The following exercises hopefully illustrate some of the problems with objects in motion. The tracking of moving objects is a vital part of image analysis as well as computer vision, so the following simple exercise is meant to give a taste of that.
Use the experience that you’ve acquired in the previous exercise regarding edges, since the principle of matrix subtraction could also come in handy here

Problem 1:

Download the image sequence toyman into your working directory as well as the functions LoadSeq.m and ShowSeq.m . The sequence shows a static background into which an object is introduced. The task is to write a program that determines whether or not an object has entered the scene as well as tracks the motion of an intruding object.

Hint: You might want to use the center of the located object and use this as the reference point for the tracking of the object’s path through the scene.

The first image (toyman0000.jpg) contains the background.

Problem 2:

A very important concept for animals and robots is the calculation of time to contact or time to impact (TTC). That is, when moving towards an object how long will it take before hitting it. Visual motion alows us to compute the time for TTC without knowing the the real size or its velocity. We will simplify matters a little bit by assuming we move towards the object with constant velocity. Concider the following figure:

Denote L the real size of the bar, with V its constant velocity and f the focal length of the camera (eye). The origin of the reference frame is the projection center. If the position of the bar on the optical axis is D(0)=D_0 at time t=0, its position at a later time t will be D=D_0-Vt. Note that L,V,f,D_0 and the choice of time origin are all unknown, but that TTC can be written as TTC = D/V.
Let l(t) = f*L/D be the apparent size of the bar at time in the image.

Show that TTC = l(t)/l'(t), where l'(t) = dl(t)/dt, the differential of l w.r.t. t.

The important thing to notice here is that the apparent size of the bar, l(t), and its time derivative, l'(t), are measured from the images, and allow us to compute TTC without any additional 3D information, like the size of the bar and its velocity.