and their weights are then noted down. After finding the appropriate weights for every neuron pair, these weights are updated with their corresponding neuron pair and the process of NN is carried out again and again. 

This gradient function is also known as the cost function if you are aware of that. Our main objective for that cost function is to minimize. In gradient descent, we jump or take steps towards negative side i.e downwards. The opposite is the case of gradient ascent where we jump towards up to find the maximum. Well, the good thing is that these objectives are executed by the NN itself automatically to gather the best parameter but there are also various parameters where it cannot be automatically done. These include the number of hidden layers, choosing the activation function, the right amount of stride, choosing the matrix size of the pooling layer, number of epochs, batch size and various other parameters.

All these can be achieved by trial and error as I do the same way to find my best NN. Although this hurts because to run a NN my Core i3 CPU (3rd Gen 😑) it takes around 3 hours to find the appropriate parameters. Well, hard works do pay off so keep on trying and explore the world of NN.

Cheers 😃

Convolutional Neural Networks III

In this post, I'll deal with dense layer, fully connected layer and backpropagation. If you have missed my previous post click here.
Before moving further, let us have a view on the filter's working on an image. I made a pixelated image of the letter 'R' and applied a 3 X 3 filter one time and 3 times. One must remember greater is the number of times a filter is applied on the same image, lessened will be the features. The pixelated image of the letter 'R' and the filter is below

         

Fig 1- Filter (Left) and the image (Right)

So when this filter is moved across the image we get feature extracted according to the filter like this below

Fig 2- Filtering applied on image(once and twice)

One can clearly see how the filter has faded the pixels that aren't in phase with the filter. The term 'phase' seems to fit here 😊. The darkened cells are ones in phase with the filter. Even if the reference image is a bit distorted or rotated or flipped or sheared the feature will still get picked up as it will be in phase with the filter.

The process is same for the filter for calculating the filtered value. It is the sum of the products of the value of 1s and 0s with the actual cell value. The sum is then divided by the total number of cells in the filter matrix (Here 9). The value gets faded if its closer to 0 and it gets darkened if it gets closer to 1. 

Rectified Linear Units ( RELU)

Now this filteres image is passed through rectification layer. We got the maximum value of cell in the below image is 0.33 and minimum value of cell as 0.11 so the middle value is 0.22. So the rule is stated as change the values of cells to 0 whose values are less than 0.22 (you can choose different values. Value closer to the maximum will be hard and fast process for the image and choosing a value closer to minimum will include some unnecessary features). So after passing the second image from Fig 2 above through the RELU layer we get an output like this

Fig 3- RELU layer applied to the filtered layer

After the application of RELU layer the image is passed through the pooling which I have already discussed in this post. So an overall process would be like this

1. Convolution (Filtered)
2. Relu activation
3. Pooling

The above process is done once or twice or can be even greater. 

What is a fully connected layer?

A fully connected layer is a single row of all the neurons connected together where every cell indicates the probability towards the actual answer. In the rectified image of 'R' darker cells have a greater value while the faded cells have a low value, thus one can conclude that the darkest cell has a greater probability to be in phase with that filter and cell having a faded value or having a lower value has quite less probability to be in phase with the filter. The above rectified image is the filtered output of a single filter and we have various filters that extract out the features so in each filter. 

Now every cell value is laid down in form of an array. This process is carried out for every filter. Now an average is taken among every dark cell. Similarly average is also taken for every faded cell. These average indicate the probability. 

The average of the darkest cells from each filter shows the probability of how close is our image (to 'R' here). On the contrary the average of all the lighter cells from each filter shows the probability of how far is our image (from 'R' here)

  

Fig 4- Fully Connected Array of all neurons (cells)

Like the above image when all arrays obtained from each filter is connected we get our fully connected layer. 

What is a dense layer?

A dense layer is just another name of fully connected layer. Similar operations take place in dense layer where every neuron is connected with each other. It is also called dense because it represents a dense connection of dense neurons. A dense layer has weights associated with every neuron pair and with unique values. Generally in Keras you may notice dense layer when working with CNN while in Tensorflow you may find fully_connected. So do not get confused with this. In keras we often use dense as Dense(10), Dense(1). Here every neuron among 10 neurons is connected with the last neuron and with unique weights. Since this is too dense and I don't think it's harmful to call it a dense layer. 😉

What is a dropout layer?

