Hello everyone and welcome back to computer vision lecture series. In this lecture we

are going to talk about corner detection. We will start from feature points and then

we move on to see how corner is a very good example of a feature point. So let us go ahead.

We are going to discuss different properties of good interest points and Harris corner

corners. We will also look into the mathematical formulation of how Harris corner works and

we are also going to look into invariances and co-variance of Harris corners. It is important

because once you know these features of Harris corners you would know or you will be in a

better position to apply Harris corner detection in a given application.

So we started with filtering and we moved on to edges and corners are natural flow to

our low to high level computer vision tasks. So corners are more distinctive features than

edges because edges tend to change in one direction, tend to remain constant in one

direction whereas corners have lesser degrees of freedom and therefore they bring out distinctive

property or they have a distinctive characteristic that they are more unique as compared to edges.

So feature points are also called, corner is one of the feature points, it is also called

interest points, key points, basically these are all considered as local features.

So what are the main components of local features? We should find a distinctive set of key points.

The first step is detection of these features and then how to describe them in a vector

form, in a compact vector form. So once you detect the features you need to know how to

represent them into either a matrix or a vector form in your machine or in the algorithm.

This is one example given here and then at the end you match those features across images

to find different correspondences. What could be the applications of this feature

point detection? So when you think about it in image alignment, for example, a panorama

stretching is a direct application of feature points because in panorama the successive

images are changing slightly and you want to match a lot of features which are common

in this slightly changing images and you want to align them and that's where feature descriptors

or feature points come into play. In panorama you also need some blending techniques

because there is some changing brightness. So you know your feature points should be

robust to noise, specifically photometric transformations like illumination in this

case of panorama to be robust. Your feature point detector should be robust to this thing

so that you are able to stitch well. 3D reconstruction obviously you need multiple views of the same

image and you need so feature points is a direct application of 3D reconstruction.

In motion tracking, for example, robots when they are navigating in the real world, the

camera is moving along with the robot and it's mapping the scene continuously and in

order to navigate you need to track or keep attention towards the specific objects in

your neighborhood and in order to keep track in successive frames because you are using

a video camera you need to detect these feature points to be able to reconstruct a 3D virtual

world and therefore it becomes easier to navigate. Same goes for indexing and database retrieval.

For example, in Google Image Search you want a particular, let's say you want to look for

a red flower or something like that and redness is a feature that you are looking for and

when you put in the search it becomes a property of image retrieval. Another example is object

recognition where you can have a vector or matrix with a collection of gradients or a

histogram of gradients and then you use these features to recognize objects across different

images. This is an example for feature point matching across different views. Basically

you find that these two stop signs are similar in some sense that they are both red in color

with stop written in white and when you want to match or you want to find an equivalent

feature representing this circular patch you are able to find it here although it's a bit

rotated and a bit more resolved. However, feature point detection helps in finding similar features

across different or similar looking images as well. A basic template matching of this

feature will not give a good result because you need robust feature alignment across different

views. So as we discussed earlier when we were talking about correlation that one of