\documentstyle[12pt]{article}
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\begin{large}

\section{Introduction}
\label{sec:intro}

Until recently, the studies of image processing and image compression have 
been analyzed as two separate research topics.  Over the past few years the 
interest in combining the two has increased.  Researchers are beginning to see 
the benefits of processing compressed images without decompression.  
Recognition of compressed images can provide savings of memory and processing 
times.  Searching databases based on particular features, which are readily 
available in the compressed domain, is also a potential benefit.  Increasing 
the compression of images without removing pertinent information will always 
be desirable, due to the continuing increase in information that is being 
transmitted, processed and stored.  Many applications rely on efficient image 
compression schemes.  Video conferencing, image databases, surveillance, and 
image networks are examples of such applications.

These applications require the compression of images for efficiency.  In some 
cases image quality is important and in other cases data that can abstracted 
from the images is of great importance.  The need for image compression and 
analysis is key to these applications.  The system proposed performs 
recognition of 3D compressed images illustrated on traffic monitoring 
applications.

A traffic monitoring network which relies on image compression schemes, may 
consist of a hierarchical image network as shown in Figure~\ref{fig:arch}.  
This network utilizes real-time image processing to count vehicles, determine 
vehicle speeds, vehicle density and much more.  These networks also transmit 
image data to higher levels in the network for accident or traffic flow 
analysis.  Along with real-time processing and transmission of image data, 
traffic control centers store images which traditionally requires lots of 
space.  A traffic monitoring system which saves on both memory and processing 
time is essential for efficient operation of the system.  The goal of my 
research is to develop a 3D compression algorithm which allows recognition 
from compressed image data without decompressing.  A 3D compression is used 
to distinguish between overlapping objects.  Conventional 2D compression 
algorithm are not conducive to detection of overlapping objects.

3D information provides a method of distinguishing objects.  This work focuses 
on providing a traffic monitoring system, which performs vehicle counting, 
vehicle speed detection and vehicle matching from 3D compressed images.

\begin{figure}[h!]
\hspace*{\fill}
\begin{minipage}{8.0cm}
\psfig{file=network.eps,width=5in,height=2.5in}
\end{minipage}
\hspace*{\fill}
  \caption{Traffic Monitoring System Architecture}
  \label{fig:arch}
%\vspace{3in}
\end{figure}


\section{Previous Work on Stereo Vision}
\label{stereo}

Stereo vision uses two images to construct a 3 dimensional view of a scene.  
Stereo vision is based on triangulation.  As shown in Figure ??? the world 
coordinates of point P(X,Y,Z) are determined by finding the difference 
(disparity) between the image coordinates of the corresponding point in the 
left and right image.  The world coordinate is determined using triangulation. 
There are a number of different stereo vision methods, which have been 
developed.  This paper will discuss two main fields of study; area and 
feature based algorithms.  Area and feature based algorithms determine 
corresponding points from the images by finding the best match based on one 
or more criteria.  

The two main difficulties in stereo vision are calibration of the cameras and 
finding the corresponding points in the two images.  The majority of the 
algorithms require the cameras' position and orientation is known for both 
accuracy and computation reduction.  The cameras' position is used to 
determine the search window of the algorithm.  It is also essential for the 
algorithms to find the corresponding points in the images to make an accurate 
calculation of the position of the point in world coordinates.  Finding the 
corresponding points in images is termed the correspondence problem.  

Many algorithms attempt to reduce the number of false correspondences based on 
similarity measures.  Improving the robustness of the similarity measure can 
improve the performance of the algorithm and significantly reduce the number 
of false correspondences.  Accurately calibrating the cameras and the 
correspondence problem are difficulties in stereo vision, which have promoted 
the research of various techniques.  These are the two main focuses of 
research in stereo vision, but processing time has also been a topic of 
interest.  The development of feature based algorithms was in part due to the 
necessity to decrease the processing time of an area based algorithm.  Feature 
based algorithms reduce the amount of data to be processed and in many cases 
change the type of calculations performed to find the best match, both the 
reduction in data and less computative operations produce a decrease in 
processing time.

\begin{figure}[h!]
\hspace*{\fill}
\begin{minipage}{8.0cm}
\psfig{file=stereo.ps,width=4.8in}
\end{minipage}
\hspace*{\fill}
  \caption{Stereo Vision}
  \label{fig:stereo}
%\vspace{3in}
\end{figure}

Both area and feature based systems use triangulation to construct the 3 
dimensional view of a scene.  In the case of feature based systems the data 
obtained is sparse and interpolation methods are used to construct the 3 
dimensional view of the entire scene, for some application the sparse data 
may be adequate information.  Figure~\ref{fig:stereo} is a system of two 
cameras displaying the image coordinates for the left and right cameras and 
the corresponding point on an object in the images' coordinates and the object 
in world coordinates.  The goal of stereo vision is to determine the world 
coordinates given the camera positions, orientations, and parameters, along 
with the left and right images.  Once the corresponding points are determined 
on the images, p(x,y) in the left and right image, the world coordinates are 
determined using similar triangles.