As per the name suggests, it dropouts or better say, it eliminates some of the activated cells (cells passed through activation layer). This has to be done in order to prevent over-fitting. An over-fit network will not be able to distinguish features from different image of the same object. The CNN has to work within a robust environment hence dropout becomes necessary. Dropout is basically chosen between 0.2 to 0.8. Dropout removes the  neurons randomly based on the parameters provided by the user like 0.4 etc.

Consider an example where you have 20 cookies and 8 of em are halftimes. An overfit network will only recognize the fully circle cookies. A fledgling CNN will pick up almost every cookie among the 8. With dropout some cookies which are either circular or halftimes will be dropped a.k.a removed randomly and retrained. This increases the quality of the network.

Cheers, See ya all soon. 

Convolutional Neural Networks III

In this post, I'll deal with dense layer, fully connected layer and backpropagation. If you have missed my previous post click here.
Before moving further, let us have a view on the filter's working on an image. I made a pixelated image of the letter 'R' and applied a 3 X 3 filter one time and 3 times. One must remember greater is the number of times a filter is applied on the same image, lessened will be the features. The pixelated image of the letter 'R' and the filter is below

         

Fig 1- Filter (Left) and the image (Right)

So when this filter is moved across the image we get feature extracted according to the filter like this below

Fig 2- Filtering applied on image(once and twice)

One can clearly see how the filter has faded the pixels that aren't in phase with the filter. The term 'phase' seems to fit here 😊. The darkened cells are ones in phase with the filter. Even if the reference image is a bit distorted or rotated or flipped or sheared the feature will still get picked up as it will be in phase with the filter.

The process is same for the filter for calculating the filtered value. It is the sum of the products of the value of 1s and 0s with the actual cell value. The sum is then divided by the total number of cells in the filter matrix (Here 9). The value gets faded if its closer to 0 and it gets darkened if it gets closer to 1. 

Rectified Linear Units ( RELU)

Now this filteres image is passed through rectification layer. We got the maximum value of cell in the below image is 0.33 and minimum value of cell as 0.11 so the middle value is 0.22. So the rule is stated as change the values of cells to 0 whose values are less than 0.22 (you can choose different values. Value closer to the maximum will be hard and fast process for the image and choosing a value closer to minimum will include some unnecessary features). So after passing the second image from Fig 2 above through the RELU layer we get an output like this

Fig 3- RELU layer applied to the filtered layer

After the application of RELU layer the image is passed through the pooling which I have already discussed in this post. So an overall process would be like this

1. Convolution (Filtered)
2. Relu activation
3. Pooling

The above process is done once or twice or can be even greater. 

What is a fully connected layer?

A fully connected layer is a single row of all the neurons connected together where every cell indicates the probability towards the actual answer. In the rectified image of 'R' darker cells have a greater value while the faded cells have a low value, thus one can conclude that the darkest cell has a greater probability to be in phase with that filter and cell having a faded value or having a lower value has quite less probability to be in phase with the filter. The above rectified image is the filtered output of a single filter and we have various filters that extract out the features so in each filter. 

Now every cell value is laid down in form of an array. This process is carried out for every filter. Now an average is taken among every dark cell. Similarly average is also taken for every faded cell. These average indicate the probability. 

The average of the darkest cells from each filter shows the probability of how close is our image (to 'R' here). On the contrary the average of all the lighter cells from each filter shows the probability of how far is our image (from 'R' here)

  

Fig 4- Fully Connected Array of all neurons (cells)

Like the above image when all arrays obtained from each filter is connected we get our fully connected layer. 

What is a dense layer?

A dense layer is just another name of fully connected layer. Similar operations take place in dense layer where every neuron is connected with each other. It is also called dense because it represents a dense connection of dense neurons. A dense layer has weights associated with every neuron pair and with unique values. Generally in Keras you may notice dense layer when working with CNN while in Tensorflow you may find fully_connected. So do not get confused with this. In keras we often use dense as Dense(10), Dense(1). Here every neuron among 10 neurons is connected with the last neuron and with unique weights. Since this is too dense and I don't think it's harmful to call it a dense layer. 😉

What is a dropout layer?

