합성곱

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  • In this part, the network will perform a series of convolutions and pooling operations during which the features are detected.[1]
  • We execute a convolution by sliding the filter over the input.[1]
  • We perfom numerous convolutions on our input, where each operation uses a different filter.[1]
  • In the case of a Convolutional Neural Network, the output of the convolution will be passed through the activation function.[1]
  • I found it hard to follow the convolutions of the book's plot.[2]
  • Each convolution captured different essential features of the image, such as edges.[2]
  • Even without that doomsday outcome, rewriting contracts that refer to Libor is fraught with byzantine convolutions.[2]
  • If we just wanted to understand convolutional neural networks, it might suffice to roughly understand convolutions.[3]
  • The advantage of this approach is that it allows us to visualize the evaluation of a convolution at a value \(c\) in a single picture.[3]
  • By shifting the bottom half around, we can evaluate the convolution at other values of \(c\).[3]
  • Convolutions are sometimes used in audio manipulation.[3]
  • And in this video, I'm not going to dive into the intuition of the convolution, because there's a lot of different ways you can look at it.[4]
  • well, actually, before I even go to the convolution theorem, let me define what a convolution is.[4]
  • So the convolution of f with g, and this is going to be a function of t, it equals this.[4]
  • and it seems a little bit bizarre, but you really can take the convolutions of actual functions and get an actual answer.[4]
  • Convolution is important because it relates the three signals of interest: the input signal, the output signal, and the impulse response.[5]
  • This chapter presents convolution from two different viewpoints, called the input side algorithm and the output side algorithm.[5]
  • Convolution provides the mathematical framework for DSP; there is nothing more important in this book.[5]
  • Convolution in the frequency domain can be faster than in the time domain by using the Fast Fourier Transform (FFT) algorithm.[6]
  • Figure 2: Calculating convolution by sliding image patches over the entire image.[6]
  • Convolution can be transformed to cross-correlation by reversing the kernel (upside-down image).[6]
  • The idea of a strided convolution is that we only process slides a fixed distance apart, and skip the ones in the middle.[7]
  • if you’re familiar with dilated convolutions, note that the above is not a dilated convolution.[7]
  • Convolution describes the output (in terms of the input) of an important class of operations known as linear time-invariant (LTI).[8]
  • See LTI system theory for a derivation of convolution as the result of LTI constraints.[8]
  • See Convolution theorem for a derivation of that property of convolution.[8]
  • {\displaystyle g(-\tau ).} The resulting waveform (not shown here) is the convolution of functions f and g .[8]
  • To understand better the concept of convolution let's do the example above by hand.[9]
  • Those results are called 'valid' convolutions.[9]
  • Usually deep learning libraries do the convolution as one matrix multiplication, using the im2col/col2im method.[9]
  • In orange, the blocks are composed of 2 stacked 3x3 convolutions.[10]
  • In blue, the blocks are composed of a single 5x5 convolution.[10]
  • Convolutions layers are lighter than fully connected ones.[10]
  • 1x1 convolution is a solution to compensate for this.[10]
  • If f is defined on a spatial variable like x rather than a time variable like t, we call the operation spatial convolution.[11]
  • Convolution lies at the heart of any physical device or computational procedure that performs smoothing or sharpening.[11]
  • To see this alternative way of understanding convolution in action, click on "animate", then "big rect".[11]
  • As you enter each value, the convolution is recomputed.[11]
  • method str {‘auto’, ‘direct’, ‘fft’}, optional A string indicating which method to use to calculate the convolution.[12]
  • direct The convolution is determined directly from sums, the definition of convolution.[12]
  • The Fourier Transform is used to perform the convolution by calling fftconvolve .[12]
  • A convolution is the simple application of a filter to an input that results in an activation.[13]
  • Technically, the convolution as described in the use of convolutional neural networks is actually a “cross-correlation”.[13]
  • What we are going to do now seems to be a simple change of symbols, but will actually give us some profound insight into convolution itself.[14]
  • However, this also happens to be a realization of the formula for convolution presented at the top of this post![14]
  • These two examples give us a bit of a feel for what convolution is.[14]
  • Convolution involving one-dimensional signals is referred to as 1D convolution or just convolution.[15]
  • Convolution results obtained for the output pixels at location (1,1) and (1,2).[15]
  • Convolution results obtained for the output pixels at location (1,4) and (1,7).[15]
  • Convolution results obtained for the output pixels at location (2,1) and (2,6).[15]
  • As you don’t know what convolution is, let’s put that word aside.[16]
  • Convolution allows you to determine the response to more complex inputs like the one shown below.[17]
  • In fact, you can use convolution to find the output for any input, if you know the impulse response.[17]
  • There are several ways to understand how convolution works.[17]
  • First convolution will be developed in an approximate form as the sum of impulse responses.[17]
  • The response of many physical systems can be represented mathematically by a convolution.[18]
  • An example small image (left) and kernel (right) to illustrate convolution.[19]
  • Convolution can be used to implement many different operators, particularly spatial filters and feature detectors.[19]
  • Convolution is a mathematical concept that implies the sum of two functions.[20]
  • Convolutions are applied in image processing for CTs and MRIs.[20]
  • Convolutions are used on the matrices of images in convolutional neural networks often facilitating edge detection in objects.[20]
  • Illustration of the convolution of a rectangular pulse and the impulse response of an ``averaging filter ( ). .[21]
  • The zero-padding serves to simulate acyclic convolution using circular convolution .[21]
  • To capture the cyclic nature of the convolution,andcan be imagined plotted on a. Thus, Fig.[21]
  • This other method is known as convolution.[22]
  • If we view all the data points outside the input range as zeros, then the convolution is said to be a linear convolution.[23]
  • It was convolution and convolutional nets that catapulted deep learning to the forefront of almost any machine learning task there is.[24]
  • You can imagine convolution as the mixing of information.[24]
  • When we apply convolution to images, we apply it in two dimensions — that is the width and height of the image.[24]
  • We now perform the actual intertwining of these two pieces of information through convolution.[24]
  • Assume the size of the input signal is ( ) and the size of is (usually an odd number), then the size of the resulting convolution is .[25]
  • Now, there's a lot about convolution that we'll want to talk about.[26]
  • There are properties of convolution which tell us about properties of linear time-invariant systems.[26]
  • Now let's shift back to the left until n is negative, and then we'll begin the convolution.[26]
  • Now let's carry out the convolution this time with an input which is a rectangular pulse instead of a step input.[26]
  • The default is to move filters by 1 pixel at a time when performing convolutions; this is called stride and it can be altered by the user.[27]
  • A convolution is an integral that expresses the amount of overlap of one function as it is shifted over another function .[28]
  • Abstractly, a convolution is defined as a product of functions and that are objects in the algebra of Schwartz functions in .[28]
  • The animations above graphically illustrate the convolution of two boxcar functions (left) and two Gaussians (right).[28]
  • The gray region indicates the product as a function of , so its area as a function of is precisely the convolution.[28]

