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Select Additive Learning: Representation Learning for Small Datasets & Identity Bias Mitigation

Summary Poster: Select Additive Learning for Representation Learning in Small Datasets & Identity Bias Mitigation

Overview

1. Convolution and its usage

2. How to contruct edge dectors and averaging filters using convolution

1. Convolution

- Convolutions are a fundamental and powerful operation in signal/image processing.

- Some form is used in almost every computer vision application.

- Convolution has been hypothesised as a good model of low-level biological visual processing.

- Convolutional Neural Networks (CNNs) are a big part of the recen wave of deep learning, and the convolutional part has enabled impressive results on a variety of tasks.

1) Usage

Simple hand-defined convolutional filters can be used to accomplish:

- Edge detection

- Image denoising

- Edge enhancement/sharpening

- Object localisation

2) What is it?

- A convolution can be thought of as concurrently applying a local function to parts of the image.

- Unlike the pixelwise operations we saw before, this looks at a group of pixels in a neighbourhood.

- The manner in which this function is applied to the image is sometimes called a sliding window, as the function only sees a small portion of the image at a time.

- Convolutions are trivially parallellised, which is one reason for their continuing success.

This little array is known by various names:

- Mask

- Weight array

- Operator

- Kernel filter

To use it, we must flip it over to make a template:

3) Code

A = [19 24 22 10 3 20 22 4 19 14]

convolve with template [-1, 1]

# Note that the template is flipped

scipy.signal.convolve(A, [1, -1], mode='valid')

Output:

([ 5, -2, -12, -7, 17, 2, -18, 15, -5])

4) Horizontal Differencing

- [-1, +1] gives a first order apporximation of the derivative (rate of change) of the image (in the x-direction) using finite differences.

- i.e. It measures the strength of vertical edges.

- Mathematically, it is approximating the derivative at the point in-between the 2 pixels.

5) 2D Templates

- Templates are not restricted to being 1-dimensional, they can be 2D as well.

- All this menas is that our convolution function operates oen neighbours in both x and y.

(1) Sobel Filter in x-axis

- Provides a mechanism for reducing noise:

a) In python

from scipy.signal import convolve2d

sobel_x_kernel = [[-1, 0, +1], [-2, 0, +2], [-1, 0, +1]]

sobel_x_img = convolve2d(img_gray, sobel_x_kernel, 'same')

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