In the remainder of this section, various techniques are described and 
analyzed, to give a sense of the algorithms available and the advantage and 
disadvantage associated with each.

\subsection{Calibration}

Calibration is an important component in many of the stereo vision algorithms.
A large number of algorithms are based on the condition that the position and 
orientation of all the cameras are known.  Even if the calibrations of the 
camera are known the calculations are not exact and these errors must be 
taken into consideration in the development of the algorithm.  Faugeras ??? 
weak calibration ???

Many systems are calibrated manually, by the design and construction of 
apparatus that will hold the cameras or by purchasing manufactured items which 
the cameras are mounted.  The system is then tested on known scenes to help 
in the calibration process.  There has also been a move toward systems which 
perform self-calibration ??? explain ???


\subsection{Preprocessing}

Preprocessing of the images may consist of performing feature extraction, 
such as edge detection or zero-crossing, ground plane determination or 
possibly a background subtraction, depending on the algorithm and application.  Preprocessing is performed to enhance some detail, eliminate irrelevant 
information or normalize the two images.

Area based methods determine correspondence based on intensity, therefore any 
differences in the intensity could adversely effect the algorithm results.  
To reduce the effects of brightness changes in the left and right images due 
brightness; many algorithms convolve the images with a Gaussian operator.  
The Gaussian operator averages the values of a pixel based on its neighbors.  

\subsubsection{Gaussian Pyramid}

\begin{figure}[h!]
\centering
\hspace*{\fill}
\vspace{2in}
\hspace*{\fill}
\caption{Construction of Pyramid}
\label{fig:pyr}
\end{figure}

Many techniques have been established which use several resolutions of the 
left and right images.  These techniques use several resolution in hopes of 
improving the accuracy of the correspondences and in some cases finding the 
areas of interest in the images.  Image pyramids are obtained by uniting 
pixels from one layer to form a new layer, as shown in Figure ???  
Figure~\ref{fig:pyramid} is an example of a set of pyramid images.  In the case
of a Gaussian pyramid the pixels are merged using the Gaussian function. For
example a 5x5??? Give equation and image of a Gaussian Pyramid???

\begin{figure}[h!]
\centering
\hspace*{\fill}
\begin{minipage}{1.5in}
\psfig{file=pyr0.ps,width=1.5in}
\end{minipage}
\begin{minipage}{.75in}
\psfig{file=pyr1.ps,width=.75in}
\end{minipage}
\begin{minipage}{.375in}
\psfig{file=pyr2.ps,width=.375in}
\end{minipage}
\hspace*{\fill}
\caption{Pyramid of Images}
\label{fig:pyramid}
\end{figure}

Franke ??? constructs the Gaussian pyramid for both the left and right images.
The edges of each image are determined, to produce a binary pyramid.  In the 
lower resolution the binary images are correlated using the SSD 
(Sum of Square Difference) or the SAD (Sum of Absolute Difference) at the 
highest resolution (original image) cross correlation is performed to get rid 
of bad matches and the disparity is found to subpixel accuracy. 

\subsubsection{Edge Detection}

Edge detection is used as one of the main feature extraction methods in 
feature based algorithms and in various techniques edge detection is used to 
find areas of interest in area based algorithms.  There are several edge 
detection algorithms to chose for a given application.  In general there are 
two types of edge detection algorithms???  

\begin{description}
 \item[Canny]

 \item[zero-crossing]

 \item[Laplacian]
\end{description}

\subsubsection{Background Elimination}
 \paragraph{Ground Plane}

\subsection{Matching}



\subsubsection{Area Based}



\subsubsection{Feature Based}



\subsection{Continuity}







\section{System Overview}

\label{sec:syst}



The system consists of three modules: 3D calculation, compression, 
and processing.  The 3D calculation module receives three input images 
and produces the edge depth map of the center image.  The compression module
uses the edge depth map, edge map and the center image to compress the 
attributes of the image.  The processing unit uses the 3D compressed data to 
determine the vehicle count, vehicle speed and vehicle matching without 
decompressing the image.  The results can be stored into memory or be 
transmitted over the network to the higher level control centers.


\begin{figure}[h!]