As per the name suggests, it dropouts or better say, it eliminates some of the activated cells (cells passed through activation layer). This has to be done in order to prevent over-fitting. An over-fit network will not be able to distinguish features from different image of the same object. The CNN has to work within a robust environment hence dropout becomes necessary. Dropout is basically chosen between 0.2 to 0.8. Dropout removes the  neurons randomly based on the parameters provided by the user like 0.4 etc.

Consider an example where you have 20 cookies and 8 of em are halftimes. An overfit network will only recognize the fully circle cookies. A fledgling CNN will pick up almost every cookie among the 8. With dropout some cookies which are either circular or halftimes will be dropped a.k.a removed randomly and retrained. This increases the quality of the network.

Cheers, See ya all soon. 

Convolutional Neural Networks III

In this post, I'll deal with dense layer, fully connected layer and backpropagation. If you have missed my previous post click here.
Before moving further, let us have a view on the filter's working on an image. I made a pixelated image of the letter 'R' and applied a 3 X 3 filter one time and 3 times. One must remember greater is the number of times a filter is applied on the same image, lessened will be the features. The pixelated image of the letter 'R' and the filter is below

         

Fig 1- Filter (Left) and the image (Right)

So when this filter is moved across the image we get feature extracted according to the filter like this below

Fig 2- Filtering applied on image(once and twice)

One can clearly see how the filter has faded the pixels that aren't in phase with the filter. The term 'phase' seems to fit here 😊. The darkened cells are ones in phase with the filter. Even if the reference image is a bit distorted or rotated or flipped or sheared the feature will still get picked up as it will be in phase with the filter.

The process is same for the filter for calculating the filtered value. It is the sum of the products of the value of 1s and 0s with the actual cell value. The sum is then divided by the total number of cells in the filter matrix (Here 9). The value gets faded if its closer to 0 and it gets darkened if it gets closer to 1. 

Rectified Linear Units ( RELU)

Now this filteres image is passed through rectification layer. We got the maximum value of cell in the below image is 0.33 and minimum value of cell as 0.11 so the middle value is 0.22. So the rule is stated as change the values of cells to 0 whose values are less than 0.22 (you can choose different values. Value closer to the maximum will be hard and fast process for the image and choosing a value closer to minimum will include some unnecessary features). So after passing the second image from Fig 2 above through the RELU layer we get an output like this

Fig 3- RELU layer applied to the filtered layer

After the application of RELU layer the image is passed through the pooling which I have already discussed in this post. So an overall process would be like this

1. Convolution (Filtered)
2. Relu activation
3. Pooling

The above process is done once or twice or can be even greater. 

What is a fully connected layer?

A fully connected layer is a single row of all the neurons connected together where every cell indicates the probability towards the actual answer. In the rectified image of 'R' darker cells have a greater value while the faded cells have a low value, thus one can conclude that the darkest cell has a greater probability to be in phase with that filter and cell having a faded value or having a lower value has quite less probability to be in phase with the filter. The above rectified image is the filtered output of a single filter and we have various filters that extract out the features so in each filter. 

Now every cell value is laid down in form of an array. This process is carried out for every filter. Now an average is taken among every dark cell. Similarly average is also taken for every faded cell. These average indicate the probability. 

The average of the darkest cells from each filter shows the probability of how close is our image (to 'R' here). On the contrary the average of all the lighter cells from each filter shows the probability of how far is our image (from 'R' here)

  

Fig 4- Fully Connected Array of all neurons (cells)

Like the above image when all arrays obtained from each filter is connected we get our fully connected layer. 

What is a dense layer?

A dense layer is just another name of fully connected layer. Similar operations take place in dense layer where every neuron is connected with each other. It is also called dense because it represents a dense connection of dense neurons. A dense layer has weights associated with every neuron pair and with unique values. Generally in Keras you may notice dense layer when working with CNN while in Tensorflow you may find fully_connected. So do not get confused with this. In keras we often use dense as Dense(10), Dense(1). Here every neuron among 10 neurons is connected with the last neuron and with unique weights. Since this is too dense and I don't think it's harmful to call it a dense layer. 😉

What is a dropout layer?