소스

  1. ↑ 1.0 1.1 1.2 1.3 An intuitive guide to Convolutional Neural Networks
  2. ↑ 2.0 2.1 2.2 Definition of Convolution by Merriam-Webster
  3. ↑ 3.0 3.1 3.2 3.3 Understanding Convolutions
  4. ↑ 4.0 4.1 4.2 4.3 Introduction to the convolution (video)
  5. ↑ 5.0 5.1 5.2 Convolution
  6. ↑ 6.0 6.1 6.2 Convolution
  7. ↑ 7.0 7.1 Intuitively Understanding Convolutions for Deep Learning
  8. ↑ 8.0 8.1 8.2 8.3 Convolution
  9. ↑ 9.0 9.1 9.2 Convolution
  10. ↑ 10.0 10.1 10.2 10.3 About Convolutional Layer and Convolution Kernel
  11. ↑ 11.0 11.1 11.2 11.3 Spatial convolution
  12. ↑ 12.0 12.1 12.2 scipy.signal.convolve — SciPy v1.5.4 Reference Guide
  13. ↑ 13.0 13.1 How Do Convolutional Layers Work in Deep Learning Neural Networks?
  14. ↑ 14.0 14.1 14.2 But Why? Intuitive Mathematics
  15. ↑ 15.0 15.1 15.2 15.3 2D Convolution in Image Processing
  16. ↑ Article 1: Understanding the Convolution function and CNN.
  17. ↑ 17.0 17.1 17.2 17.3 The Convolution Integral
  18. ↑ Oilfield Glossary
  19. ↑ 19.0 19.1 Convolution
  20. ↑ 20.0 20.1 20.2 Radiology Reference Article
  21. ↑ 21.0 21.1 21.2 Mathematics of the DFT
  22. ↑ Concept of Convolution
  23. ↑ Help Online
  24. ↑ 24.0 24.1 24.2 24.3 Understanding Convolution in Deep Learning — Tim Dettmers
  25. ↑ convolution
  26. ↑ 26.0 26.1 26.2 26.3 Lecture 4: Convolution
  27. ↑ 2D Convolution block
  28. ↑ 28.0 28.1 28.2 28.3 Convolution -- from Wolfram MathWorld

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