\hspace*{\fill}

\begin{minipage}{8.0cm}

\psfig{file=overview.eps,width=5in}

\end{minipage}

\hspace*{\fill}

  \caption{System Overview}

  \label{fig:view}

%\vspace{3in}
\end{figure}


\subsection{Image Acquisition}



The 3D calculation uses 3 images captured simultaneously to determine the 
depth information of objects in a scene.  The initial system used to acquire 
the images consisted 
of three monochrome cameras (Sony XC-75) which were 
connected to a frame 
grabber as shown in Figure~\ref{fig:pc1}.  The 3 
cameras were aligned on a metal bar to help ensure alignment.  The frame 
grabber is a PCI board and consists of 3 components an acquisition module, 
frame memory and convolver.  A channel for each camera was used to acquire 
the images simultaneously.  Edge detection of the images was performed on the 
PCI board all further processing is performed on the CPU of the host computer.

\begin{figure}[h!]
%\hspace*{\fill}
%\begin{minipage}{8.0cm}
%\psfig{file=overview.eps,width=4.8in}
%\end{minipage}
%\hspace*{\fill}
\vspace{3in}
  \caption{PC Implementation I}
  \label{fig:pc1}
\end{figure}

The second system displayed in Figure~\ref{fig:pc2} acquires 2 monochrome and 
1 color image simultaneously.  Color information is added to increase the 
reliability of the system.  This implementation consists of two frame grabbers 
(PCI boards).  One frame grabber is used to capture the color image and the 
other frame grabber is used to capture the 2 monochrome images.  The images 
are stored on the hard drive and all processing is performed on the CPU host 
computer.

\begin{figure}[h!]
%\hspace*{\fill}
%\begin{minipage}{8.0cm}
%\psfig{file=overview.eps,width=4.8in}
%\end{minipage}
%\hspace*{\fill}
\vspace{3in}
  \caption{PC Implementation II}
  \label{fig:pc2}
\end{figure}

\section{Three-Dimensional Calculation}
\label{sec:prep}

The 3D algorithm~\cite{ber} performs fast calculations due to the feature 
matching rather than area correlation.  Feature matching is faster due to 
the decrease in data and the decrease in calculations in the algorithm.  The 
3D calculation is based on a trinocular vision algorithm, which produces an 
edge depth map of the center image.  Figure~\ref{fig:flow} is a flow chart of 
the algorithm. 


\begin{figure}

\hspace*{\fill}

\begin{minipage}{3in}

\centerline{

\psfig{figure=flow.ps,height=3in}}

\caption{Flow chart.}

\label{fig:flow}

%\vspace{3in}
\end{minipage}

\hspace*{\fill}

\end{figure}



The images are acquired simultaneously from all three cameras as described in
Section~\ref{sec:image}.  The cameras are equally spaced, with their optical 
axes aligned, with lenses 
of focal length 35~mm.  Figure~\ref{fig:triple} 
shows a sample of three images taken by the cameras.


\begin{figure}[h!]

\hspace*{\fill}

\begin{minipage}{3.4in}

\psfig{figure=occ1.ps,height=3.2in}

\caption{Sample input triple.}

\label{fig:triple}

\end{minipage}

\hspace*{\fill}

%\vspace{3in}
\end{figure}





The first step is to generate the vertical edge gradient for each image.  
Edge points in the left and right images are matched using the center camera 
to help eliminate false correspondences.  





\subsection{Edge Detection}
\label{sec:edge}

Edge detection consists of finding the local maximum or minimum in a given 
region.  There are 3 main types of edge detection, (1) gradient, (2) template, 
and (3) parametric.  The gradient based methods find the partial derivatives 
in the desired direction and perform thresholding to determine if there is a 
pixel at a particular location.  As an approximation of the gradient an 
appropriate weighted kernel is convolved with the original image.
%??? Pros and Cons

\begin{figure}[h!]
%\hspace*{\fill}
%\begin{minipage}{8.0cm}
%\psfig{file=overview.eps,width=4.8in}
%\end{minipage}
 %\hspace*{\fill}
\vspace{2in}
  \caption{Sobel Kernel}
  \label{fig:sobel}
\end{figure}

The template method determines the correlation of a given template with the 
original image.  Correlation is a similarity measurement.  The template which 
contains the ideal edge for a small region is correlated with the original 
image.  The result is then thresholded to determine if an edge is at a 
particular location.