As per the name suggests, it dropouts or better say, it eliminates some of the activated cells (cells passed through activation layer). This has to be done in order to prevent over-fitting. An over-fit network will not be able to distinguish features from different image of the same object. The CNN has to work within a robust environment hence dropout becomes necessary. Dropout is basically chosen between 0.2 to 0.8. Dropout removes the  neurons randomly based on the parameters provided by the user like 0.4 etc.

Consider an example where you have 20 cookies and 8 of em are halftimes. An overfit network will only recognize the fully circle cookies. A fledgling CNN will pick up almost every cookie among the 8. With dropout some cookies which are either circular or halftimes will be dropped a.k.a removed randomly and retrained. This increases the quality of the network.

Cheers, See ya all soon. 

Convolutional Neural Networks II

This is my second post in CNN regarding max pooling, strides and padding.

In the previous post we extracted the features from the image of '3'. Although the dimensions of the image were 4 X 24 which is quite small. But what to do when the size of the image is big having a very high resolution. Greater is the size of image more are the parameters which the CNN has to extract from the image and hence it will take a longer time to identify the class of that image so how do we reduce the size of an image without losing any details from it and also maintaining the spatial arrangement. The only thing that comes at this position to solve this problem is Max pooling or Average pooling. Pooling is basically a technique by which you reduce the size of the image but also maintain the details and features within it in order to lessen the parameters. However, with pooling in the images might guesstimate updated started but still gets picked up by this CNN so that good news

Max Pooling

In Max pooling we choose the maximum value within a matrix. The size of the matrix could be 2 X 2 or 3 X 3 also. Here is an image showing the max pooling of the reference image of 3

Fig - Max Pooling of reference image of '3' with stride 1

As you can see with max pooling size of the resultant image gets reduced and also retaining the image information.

 Here is an explaining the process of max pooling.

I have used 2 X 2 size pooling that extracts the maximum value of cells. The size also gets reduced.

Initial Size of matrix 4 X 6. Pooled image is 3 X 5. Notice that the stride here is 1.

 What is Stride?

Stride is the number of steps that the pooling matrix will jump. Notice in the GIF image above, the matrix jumps only 1 step horizontally as well as vertically. 

Here is an example showing max pooling with stride 2

Fig - Max Pooling with stride 2

Another example with stride 2

Average Pooling

Average pooling does the same job like max pooling but instead of calculating the maximum value, it takes the average value within the matrix. 

Fig - Average Pooling with stride 1

Average Pooling retains a bit less information when compared with the max pooling. Average Pooling is somewhat less accurate than max pooling.

Padding

We noticed that with pooling our parameters has been reduced as well as the image size. It is important to maintain the spatial arrangement of the image. So to lessen the parameters and also maintaining the image size we use padding.

Padding is the technique in which we add a row and a column on zero around the image matrix. When this image is pooled it retains the information with the same size and fewer parameters.

Fig- Max Pooling with padding to retain the image size

Another example showing Average Pooling with padding and stride equal to 1

Fig - Padding with Average Pooling

✌ Image Size Retained!!! 😅

In the next post, I will deal with fully connected layer, dropout, and dense layer.

Convolutional Neural Networks II

This is my second post in CNN regarding max pooling, strides and padding.

In the previous post we extracted the features from the image of '3'. Although the dimensions of the image were 4 X 24 which is quite small. But what to do when the size of the image is big having a very high resolution. Greater is the size of image more are the parameters which the CNN has to extract from the image and hence it will take a longer time to identify the class of that image so how do we reduce the size of an image without losing any details from it and also maintaining the spatial arrangement. The only thing that comes at this position to solve this problem is Max pooling or Average pooling. Pooling is basically a technique by which you reduce the size of the image but also maintain the details and features within it in order to lessen the parameters. However, with pooling in the images might guesstimate updated started but still gets picked up by this CNN so that good news

Max Pooling

In Max pooling we choose the maximum value within a matrix. The size of the matrix could be 2 X 2 or 3 X 3 also. Here is an image showing the max pooling of the reference image of 3

Fig - Max Pooling of reference image of '3' with stride 1

As you can see with max pooling size of the resultant image gets reduced and also retaining the image information.

 Here is an explaining the process of max pooling.

I have used 2 X 2 size pooling that extracts the maximum value of cells. The size also gets reduced.

Initial Size of matrix 4 X 6. Pooled image is 3 X 5. Notice that the stride here is 1.

 What is Stride?

