Discussion

Frame differencing is a simple direct method to detect motion as a change between successive frames from video data. However, it suffers from the ex- traction of unwanted regions from the background. This is due to the change in illumination and the moving of non-interesting objects in the background such as trees, clouds and so on.

The methods based on the optical flow give not only information about the sizes and locations of the moving objects in the scene, but also informa- tion about the direction and velocity. The movements that take place in the background or by objects that are not interesting for the monitoring process can easily neglected by the use of a simple velocity threshold.

However, these methods face two main problems in addition to the com- putation complexity. First, if the images are in low overall contrast because of a bad ambient conditions, then the number of significant vectors will de- crease, which inhibits the grouping of vectors in blocks and hence inhibits a meaningful segmentation result. Second, a long observation time is required to produce a reliable optical flow field for the active traffic area.

The methods based on background estimation and subtraction are de- pendent on the update parameters and the initialisation of the background. Small values of the updating parameters imply an integration of the moving objects that are not active for a while as a part of the background. On the other hand, if the values of the updating parameters are too high, the meth- ods need a relative long interval for a stable estimation of the background and they fail to adapt to the changes in the illumination. The update pa- rameters and the initial background need to be set before the running of the methods by an expert. They have to be set carefully and for every new scene. The application investigated in the case of video segmentation is moving object detection for traffic monitoring using a stationary camera. For this purpose, a method that is based on the frame differencing may lead to robust results if not only the temporal changes are considered but also the spatial changes, and if the active area from the scene are processed differentially from the background. The method must be computationally efficient and must offer segmentation with simple operations that can be easily imple- mented in hardware.

The use of the 3D wavelet transform meets these needs. It is able to anal- yse the input data spatially as well as temporally. Moreover it is hardware friendly, since it can be implemented by simple arithmetic operations.

Chapter 3

The Multiresolution Image

Analysis

The subject of multiresolution analysis is to be found usually as a part of the fundamentals of the wavelet analysis. However, the term Multiresolution is much older than the wavelet transform. Some references go back to the end of 1970s. One of the first workshops titled “Multiresolution Image Processing and Analysis” was held in Leesburg, VA, USA on July 1982 [Ros84b].

In this chapter the multiresolution analysis is introduced as an indepen- dent concept instead of being a part of the wavelets. Starting with the formal definition, examples from early and recent work are given.

3.1

Introduction

Multiresolution analysis of a signal is a successive coarser approximation of the original signal. This can be interpreted as representing the signal by different levels of resolution. Each level contains information about different features of the signal. Finer resolution shows more details, while coarser res- olution shows the approximation of the signal and only strong features can be detected.

A function or signal can often be viewed as a composition of a smooth background and actions or details in the foreground. The distinction between a smooth part and details is determined by the resolution. At a given reso- lution a signal is approximated by ignoring all details with higher resolution. Consider progressively increasing resolution, at each stage of the increase in resolution finer details are added to the coarser description providing a successive better approximation to the signal.

Eventually, when the resolution goes to infinity, the exact signal is recov- ered. Vice versa, for progressive decrease in the resolution at each stage more details are lost from the signal. This provides a successive coarser approxi- mation of the signal until a point is reached where only one value describes the whole signal: the global average. Fig. 3.1 shows an image of a traffic scene in its original sampling resolution and two approximations.

(a) (b) (c)

Figure 3.1: Image in multiresolution representation. (a) Original resolution. (b) Approximation in one lower resolution level. (c) Approximation in three lower resolution levels.

The most obvious advantage of multiresolution representations is that they provide a possibility for reducing the computational cost of various im- age processing operations. For example, they can be used to perform coarse feature detection operations, such as spot or bar detectors, by applying the corresponding fine feature detection operations at a higher level [Ros84a].

The information contained in a signal is distributed into the levels of the resolution. Local information may be better processed in the high resolution levels, while global information may be processed in the low resolution lev- els. Working in a cross-resolution manner can help to process each type of information of the signal.