The parametric method (??? see Hueckel p112 CV Ballard and Brown) The Sobel 
edge detection method was decided upon based on the computation and 
accuracy.  The sobel edge detection is a gradient based method.  Only the 
vertical edges are used in the 3D calculation.  The intensity gradient in the 
y-direction is ...
The Sobel kernels used for the system are displayed in Figure~\ref{fig:sobel}.
The positive and negative edges are distinguished to increase the accuracy of 
the matches.  Figure~\ref{fig:vedges} shows and example of the positive 
vertical edges and the negative vertical edges.  The left and right images are 
obtained to subpixel accuracy, which is achieved by an approximation method.



\begin{figure}[h!]
%\hspace*{\fill}
%\begin{minipage}{8.0cm}
%\psfig{file=overview.eps,width=4.8in}
%\end{minipage}
%\hspace*{\fill}
\vspace{3in}
  \caption{Positive and Negative Vertical Edges}
  \label{fig:vedges}
\end{figure}





\subsection{Subpixel Accuracy}
\label{sec:subpixel}

Subpixel accuracy is used to expand the resolution of the image through 
approximations.  Given the size and resolution of an image, determining the 
"true" location of an edge is difficult.  The edge may occur directly between 
two pixels or anywhere within one pixel.  There are several methods available 
to approximate the location of an edge.  

This system uses a parabolic approximation to reduce the computation.

Three pixels are used to approximate a parabola and the maximum (or minimum)
of the parabola is determined, the location of the edge is know calculated to
subpixel accuracy.  Figure~\ref{fig:subpixel} shows the parabola approximation.
???Talk about details of the approximation (eqns, error, incr in accuracy 
(determine)...)

\begin{figure}[h!]
%\hspace*{\fill}
%\begin{minipage}{8.0cm}
%\psfig{file=overview.eps,width=4.8in}
%\end{minipage}
%\hspace*{\fill}
\vspace{3in}
  \caption{Subpixel Approximation}
  \label{fig:subpixel}
\end{figure}

\subsection{Correspondence}
\label{sec:corr}
\vspace{2in}
\subsection{Depth}
\label{sec:depth}
 
The depth may be calculated directly for each disparity using 
\[z = b \frac{f}{x'_l - x'_r}\] where $b$ is the length of the baseline, $f$ 
is the focal length, and $x'_l$ and $x'_r$ are the $x$-coordinates in the 
left and right images respectively.  Figure~\ref{fig:depth} is the edge depth 
map after correlation.  A histogram of the number of edge points versus depth 
can be constructed, and 
after some bin averaging, the significant peaks 
correspond to objects. 



\begin{figure}[h!]

\hspace*{\fill}

\begin{minipage}{3.2in}

\psfig{figure=ad1occ1.ps,width=4.5in}

\caption{Depth map}

\label{fig:depth}

\end{minipage}

\hspace*{\fill}

\hspace*{\fill}

\begin{minipage}{3.2in}

\psfig{figure=map2.ps,width=4.5in}

\caption{Color Scheme for Distances}

\label{fig:colormap}

\end{minipage}

\hspace*{\fill}

%\vspace{3in}
\end{figure}




\subsection{Histogram}
\label{sec:hist}

\subsection{Results}
\label{sec:results}

\subsection{Object Detection}
\label{sec:objdet}




\section{Compression}

\label{sec:comp}


Conventional compression schemes such as DCT (Discrete Cosine Transform) are 
spatial-frequency-based and are not suitable for recognition from compressed 
data.  The goal of the compression algorithm is two-fold; first to compress 
the data as much as possible without losing any of the relevant information; 
second to provide a representation of the data which is conducive to object 
recognition.  The decision was made to use a contour based lossy compression 
method based on Mizuki's algorithm~\cite{miz}.  Mizuki proposed a 2D 
compression algorithm, which has been extended to 3D in this research.  The 
lossy method produces a high compression ratio and enhances the recognition 
component of the system.  

Many image processing schemes use the edge information as a guide in object 
recognition, for this reason a contour based algorithm was used~\cite{mas}.  
The contours provide a skeleton of the contents of the image which is used for 
recognition of objects as well as compression.  The details of the compression 
algorithm will be discussed later.  