Stride is the number of steps that the pooling matrix will jump. Notice in the GIF image above, the matrix jumps only 1 step horizontally as well as vertically. 

Here is an example showing max pooling with stride 2

Fig - Max Pooling with stride 2

Another example with stride 2

Average Pooling

Average pooling does the same job like max pooling but instead of calculating the maximum value, it takes the average value within the matrix. 

Fig - Average Pooling with stride 1

Average Pooling retains a bit less information when compared with the max pooling. Average Pooling is somewhat less accurate than max pooling.

Padding

We noticed that with pooling our parameters has been reduced as well as the image size. It is important to maintain the spatial arrangement of the image. So to lessen the parameters and also maintaining the image size we use padding.

Padding is the technique in which we add a row and a column on zero around the image matrix. When this image is pooled it retains the information with the same size and fewer parameters.

Fig- Max Pooling with padding to retain the image size

Another example showing Average Pooling with padding and stride equal to 1

Fig - Padding with Average Pooling

✌ Image Size Retained!!! 😅

In the next post, I will deal with fully connected layer, dropout, and dense layer.

Convolutional Neural Networks I

Every time I imagine CNN something spills out from my brain and forces me to restart my learning. I guess it was because I wasn't doing practicals on CNN. Many guys basically look on CNN as a theory and that is where even I lost my way of learning. However, Coursera, Edx, and Udacity helped me to amplify my knowledge about CNN and those big words like pooling, strides etc. I am not a genius in CNN but yes I know something about CNN.


So What is CNN?

Convolution Neural Network is a branch of AI where features from images are gathered up and compared with the input data. It is basically a voting system where every pixel votes for the outcome and as usual the one with maximum votes win in this game and we get a result like this

So how does this happen is what comes in my mind first.

A CNN takes an image as input and converts them into arrays. Yes those numpy arrays are for the same !! Do remember that a CNN never matches the whole image instead it matches small features of images with the input image.
So let us pass an image of a number '3' to our CNN. The CNN will look at the image like this

The human eye can clearly see the digits 3 being displayed. However, it's not so easy for the machine to see the image. Now to extract out the details this CNN will multiply a weight Matrix to the above mattress that represents the number 3. After multiplying the weight Matrix the result will be like this

Fig - Reference Image of 3 to classify

Comparing both the images side by side you will recognize that the following image represents more features and detail than the previous image

 Every cell is multiplied with a weight which enhances the features of the image for better recognition. Now in my post of Image Classification, I used the syntax

 model.add(32, (3, 3), input_shape = (3, width, height))).

Here we have 32 filters of size 3 X 3. 

 *** To clear out the confusion I will say it again. The CNN has been trained on a variety of images of 3. It now knows the features so what CNN does is that it will grab a filter with "trained" details and will match "that with the validation data" i.e the above image of '3' is an image that we want to check. The network hasn't seen this image before. The filter contains the cell data from the trained image. ***

So here I have taken a 3 X 3 filter that knows the feature of '3' which will repartition the cell by a rule which state mark all cells 1 whose value is greater than 128 and 0 whose value is less than 129. Thus our filter belonging to the top left corner will represent like this

Now, this filter will move across every part of the reference image ('3') matrix to match and find the feature pixel by pixel.

So how it's done?

Each cell content from the filter will be multiplied with the similar cell in the image that we want to classify. 

After multiplication and addition, we get something like this

 Moving this filter at every step across the reference image we get the following information 

Voila !. The filter matches itself with every part of the reference image and outputs the probability of value in each cell. Do notice that the fourth column of reference 3 image has been neglected by the filter in the fourth column of the filtered image. It is because our filter is 3 X 3 thus square in shape and every 3 X 3 matrix in the reference image has to match this filter whereas the fourth column doesn't. Similarly, we place 32 filters across the reference image and extract out the features. Every filter will be from a trained image and it will move across the reference image and compare each pixel. The pixel which passes through the filter gets a higher probability thus, it gets darker. On the contrary, the pixel which cannot pass the filter is lightened. 

We can clearly see how the red circled pixels match the reference image and also the filter. 

After applying 3 more filters you will get this as the output

This methodology of stacking various filters containing a bunch of features in them, over an image is called a Convolution Layer. Thus each image is a stack of various filtered images. Moving the filter across the whole image, we get the information about the location of the pixels. 

