Revision 9fa963924e8e46e33af266e41e39e85d1e473e2f (click the page title to view the current version)


Changes from 9fa963924e8e46e33af266e41e39e85d1e473e2f to current

title: Edge Detection
categories: session

**Date** 29 September 2021
**Date** 13 or 14 October

**Briefing** Status on the Tracker Project.  
If we need the Thursday session for this only, the Edge Detction will be postponed
to the Friday.

**Briefing** [Edge Lecture]()

# Exercise
**Reading** Ma (2004) Ch 4.4;
Tutorials on OpenCV:
[Canny Edge Detection](;
[Hough Circle Transform](

Implement a prototype able to track a simple object in a video scene.
You have full freedom to do this as you please, but bear in mind
that we only ask for a *prototype*.  The goal is to learn constituent
techniques, not to make a full solution for production.
We look at
[Hough Circle Transform](
as an example of reading mathematical texts.

1.  You can set up your own scene, recording your own video, with a
    characteristic, brightly coloured object moving through the scene.
    E.g. a bright, red ball rolling on the floor.
2.  Start with the feature detector.  Make sure that it works.
3.  Can you use the feature detector to detect your particular object in
    a still image?
4.  Visualise the detected object, by drawing a frame around it in the image.
5.  Introduce tracking only when you have a working prototype for still
# Exercises

## Modularisation
## Python API

There are several subproblems which can most easily be handled separately.  Try to identify such problem, solve them one by one, and test the solutions.  The ones listed below are just examples.
This is based on Ma (2004) Exercise 4.9, which is written for Matlab.

### Time derivative
### The Canny 

One key challenge is to calculate the time derivative $I_t$.
1.  Find a test image.
2.  Test the `Canny` edge detector in OpenCV.
    See the [tutorial](
    for an example. 
    What kind of data does it generate?  What do the data look like?
3.  Experiment with different thresholds and different window sizes
    See the [docs]( for overview of the parameters
    for `Canny`.

1. The easiest approach will be to take each pixel, and make a one-dimensional signal by taking the same pixel from every frame, and apply a (1D) Sobel filter (or other derivation filter). From these per-pixel $I_t$ signals, a frame (matrix) $I_t(t)$ for each time step can be reconstructed.
2. It is possible to process all the pixel signals in parallel using matrix operations in numpy.  This requires a little more abstract thought, but once mastered, the code is simpler and more efficient.
It is not difficult to implement your own Canny edge detector.
The exercise would be very similar to the Harris corner detector,
and add little new.

# Debrief
### Connected Components

The edge detector gives a binary image.  How can you find collections
of pixels forming edges?

You can either,

1. implement your own connected components function, using the ideas
   from the [briefing](Edge Lecture), or
2. test the `ConnectedComponents` function in OpenCV.

Visualise the components you find, for instance by using different
colours  Do they correspond to the objects *you* see in the image?

### Line fitting

If you do not have time to try both approaches, that's all right,
but you should at least try one.  Feel free to choose,

#### Basic approach

1.  Implement a simple line fitter using the ideas from the
    [briefing](Edge Lecture).
2.  Can you identify straight lines among the components?
3.  Calculate the angle $\theta$ and the distance $\rho$ from the
    origin for each component.

#### Hough transform

1.  Run through the tutorial to [Hough Circle Transform](
2.  Tweak the code to print out the co-ordinates of the lines detected, that is $\theta$ and $\rho$
3.  Write a function to find the lines intersect the $x$- and $y$-axes, and list this information too.
4.  Can you see (easily) where each edge ought to be in the visual image?
5.  Write a routine, using OpenCV or otherwise, to plot the lines from the Hough transform on top of
    the image from the Canny detector.  Do they match?  It is probably best if you use different colours.
    - You can make an RGB image and copy the result from Canny into one colour channel, and write the edges
      in a different one.

## Project

1.  Can you use edge detection in your tracker project?
2.  Is it possible to match the edges to the object you want to track?
3.  Can the multiple connected components be used to give an idea about
    different objects in the scene?

Use the rest of the time to improve the tracker.