Marshall~\cite{mar} uses a contour based compression method for shape 
recognition.  Marshall's work assumes that a contour with length larger than 
some threshold is an object, this assumption creates a problem if the contour 
of an object is disconnected.  An object with 2 or more long contours would be 
considered to be more than one object in Marshall's algorithm.  The differences
between Marshall's algorithm and this compression algorithm is the addition of 
three-dimensional data and the allowance of broken contours.  Although 
Marshall's method has problems with overlapping objects and objects consisting 
of several contours, his work demonstrates the potential of a contour based 
compression domain used for shape recognition.  

The compression algorithm is a lossy method which removes detail information 
which is not relevant in detecting an object.  The algorithm focuses on 
retaining information relevant to recognition, such as contour, color, and 
distance attributes.  A flow chart of the steps are shown in 
Figure~\ref{fig:compress}.  

The algorithm can be divided into two parts, Static and Dynamic.  In the 
static part the image is compressed without using any previous information.  
In the dynamic part the image compressed relative to a previous image using 
motion vectors to describe the change in the image.  

\subsection{Static}
\label{sec:static}
The static algorithm begins with the contour extraction.  The contour
 
extraction consists of eliminating short contours below some threshold.
  The 
contours are determined from the center edge map.  
The contour is then used 
to extract the color information of the image.  
The original center image is 
quantized.  The color on both sides of the 
contour are retained.  
Figure~\ref{fig:color} shows an example of the color information that is 
retained.

\begin{figure}[h!]
%\hspace*{\fill}
%\begin{minipage}{8.0cm}
%\psfig{file=overview.eps,width=4.8in}
%\end{minipage}
%\hspace*{\fill}
\vspace{3in}
  \caption{Color Information}
  \label{fig:color}
\end{figure}
%??? Section for each component
A description of the components are as follows:\\
\begin{description}

\item[Depth Map] The depth map contains the distance of edge pixels from the 
center camera.  The method of determining the distance is described in 

{\bf Section 3}.


\item[Contour Coding] The contours are determined by tracing edges with 
similar color and distance information.  The contours are then coded by using 
the start location and the directional codes for subsequent points in the 
contour.  Short contours are eliminated.


\item[Mean Coding] The mean RGB value of pixels between contours is coded.


\item[Distance Coding] The mean distance value of contour pixels is coded.


\item[Color Extraction] RGB values for pixels between contours is determined 

and a line approximation is used to represent the information.


\item[Color Coding] The endpoints of the line approximating the RGB values for 
pixels between contours is coded.


\item[Binary Block Matching] The edge maps from two consecutive images are used
to determine the motion vectors of each $n$~x~$n$ block.

\item[Error Coding] The reconstructed image from the motion vectors is compared
with the second image to produce an error which is encoded.

\end{description}

\begin{figure}[h!]

\hspace*{\fill}

\begin{minipage}{8.0cm}

\psfig{file=alg.ps,width=4.8in}

\end{minipage}

\hspace*{\fill}

  \caption{Compression Algorithm}

  \label{fig:compress}

%\vspace{3in}
\end{figure}

The algorithm combines contour, color, and distance attributes to produce an 
image coding system which can be used for recognition.

???Section for decompression

???Results

\subsection{Dynamic}
\label{sec:dynamic}

\subsubsection{Binary Block Matching}
\label{sec:bbm}

\subsubsection{Error Coding}
\label{sec:error}

\subsubsection{Decompression}
\label{sec:decomp}

\subsubsection{Results}
\label{sec:res}

\section{Object Recognition}
\label{sec:objrec}

Three applications are being developed to demonstrate processing of an image
in the 3D compressed domain.  These applications are vehicle counting, 
vehicle
 speed detection and vehicle matching.  Vehicle counting requires 
object detection and tracking, vehicle speed detection requires object motion 
estimation, and vehicle matching utilizes template matching and scaling of the 
images.  These applications, though specific to traffic monitoring, 
demonstrate the capabilities of the system and can be used on any system 
requiring recognition of 3D compressed images.  


\section{Traffic Monitoring}
\label{sec:traf}

The transportation industry has always been concerned 
with the efficient and 
safe movement of traffic.  The data gathered from 
traffic monitoring is used 
to make real-time traffic control decisions which 
affect the movement and 
safety of traffic.  This research is 
geared towards highway monitoring to 
demonstrate the feasibility and 
benefits of recognition of 3D compressed 
images.  Current traffic monitoring
 systems have problems with shadows and 
overlapping vehicles~\cite{keh}
 ~\cite{mal}.  The 3D data will provide the 
necessary information to eliminate
 the problems of shadows and overlapping 
vehicles.  Three applications 
(vehicle counting, vehicle speed detection and 
vehicle matching) will 
demonstrate the feasibility of the 
system.  All 
three applications require the detection of vehicles in the 
image.  Vehicle 
counting and speed detection require the tracking of 
vehicles in subsequent 
images.  Vehicle speed detection utilizes motion
 estimates to determine the 
vehicle speeds.  


