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- Introduction Table of Contents
- 1.1. Problem Definition..............................................................................................
- 1.2. Scope
- 1.3. Application
- 1.4. Project Objectives
- Object Detection and Tracking
- 2.1. Object Detection
- 2.1.1. Background Subtraction...............................................................................
- 2.1.1.1. Frame Differencing
- 2.2. Object Tracking
- 2.2.1. Template Matching based Tracking.............................................................
- 2.2.1.1. Advantages of Template Matching
- 2.2.1.2. Disadvantages of Template Matching
- 2.3. Template based Tracking
- 2.3.1. Template Selection.......................................................................................
- 2.3.1.1. Complications using Template Matching Technique
- 2.3.2. Flow Chart Representation
- 2.3.3. Mean Shift based Tracking
- 2.3.3.1. Advantages
- 2.3.3.2. Limitations
- 2.3.4. Flow Chart Representation
- Kalman Filter
- 3.1. Why Kalman Filter?
- 3.1.1. Prediction Accuracy
- 3.1.2. Optimal Filtering
- 3.1.3. Priori Information
- 3.1.4. Target Dynamics
- 3.2. Models for Kalman Filter..................................................................................
- 3.2.1. Constant Velocity Model
- 3.2.2. Constant Acceleration Model
- 3.3. Discrete Kalman Filter
- 3.3.1. System Dynamics.......................................................................................
- 3.3.1.1. State Equation
- 3.3.1.2. Output Equation
- 3.3.2. Probabilistic basis of Kalman filter............................................................
- 3.3.3. The Discrete Kalman Filter Algorithm
- 3.3.4. Flow Chart Representation
- Task Scheduling
- Future Work and Conclusion
- References
- Figure 1-1: Block Diagram of the System List of Figures
- Figure 2-1: Flow Chart representation of Template Matching Technique
- Figure 2-2: Flow Chart representation of Fast Mean Shift Algorithm
- Figure 2-3: Flow Chart representation of Fast Mean Shift Algorithm (cont-I)
- Figure 2-4: Flow Chart representation of Fast Mean Shift Algorithm (cont-II)
- Figure 3-1 Constant Velocity Model
- Figure 3-2 Random Walk Model
- Figure 3-3 Constant Acceleration Model
- Figure 3-4 Constant Acceleration Model with Random Walk
- Figure 3-5 Random Velocity Random Acceleration Model
- Figure 3-6: Discrete Kalman Filter
- Figure 3-7: Flow Chart representation of Discrete Kalman Filter
- Figure 4-1: Project Timeline
system can easily get low priced surveillance cameras but they still need many security agents to keep a constant watch on all monitors .This approach is not efficient, and in fact most of the time video tapes or files are replayed a number of times to check on a particular event after it has happened thus the automation of this system is highly desired.
1.3. Applications
Object detecting and tracking has a wide variety of applications in computer vision such as video compression, video surveillance, vision-based control, human-computer interfaces, medical imaging, augmented reality, military applications, traffic monitoring and robotics. Additionally, it provides input to higher level vision tasks, such as 3D reconstruction and 3D representation. It also plays an important role in video database such as content-based indexing and retrieval. In today‟s technologically emerging world this very technology of moving object detection is used for the movement assistance of disables in their homes.
1.4. Project Objectives
The project Moving object tracking from video sequences is an attempt to study some algorithms, which are robust for the tracking of mobile objects. The main objective of the project is the study of some tracking algorithms for moving objects from the image sequences crisply called video. The Figure 1-1 shows the basic working grid of the processes involved in the system .Figure 1-1 also includes pre and post processing sequences as well which includes noise removal, image enhancement issues and classification etc. but these issues are not of primary importance as far as this project is concerned so not addressed in detail.
Figure 1-1: Block Diagram of the System
Preprocessing
Apply tracking Algorithms
Verification of results Obtained
Post processing
Image acquisition
The object detection is performed through background subtraction algorithm.
