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In: Natural Language Processing

‘Self-information In information theory, a self-information is the information value of an event.’

Convolution Kernels: An Authoritative, Informative and Persuasive Guide

Convolution kernels are a matrix used in image processing to alter an image [1]. In image processing, a kernel, convolution matrix, or mask is a small matrix used for blurring, sharpening, embossing, edge detection, and more [1]. In this article, we will explore the basics of convolution kernels, their origin, and how to use them to optimize your image processing [2].

What is a Convolution Kernel?

A convolution kernel is a matrix used in image processing to alter an image [1]. In image processing, a kernel, convolution matrix, or mask is a small matrix used for blurring, sharpening, embossing, edge detection, and more [1].

2D Convolution

2D convolution is the process of adding each element of the image to its local neighbors, weighted by the kernel [1]. The values of a given pixel in the output image are calculated by multiplying each kernel value by the corresponding input image pixel values [1].

Kernel Crop

Any pixel in the kernel that extends past the input image isn’t used and the normalizing is adjusted to compensate [1]. This will ensure the average pixel in the modified image is as bright as the average pixel in the original image [1].

Origin

The origin is the position of the kernel which is above (conceptually) the current output pixel [1]. Every element of the filter kernel is considered by − a ≤ d x ≤ a {\displaystyle -a\leq dx\leq a} and − b ≤ d y ≤ b {\displaystyle -b\leq dy\leq b} [1].

Optimisation

Fast convolution algorithms include: separable convolution and Separable convolution. 2D convolution with an M × N kernel requires M × N multiplications for each sample (pixel) [2]. Each kernel element should be multiplied with the pixel value it overlaps with and all of the obtained values should be summed [1].

Types of Convolution Kernels

There are several types of convolution kernels, which are used to extract different types of features from an image. For example, the kernel used above is useful for sharpening the image [2]. Some of the more popular convolution kernels include Sobel, Prewitt, Roberts, and Canny.

Understanding Convolutional Filters and Convolutional Kernels

A filter is a concatenation of multiple kernels, each kernel assigned to a particular channel of the input [2]. A kernel is, as described earlier, a matrix of weights which are multiplied with the input to extract relevant features [2]. For example, in 2D convolutions, the kernel matrix is a 2D matrix [2]. The dimensions of the kernel matrix is how the convolution gets it’s name [2].

Instead of using manually made kernels for feature extraction, through Deep CNNs we can learn these kernel values which can extract latent features [2].

Information Theory in Deep Neural Network

Information Theory in Convolution Kernels is an important aspect of understanding how convolutional filters and kernels work [2]. Almost any serious practitioner of CNN must already have a solid understanding of what convolution kernels do, including stride and feature extraction, at high-level understanding [2].

Self-information measures the information value of a single discrete event, while Entropy goes further to capture the information value of a random variable, whether it is discrete or continuous. Then we define the information value I of event x as follow: The meaning of value I is simply to measure how much / how valuable knowledge of event x happening is. The smaller the chance of happening p is, the higher the information value.

In the end, what in CNNs are just numbers, numbers, and numbers. This property is particularly important as it is directly related to the information theory in Computer Vision at a level as low as pixel level.

Conclusion

In this article, we have discussed the basics of convolution kernels, their origin, and how to use them to optimize your image processing [2]. We have also looked at the different types of convolution kernels and how they can be used to extract features from an image [2]. Finally, we have explored the Information Theory of Convolution Kernels, which is an important aspect of understanding how convolutional filters and kernels work [2].

References:-

  1. https://en.wikipedia.org/wiki/Kernel_(image_processing)
  2. https://towardsdatascience.com/types-of-convolution-kernels-simplified-f040cb307c37
  3. https://programmathically.com/understanding-convolutional-filters-and-convolutional-kernels/

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