\subsection{Detection of Vehicles}

\label{sec:dete}



Vehicle counting, speed detection and vehicle matching rely on the detection 
of vehicles in a scene.  Detection methods utilizing color, edge and depth 
maps still apply in the 3D compressed domain.  The important information for 
performing object detection has been retained.  The contour's attributes in 
the
 compression algorithm can be used to detect the vehicles in the scene. 
Each vehicle is made up of several contours.  In detecting the vehicle 
within the 3D compressed data, a histogram of the number of edges at given 
distances can be constructed and used to classify the vehicles.  
Figure~\ref{fig:hist} shows the histogram of the edges from the image used 
in Figure~\ref{fig:triple}.  Based on the histogram the edges can be 
classified, distinguishing the objects in the scene.  Figure~\ref{fig:hist} 
shows an example of the detection of vehicles using only the distance and 
proximity information.  Color information will also be used to aid in the 
detection of vehicles.


\begin{figure}[h!]

\hspace*{\fill}

\begin{minipage}{8.0cm}
\psfig{file=colview.ps,width=4.8in,height=4.8in}
\end{minipage}
\hspace*{\fill}
  \caption{Histogram and detected objects}
  \label{fig:hist}
%\vspace{3in}
\end{figure}

\subsection{Tracking Vehicles in Subsequent Images}
\label{sec:trac}

Once a vehicle has been detected, vehicle counting and speed detection require 
tracking of the vehicle through subsequent images.  Assuming little or no 
changes in the shape of the contour of a vehicle, only translational motion, 
the matching of contours based on color, shape, and restricted possible 
locations as well as predicting the motion of the vehicle to track in 
subsequent images can be determined.

Groups of contours are assigned to a vehicle from the detection component and 
tracking the vehicle will consist of matching the overall color of the vehicle 
or if necessary the color distribution of the contours.  Also matching the 
shape or more precisely the grouping of the contours which make up the car is 
important in ensuring the correct vehicle has been located.  Another key 
component is the search, specifically where to search.  Limiting the search of 
vehicles and checking the most likely positions first can increase the 
performance and decrease the processing time of the system. 

\subsection{Speed Estimation}
\label{sec:vehi}

Once a vehicle has been detected and tracked through subsequent images an 
estimate of the speed can be determined using the three-dimensional data.  The 
location of the vehicle can be determined in the 3D domain from the calculation
of the depth map and the added knowledge from tracking and frame speed is 
enough information to estimate the speed of the vehicle through subsequent 
images.  To estimate the speed the $x$,$y$, and $z$ component of the average 
velocity is calculated and the magnitude of the average velocity is taken as 
the estimated speed of the vehicle.  All velocity components follow this basic 
form: \[\begin{array}{lr} v_x = \frac{X_{i+j} - X_i}{j}F_r & i \geq 0, j \geq 1
\end{array} \] where $X_i$ is the $x$-coordinate in the real world of a point 
in the $i^{th}$ frame, $j$ is the difference between the two frames used to 
calculate the average speed, and $F_r$ is the frame rate.  The magnitude of 
the velocity is \[ v_{avg}~=~\sqrt{{v_x}^2 + {v_y}^2 + {v_z}^2}. \]  The speed 
of the vehicle will be calculated by taking the average of all points with 
known estimated speed for the particular vehicle.  The motion vectors can 
also be used to estimate the speed of vehicles once the vehicles have been 
detected.

\section{Conclusion}
\label{sec:conc}

This research focuses on recognition of 3D compressed images without 
decompression.  Traffic monitoring applications are developed to demonstrate 
the benefits of combining image processing and image compression techniques 
to produce an efficient system which can be used for image networking systems 
and dynamic route guidance.  Any applications requiring the transmission, 
storage and processing of images can benefit in reduced usage of memory and 
processing time by combining processing and compression.  The combination of 
compression and processing is a natural extension of image compression, 
utilizing its attributes and increasing its benefits.  The increasing interest 
in this combination may lead to new image compression standards which will 
focus on the capability of recognition without decompression as well as 
compression performance.

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\end{document}