2.1.1. Background Subtraction
Identification of moving objects from a sequence of frames is a primary and critical task in many computer-vision applications. A common approach is to carry out background subtraction, which identifies the specific moving objects from the segment of a video frame that differs distinctly from a background model. There are a number of challenges in developing a good background subtraction algorithm. First, it must be robust against changes in illumination. Second, it should avoid detecting non- stationary background objects such as moving leaves, rain, snow, and shadows cast by moving objects. Other background subtraction methods include
- Frame differencing
- Median filter
- Linear predictive
- Non parametric method Frame difference method has been studied and used in this project.
2.1.1.1. Frame Differencing
Frame differencing method is used for this purpose results after applying the simple algorithm for subtraction of successive frames from the previous one. Frame differencing arguably the simplest background modeling technique, frame differencing uses the video frame at time t - 1 as the background model for the frame at time t. Since it uses only a single previous frame, frame differencing may not be able to identify the result.
2.2. Object Tracking
The aim of object tracking is to establish a correspondence between objects or object parts in consecutive frames and to extract temporal information about objects such as trajectory, posture, speed and direction. Tracking detected objects frame by frame in video is a significant and difficult task. It is a crucial part of smart surveillance systems since without object tracking the system could not extract cohesive temporal information about objects and higher level behavior analysis steps would not be possible [5].
Object tracking using template matching method and fast mean shift method have been performed and discussed briefly in this section
2.2.1. Template Matching based Tracking
Template matching is a progression that determines how narrowly a template matches a segment of an image called a window, or correlation window. The set of windows considered may cover all or part of the image. How well a template matches, or the degree of similarity, is computed by correlating the template against each window. The correlation method is performed by considering each pixel in the template and its corresponding pixel in the frame. The value of these pixels is used in a correlation function that gives a correlation or similarity score. There are various types of correlation functions such as sum of squared differences, sum of absolute valued differences, mean-squared differences, and cross correlation. Template-based tracking using the sum-of-squared differences (SSD) is a classic technique for maintaining the location of a target throughout a video. For detail of template based tracking consider reference [1].
2.2.1.1. Advantages of Template Matching
Some advantages of template matching are its simplicity and its suppleness. Its correlation-based algorithm is uncomplicated to implement and it allows us to use templates that have either been produced using a segment of the image or derived.
2.2.1.2. Disadvantages of Template Matching
On the other hand, one of the main disadvantages of template matching is its computational cost since correlating requires the "scrutiny" of each pixel in the template over several windows in the image. Another disadvantage of template-based tracking is that if shape or orientation of target is changed then tracker starts loosing target and eventually results in futile tracking.
2.3. Template based Tracking
The objective of template-based tracking is to uphold a replica of the target in terms of a 2D template of image intensities and compute the target location in a new image
2.3.2. Flow Chart Representation
Figure 2-1: Flow Chart representation of Template Matching Technique
2.3.3. Mean Shift based Tracking
The Mean shift algorithm is a non-parametric technique as it requires no input to locate density extrema or modes of a given distribution by an iterative procedure. The method was originally proposed by Fukunaga and Hostetler [6]. Cheng [7] generalized the method and pointed out, that the mean shift algorithm is a mode- seeking process on the density function surface. Comaniciu and Meer [8] proved the convergence of the iterated mean shift procedure on discrete data, proposed several extensions and presented its benefits for practical applications. Belenzai and Bernhard [9] stretch the conservative step of mean shift method and introduced fast mean shift method. For detail of this algorithm consider reference [7] and [9].
2.3.3.1. Advantages
Mean shift offers following advantages
- It is application sovereign tool.
- Mean shift is also appropriate for real data analysis.
- It does not presume any former shape on data clusters.
- It can easily handle random feature spaces.
2.3.3.2. Limitations
Though mean shift algorithm is an efficient approach to track objects but also it has some limitations.
- The window sizing is not trivial.
- improper window size can cause modes to be amalgamated or generate some additional “shallow” modes.
Figure 2-3: Flow Chart representation of Fast Mean Shift Algorithm (cont-I)
Figure 2-4: Flow Chart representation of Fast Mean Shift Algorithm (cont-II)
3.1.2. Optimal Filtering
Kalman filter make optimal use of the target measurements by adjusting the filter weights to take into account the accuracy of the nth measurement [10]. If the target measurement was more accurate, then weights will be automatically adjusted in such a way that more weight will be given to measurement than prediction.
