Programming Computer Vision with Python

Chapter 2. Local Image Descriptors

This chapter is about finding corresponding points and regions between images. Two different types of local descriptors are introduced with methods for matching these between images. These local features will be used in many different contexts throughout this book and are an important building block in many applications, such as creating panoramas, augmented reality, and computing 3D reconstructions.

2.1 Harris Corner Detector

The Harris corner detection algorithm (or sometimes the Harris & Stephens corner detector) is one of the simplest corner indicators available. The general idea is to locate interest points where the surrounding neighborhood shows edges in more than one direction; these are then image corners.

We define a matrix M_I = M_I(x), on the points x in the image domain, as the positive semi-definite, symmetric matrix

Equation 2-1. 

whereas before ∇I is the image gradient containing the derivatives I_x and I_y (we defined the derivatives and the gradient in Image Derivatives). Because of this construction, M_I has rank one with eigenvalues λ₁ = |∇I|² and λ₂ = 0. We now have one matrix for each pixel in the image.

Let W be a weight matrix (typically a Gaussian filter G_σ). The component-wise convolution

Equation 2-2. 

gives a local averaging of M_I over ...