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To conclude, CNNs are very useful to process images and extract features from them because they use convolution operations (and downsampling and upsampling operations). They can be used for image (or object) classification, object detection (i.e. object localization with a bounding box + object classification), image segmentation (including semantic segmentation and instance segmentation), and possibly many other tasks where you need to learn a function that takes as input images and needs to extract information from those images to get someone high-level (but also low-level) output (e.g. the name of the object in the image), given some training data.

To conclude, CNNs are very useful to process images and extract features from them because they use convolution operations (and downsampling and upsampling operations). They can be used for image (or object) classification, object detection (i.e. object localization with a bounding box + object classification), image segmentation (including semantic segmentation and instance segmentation), and possibly many other tasks where you need to learn a function that takes as input images and needs to extract information from those images to get someone high-level (but also low-level) output (e.g. the name of the object in the image), given some training data.

A convolutional neural network (CNN) is a neural network that performs the convolution (or cross-correlation) operation typically followed by some downsampling (aka pooling) operations.

In the context of CNNs, $f$ is the image (in the case of the first layer of the CNN) or a so-called feature map (in the case of hidden layers), $h$ is the kernel (aka filter) and $g$ is also a feature map. (In this answer, I explain these concepts, including how an image can be viewed as a function, more in detail, so I suggest that you read it).

Essentially, the convolution is a series of dot products between the kernel and different patches (or parts) of the image. The convolution can even be represented as matrix multiplication, so the name convolution shouldn't scare you anymore, if you are familiar with dot products and matrix multiplications.

As opposed to many operations in image processing where the kernels are typically fixed, in the context of CNNs, the kernels are learnable parameters, i.e. they change depending on the loss function, so they are supposed to represent functions that when convolved with their respective input functions are useful to extract meaningful information (i.e. features) to solve the task the CNN is being trained to solve. For this reason, the convolution is often thought of as an operation that extracts features from images. In fact, the output of the convolution, in the context of CNNs, is often called feature map.

To conclude, CNNs are very useful to process images and extract features from them because they use convolution operations (and downsampling and upsampling operations). They can be used for image (or object) classification, object detection (i.e. object localization with a bounding box + object classification), image segmentation (including semantic segmentation and instance segmentation), and possibly many other tasks where you need to learn a function that takes as input images and needs to extract information from those images to get someone high-level (but also low-level) output (e.g. the name of the object in the image).

A convolutional neural network (CNN) is a neural network that performs the convolution (or cross-correlation) operation typically followed by some downsampling (aka pooling) operations.

In the context of CNNs, $f$ is the image (in the case of the first layer of the CNN) or a so-called feature map (in the case of hidden layers), $h$ is the kernel (aka filter) and $g$ is also a feature map. (In this answer, I explain these concepts, including how an image can be viewed as a function, more in detail, so I suggest that you read it).

Essentially, the convolution is a series of dot products between the kernel and different patches (or parts) of the image. The convolution can even be represented as matrix multiplication, so the name convolution shouldn't scare you anymore, if you are familiar with dot products and matrix multiplications.

As opposed to many operations in image processing where the kernels are typically fixed, in the context of CNNs, the kernels are learnable parameters, i.e. they change depending on the loss function, so they are supposed to represent functions that when convolved with their respective input functions are useful to extract meaningful information (i.e. features) to solve the task the CNN is being trained to solve. For this reason, the convolution is often thought of as an operation that extracts features from images. In fact, the output of the convolution, in the context of CNNs, is often called feature map. Moreover, a CNN is typically thought of as a data-driven feature extractor for the same reason.

To conclude, CNNs are very useful to process images and extract features from them because they use convolution operations (and downsampling and upsampling operations). They can be used for image (or object) classification, object detection (i.e. object localization with a bounding box + object classification), image segmentation (including semantic segmentation and instance segmentation), and possibly many other tasks where you need to learn a function that takes as input images and needs to extract information from those images to get someone high-level (but also low-level) output (e.g. the name of the object in the image), given some training data.

The convolution operation comes from the mathematical equivalent and homonymous operation, which is an operation that takes as inputs two functions $f$ and $h$ and produces another function $g$ as output, which is often denoted as $f \circledast h = g$, where $\circledast$ is the convolution operation (or operator).

In the case of CNNs, $f$ is the image (in the case of the first layer of the CNN) or a so-called feature map (in the case of hidden layers), $h$ is the kernel (aka filter) and $g$ is also a feature map. (In this answer, I explain these concepts, including how an image can be viewed as a function, more in detail, so I suggest that you read it).

The convolution operation comes from the mathematical equivalent operation, which is an operation that takes as inputs two functions $f$ and $h$ and produces another function $g$ as output, which is often denoted as $f \circledast h = g$, where $\circledast$ is the convolution operation (or operator).

In the context of CNNs, $f$ is the image (in the case of the first layer of the CNN) or a so-called feature map (in the case of hidden layers), $h$ is the kernel (aka filter) and $g$ is also a feature map. (In this answer, I explain these concepts, including how an image can be viewed as a function, more in detail, so I suggest that you read it).