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\newcommand{\lecturetitle}[4]{
  \noindent
  CS 294-2, Visual Grouping and Object Recognition(Prof. Jitendra Malik) \hfill #3\\
  Lecture \##1 (#2) \hfill {\bf DRAFT} Notes by #4\\[-.05in]
  \mbox{}\hrulefill \mbox{}\\}

\begin{document}

% MODIFY THE FOLLOWING TO INCLUDE THE LECTURE #, TOPIC, DATE, and YOUR NAME
\lecturetitle{1}{The 3 Problems: Grouping, Figure/Ground and Recognition, 
                and their Inter-relationship}{August 23, 1999}{Ye Sheng}

% INCLUDE AN OUTLINE OF THE CLASS TOPICS

\begin{itemize} 
    \item The 3 Problems and their Inter-relationship
        \begin{itemize} 
          \item Grouping 
          \item Figure/Ground
          \item Recognition
          \item Inter-relationship between Grouping, Figure/Ground and Recognition
        \end{itemize}
    \item Principal Factors that lead to Grouping, Figure/Ground and Recognition
        \begin{itemize} 
          \item Principal Factors that lead to Grouping
          \item Principal Factors that lead to Figure/Ground
          \item Principal Factors that lead to Recognition
        \end{itemize}

\end{itemize}

% THE NOTES WILL GO HERE
\section{The 3 Problems and their Inter-relationship}
The 3 Problems: Grouping, Figure/Ground and Recognition, 
and their Inter-relationship will be discussed in this section. 

\subsection{Grouping} 
Grouping is to get a kind of hierachic tree as shown in Fig.(\ref{fig:1}).

\begin{figure}[htb]
\centering
\includegraphics[height=2.5in,width=4.5in]{group.eps}
\caption{Hierachic Tree}
\label{fig:1}
\end{figure}

For example, for an image in which there are a number of zebra 
standing at the side of a river with some bush around them, how to group the image?
As shown in Fig.(\ref{fig:2}), the image can first be divided into 
three level $1$ groups such as bush, zebra and water. Furtherly, the image
of zebra can be divided into a set of level $2$ subgroups such as zebra $1$,
zebra $2$, $\cdots$, i.e. Z$1$, Z$2$, $\cdots$.

\begin{figure}[htb]
\centering
\subfigure[]{
\includegraphics[height=1.5in,width=2.in]{group_2.eps} }
\subfigure[]{
\includegraphics[height=1.5in,width=2in]{group_3.eps} }
\caption{An Example of Grouping}
\label{fig:2}
\end{figure}


\subsection{Figure/Ground}
In order to discuss Figure/ground, or depth ordering or surface layout problem,
let's first consider a famous example by Rubin in 1915. 

\begin{figure}[htb]
\centering
\includegraphics[height=1.8in,width=3in]{figgro.eps}
\caption{An example of Figure/Ground: Vase/2-face example by Rubin in 1915}
\label{fig:3}
\end{figure}

As shown in 
Fig.(\ref{fig:3}), if the image is interpreted as a vase, pixel B is nearer than pixel A. 
On the other hand, if the image is interpreted as 2-face, pixel A is nearer than pixel B.
Note that the nearer pixel is called $figure$ and the farther pixel is called 
$ground$ correspondingly.



\subsection{Recognition} 
Recognition is {\bf Naming Objects}.  
The task of Recognition is to tell us what kind of shape, what kind of material
or what kind of movement the object in the image is. For example, 
as shown in Fig.(\ref{fig:2}), you should tell us which is bush, which are zebra and 
which is water.
In a word, here you need to decide which is which. Note that you don't need to do so in 
grouping in which the goal is only to divide the image into different groups 
with different characteristics and you don't care what they are in fact. 

\subsection{Inter-relationship between Grouping, Figure/Ground and Recognition} 
Inter-relationship between Grouping, Figure/Ground and Recognition can be 
represented by Fig.(\ref{fig:4}). 

\begin{figure}[htb]
\centering
\includegraphics[height=2.8in,width=4.5in]{relation.eps}
\caption{Inter-relationship between Grouping, Figure/Ground and Recognition}
\label{fig:4}
\end{figure}

For example, you can either do recognition 
after grouping or do grouping after recognition. As shown in Fig.(\ref{fig:5}),
you can first divide the image into two parts, i.e. the images which are inside
the ellipse and those which are outside of it. Then you can recognize that the 
inside part is a face and so on. This is the technique of recognition after 
grouping. In other way, you can first find that there is a familar face in the 
image. Then you can group it as face part and non-face part. This is in fact the 
technique of grouping after recognition.
 
\begin{figure}[htb]
\centering
\includegraphics[height=2in,width=2in]{face.eps}
\caption{An example image of face}
\label{fig:5}
\end{figure}

Note that the tool used in the inference between different parts is the 
{\bf Probability Inference}. The reason is that conditions are changing all time 
so that no rule will be always right.


\section{Principal Factors that lead to Grouping, Figure/Ground and Recognition}
In this section, principal factors that lead to grouping, figure/ground and 
recognition are discussed. First let's consider principal factors that lead 
to grouping.