3.1.3. Priori Information
Kalman filter optimally make use of prior information [10]. This is especially useful when using two separate devices for searching and tracking. Data from the searching devices can be optimally used to initialize the filter weights that will result in small transient in tracking filter.
3.1.4. Target Dynamics
Kalman filter is model-based predictor. It uses target dynamic model to predict the next state of the target. Target dynamic model allows direct filter update rate [10]. It is also possible to use more than one dynamic model in the filter. This helps to track the more complex maneuvers made by the target. Now days, it has been widely accepted that accurate targeting tracking requires multiple target models. Interacting Multiple Model (IMM) has become a generally accepted best method for multiple models filtering [11]. By probabilistically combining predictions of these models (typically by Kalman), a best guesstimate of target state can be made.
3.2. Models for Kalman Filter
There are two types of tracking models for Kalman filter
- Constant velocity model
- Constant Acceleration model
3.2.1. Constant Velocity Model
In constant velocity model, velocity of the target is assumed to be constant between successive samples and not the whole length of time. This model is described by the following equations [10].
.
xn 1 xn T x (3.1)
.
xn 1 xn (3.2)
where T is sampling time. Accuracy of this model improves with decrease in sampling time. Therefore, smaller the sampling time better will be results. This model is especially suitable for slow moving objects. It is also possible to model a fast charging target with these dynamics if sampling time is appreciably small.
In state space, this model is represented by pure inertia model. Since there is no input for the dynamics, so it is given by the following state space model.
. .
0 1 0 0
x x v v
(^) ^ ^
From this model, state matrix is obtained.
0 1 A (^) 0 0 ^
The state transition matrix for this model can be found using the formulae [10].
(^2 2 )
( t T ) I TA ^ T 2!^ A T 3! A .... (3.4)
Using above formulae, state transition matrix is obtained is:
( ) 1 0 1
t T ^^ T
^ (3.5)
This can be discretezed to following state space model.
1 1
n n n n
x T x
v v
This model is known as “Constant Velocity Model”. Since, there is no input that can influence the target motion, input coupling matrix is not present in this model. Only possible input for this model can be a random noise. This random noise is introduced in the velocity variable of the target. Model that incorporates this random component in velocity variable is known as “Constant Velocity Model with Random Walk”.
(^00 10 20 30 40 50 60 70 80 90 )
2000
4000
6000
8000
10000 Range
(^900 10 20 30 40 50 60 70 80 90 )
95
100
105 Range Rate
Figure 3-2 Random Walk Model
Again, it can be seen that still the range of the target is changing linearly but now the velocity or range rate of the is not constant. Range rate is having random variation between 100 and 95. This model is more realistic than the previous one as velocity of an object seldom remains constant. There is always a fluctuation in velocity. This random walk model was used, most of the time, to generate the data for the target azimuth and elevation angles.
3.2.2. Constant Acceleration Model
This model assumes the acceleration of the target to be constant during the sampling time only and not the entire duration of time. Velocity of the target is taken to be variable. This model is good for accelerating bodies. This is a third order model that introduces one additional variable. This model can be represented by the following equations. . . .
0 1 0 0 0 1 0 0 0
x (^) x v v a a
^ ^ ^
where x , v and a are the position, velocity and acceleration of the target. The state matrix A obtained from this model is:
A
^
Thus, the state transition matrix can be obtained using formulae [10].
(^2 2 )
( t T ) I TA ^ T 2!^ A T 3! A .... (3.8)
State transition matrix thus obtained is:
2 (^1 ) ( ) 0 1 0 0 1
T^ T t T T
^
Using this state transition matrix, this model is discredited into following state space model [12].
1 2 1 1
n n n n n n
x T T x
v T v
a a
^
^
^
^
This model was used generate the trajectories for the target range, range rate and range acceleration show in Fig 3.3.
(^00 10 20 30 40 50 60 70 80 90 )
1
2
3 x 10
(^4) Range
(^00 10 20 30 40 50 60 70 80 90 )
500 Range Rate
(^40 10 20 30 40 50 60 70 80 90 )
5
6 Range Acceleration
Figure 3-3 Constant Acceleration Model
