CSC 578 Neural Networks and Deep Learning

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Presentation transcript:

CSC 578 Neural Networks and Deep Learning 6-2. Convolutional Neural Networks (2) Noriko Tomuro

What is an Image?

Image An image is matrix that specifies the color of various pixels in terms of the amount of red, green and blue components. Every pixel is assigned an RGB value, each component being a value between 0 to 255. These components are mixed together to form a unique color value. E.g. Blue is rgb(0,0,255) and Black is rgb(0,0,0)

Displaying an Image Any display of an image consists of an arrangement of red, green, and blue dots. A set of one dot of each color form a pixel

What is a Kernel Filter ?

Kernel A kernel is a square matrix that specifies spatial weights of various pixels in an image. Different image processing techniques use different kernels. 1 4 7 16 26 41 1 2 1 -1 -2 3*3 Mean Kernel 3*3 Sobel Kernel 5*5 Gaussian Kernel

What is Convolution? BIG CONCEPT

Convolution Convolution of a matrix involves laying a matrix over another and then calculating the weighted sum of all pixel values.

Image Processing

How to process an image? Kernel Input Image Output Image Convolution

RGB to Grayscale Edge detection -1 1 -2 2

Convolution Neural Network

Convolution Layer 32*32*3 image -> Preserve spatial structure

Convolution Layer

Convolution Layer

Convolution Layer

Convolution Layer Consider a second, green filter

Convolution Layer E.g. if we had 6 5*5 filters, we’ll get 6 separate activation maps We stack themup to get a “new image” of size 28*28*6

Convolution Layer ConvNet is a sequence of Convolution Layers, interspersed with activation functions

Convolution Layer ConvNet is a sequence of Convolution Layers, interspersed with activation functions

Fully Connected Layer 32*32*3 image -> stretch to 3072*1

A closer look at spatial dimension (1)

A closer look at spatial dimension

A closer look at spatial dimension (2)

A closer look at spatial dimension (3)

Constraints on Output Size For the input volume size (W), the receptive field size of the Conv Layer neurons (F), the stride with which they are applied (S), and the amount of zero padding used (P) on the border, the size of the output is (W−F+2P)/S+1 Examples: For a 7x7 input and a 3x3 filter with stride 1 and pad 0, we would get a 5x5 output. With the same input and filter but with stride 2, we would get a 3x3 output.

Use of zero-padding To avoid shrinking output To throw away information from edges Setting zero padding to be P=(F−1)/2 when the stride S=1 ensures that the input volume and output volume will have the same size spatially.

Exercise (1)

Exercise (2)

Reference: http://cs231n. github Reference: http://cs231n.github.io/convolutional-networks/ for explanation and animation on the DEPTH of input volume.

CAUTION: E.g. 32*32 input convolved repeatedly with 5*5 filters shrinks volumes spatially. BUT shrinking too fast is not good, because feature maps lose information as they get deeper.

Pooling Layer Makes the representations smaller and more manageable

Max Pooling

Intervening Activation Layer

CNN Architectures

AlexNet

AlexNet

AlexNet

AlexNet

AlexNet

AlexNet

AlexNet

VGGNet

GoogleNet