\subsection{Principal Factors that lead to Grouping} 

{\bf Boundaries of image regions} are defined by a lot of attributes such as:
 \begin{itemize} 
   \item Brightness and color 
   \item Texture (texture is often defined as a repeated pattern)
   \item Motion, e.g. bird flys in the bush. With single black and white image,
it is hard to tell which is the bird. But the motion of the bird provides us a 
cue to pick it out from its "camouflage".
   \item Stereoscopic depth: Human vision system is born to use the 
stereoscopic feature. With built-in knowledge of disparity between left and
right eyes, we can tell the depth of $0.4mm$ when the objects are placed in
$1$ meter ahead of us, referred  to the notes of CS280.

   \item Familiar configuration: it is the familiar configuration from our 
own knowledge, e.g. table from a sheet of paper, moon from ballon, etc.
 \end{itemize}


{\bf Principal factors which lead to grouping} are:

 \begin{itemize} 
   \item Similarity of (Brightness, color, texture, disparity, motion)
   \item Proximity
   \item Good continuation of boundary contours
   \item Closure
   \item Symmetry and Parallelism
   \item Familiar configuration
 \end{itemize}
we will discuss it separately in the folowing section.

\subsubsection{Similarity of (Brightness, color, texture, disparity, motion)}

As shown in Fig.(\ref{fig:sec2_1}), most people will percive two groups, i.e.
one group of red dots and another group of green dots. This is an example 
of similarity in color. As to the similarity in motion, recall the example of bird flys 
in the bush, points that move together can be grouped together.  

\begin{figure}[htb]
\centering
\includegraphics[height=0.5in,width=2in]{gro1.eps}
\caption{An example of Color Similarity}
\label{fig:sec2_1}
\end{figure}


\subsubsection{Proximity}

\begin{figure}[htb]
\centering
\includegraphics[height=0.4in,width=2in]{gro2.eps}
\caption{An example of Proximity}
\label{fig:sec2_2}
\end{figure}
As shown in Fig.(\ref{fig:sec2_2}), most people will percive two groups, i.e.
one group of red dots in the left side and another group of red dots in the 
right side. Why do we percive this as two seperate groups of black dots? The
insight of 
this and other factors which lead to grouping comes from ecological statistics. 
In computer vision, we are given an image and trying to deduce the world that
has highest probability of giving rise to that image. This can be considered 
as a Bayesian view, find the most probable interpretation in the context of 
prior world knowledge. Statistically, the probability of two pixels are 
in the same object decreases when the distance between the two pixels 
increases.


\subsubsection{Good continuation of boundary contours}
Most objects in the world have smooth continuous boundaries. Objects in our 
world do have sharp corners, but the probability of an object being smooth 
is much higher, as shown in Fig.(\ref{fig:sec2_3}). The question to ask is 
how often is the tangent of a contour 
continuous vs. discontinuous. Again this is a statistical justification.

\begin{figure}[htb]
\centering
\subfigure[]{
\includegraphics[height=1.5in,width=2.in]{gro3a.eps} }
\subfigure[]{
\includegraphics[height=1.5in,width=2in]{gro3b.eps} }
\caption{Examples of continuation and discontinuation of boundary contours:
   (a) contour with good continuation (b)contour with discontinuation}
\label{fig:sec2_3}
\end{figure}



\subsubsection{Closure}
Most objects in the world appear to be enclosed in their contour, as shown in 
 Fig.(\ref{fig:sec2_4a}). However, 
there are cases where they are separated, e.g. the sky in 
Fig.(\ref{fig:sec2_4b}) which is separeted by the tree.
But again, the probability of the object being enclosed by its contour is much
higher and hence we can use closure as a factor for grouping.

\begin{figure}[htb]
\centering
\subfigure[]{
\includegraphics[height=1.5in,width=2.in]{gro4a.eps} }
\subfigure[]{
\includegraphics[height=1.5in,width=2in]{gro4b.eps} }
\caption{Examples of closure:
   (a) contour enclosed in its closure (b)contour which is not enclosed
 in its closure}
\label{fig:sec2_4a}
\end{figure}


\begin{figure}[htb]
\centering
\includegraphics[height=2.2in,width=4.in]{gro4c.eps}
\caption{An example of Symmetry}
\label{fig:sec2_4b}
\end{figure}




\subsubsection{Symmetry and Parallelism}
As shown in Fig.(\ref{fig:sec2_5}), most people will percive that L1 and L2 are parts of the same object due to 
symmetry. Again this is a ecological statistic as most of objects in the 
natural world exhibit symmetry. The two types of symmetry seen the most often 
are Rotational Symmetry (symmetry around an axis like a limb, i.e. your arm) 
and Bilateral Symmetry (i.e., the left and right sides of human body).  

\begin{figure}[htb]
\centering
\includegraphics[height=2.5in,width=2.5in]{gro5.eps}
\caption{An example of Symmetry}
\label{fig:sec2_5}
\end{figure}

\subsubsection{Familiar configuration}
\begin{figure}[htb]
\centering
\includegraphics[height=2in,width=1.6in]{gro6.eps}
\caption{An example Image of Familiar configuration}
\label{fig:sec2_6}
\end{figure}
As shown in Fig.(\ref{fig:sec2_6}), most people will interpret this as a face. This is duo to high level
 knowledge that humans use. 

\subsection{Principal Factors that lead to Figure/Ground} 
\subsection{Principal Factors that lead to Recognition} 

\end{document}