Coming to the input shape of the image, the input shape is represented in Keras as (3, width, height) or by (width, height, 3). So to find the width just calculate the no. of pixels horizontally of the reference 3 image. You will get 4. Similarly calculate the no. of pixels vertically. You will get 24. Now each pixel is represented in form of RGB. Thus, it has 3 channels. So our input shape for the CNN will be (3, 4, 24) or (4, 24, 3). 

I will deal with Max Pooling, Padding and Strides in the next post.

Cheers. 🙂

Convolutional Neural Networks I

Every time I imagine CNN something spills out from my brain and forces me to restart my learning. I guess it was because I wasn't doing practicals on CNN. Many guys basically look on CNN as a theory and that is where even I lost my way of learning. However, Coursera, Edx, and Udacity helped me to amplify my knowledge about CNN and those big words like pooling, strides etc. I am not a genius in CNN but yes I know something about CNN.

So What is CNN?

Convolution Neural Network is a branch of AI where features from images are gathered up and compared with the input data. It is basically a voting system where every pixel votes for the outcome and as usual the one with maximum votes win in this game and we get a result like this

So how does this happen is what comes in my mind first.

A CNN takes an image as input and converts them into arrays. Yes those numpy arrays are for the same !! Do remember that a CNN never matches the whole image instead it matches small features of images with the input image.
So let us pass an image of a number '3' to our CNN. The CNN will look at the image like this

The human eye can clearly see the digits 3 being displayed. However, it's not so easy for the machine to see the image. Now to extract out the details this CNN will multiply a weight Matrix to the above mattress that represents the number 3. After multiplying the weight Matrix the result will be like this

Fig - Reference Image of 3 to classify

Comparing both the images side by side you will recognize that the following image represents more features and detail than the previous image

 Every cell is multiplied with a weight which enhances the features of the image for better recognition. Now in my post of Image Classification, I used the syntax

 model.add(32, (3, 3), input_shape = (3, width, height))).

Here we have 32 filters of size 3 X 3. 

 *** To clear out the confusion I will say it again. The CNN has been trained on a variety of images of 3. It now knows the features so what CNN does is that it will grab a filter with "trained" details and will match "that with the validation data" i.e the above image of '3' is an image that we want to check. The network hasn't seen this image before. The filter contains the cell data from the trained image. ***

So here I have taken a 3 X 3 filter that knows the feature of '3' which will repartition the cell by a rule which state mark all cells 1 whose value is greater than 128 and 0 whose value is less than 129. Thus our filter belonging to the top left corner will represent like this

Now, this filter will move across every part of the reference image ('3') matrix to match and find the feature pixel by pixel.

So how it's done?

Each cell content from the filter will be multiplied with the similar cell in the image that we want to classify. 

After multiplication and addition, we get something like this

 Moving this filter at every step across the reference image we get the following information 

Voila !. The filter matches itself with every part of the reference image and outputs the probability of value in each cell. Do notice that the fourth column of reference 3 image has been neglected by the filter in the fourth column of the filtered image. It is because our filter is 3 X 3 thus square in shape and every 3 X 3 matrix in the reference image has to match this filter whereas the fourth column doesn't. Similarly, we place 32 filters across the reference image and extract out the features. Every filter will be from a trained image and it will move across the reference image and compare each pixel. The pixel which passes through the filter gets a higher probability thus, it gets darker. On the contrary, the pixel which cannot pass the filter is lightened. 

We can clearly see how the red circled pixels match the reference image and also the filter. 

After applying 3 more filters you will get this as the output

This methodology of stacking various filters containing a bunch of features in them, over an image is called a Convolution Layer. Thus each image is a stack of various filtered images. Moving the filter across the whole image, we get the information about the location of the pixels. 

Coming to the input shape of the image, the input shape is represented in Keras as (3, width, height) or by (width, height, 3). So to find the width just calculate the no. of pixels horizontally of the reference 3 image. You will get 4. Similarly calculate the no. of pixels vertically. You will get 24. Now each pixel is represented in form of RGB. Thus, it has 3 channels. So our input shape for the CNN will be (3, 4, 24) or (4, 24, 3). 

I will deal with Max Pooling, Padding and Strides in the next post.

Cheers. 🙂