Ag.Cu-System/Theory.Methods/Ag.Cu.Theory.tex

   1
   2 %%% Chapter heading commands %%%
   3
   4 %%% Path to the directorz containing the graphics and figures
   5 %\graphicspath{{./png/}}
   6
   7 \chapter{Contour Detection Based on non-CRF Inhibition}
   8 \label{chapter:contour_detection}
   9
  10 \renewcommand{\publ}{\flushleft\footnotesize{Published as:
  11 C. Grigorescu, N. Petkov and M.A. Westenberg -- \textit{``Contour
  12 Detection Based on non-CRF Inhibition,''} IEEE Transactions on Image
  13 Processing, vol. 12, no. 7, pp. 729--739, July 2003.}}
  14
  15 \epigraph{The question is not what you look at, but what you
  16 see.}{Henry David Thoreau}
  17 \index{Contour detection techniques!non-CRF inhibition}
  18
  19 %%% Abstract %%%
  20
  21 \begin{Abstract}
  22 We propose a biologically motivated computational step, called
  23 non-classical receptive field (non-CRF) inhibition, more generally
  24 surround inhibition or suppression, to improve contour detection in
  25 machine vision. Non-CRF inhibition is exhibited by 80\% of the
  26 orientation selective neurons in the primary visual cortex of monkeys
  27 and has been demonstrated to influence the visual perception of man as
  28 well. The essence of this mechanism is that the response of an edge
  29 detector in a certain point is suppressed by the responses of the
  30 operator in the region outside the area of operator support. We
  31 combine classical edge detection with two types of inhibitory
  32 mechanism, isotropic and anisotropic inhibition, both of which have
  33 counterparts in biology. For edge detection, we also use a
  34 biologically motivated method (the Gabor energy operator). The
  35 resulting operator responds strongly to isolated lines, edges, and
  36 contours, but exhibits a weaker or no response to edges that make part
  37 of texture.
  38
  39 \end{Abstract}
  40
  41 %%% Chapter sections %%%
  42
  43 \index{Visual system}
  44 \section{Introduction}
  45 \label{sec:biological_aspects}
  46 \PARstart{O}ne of the most frequently encountered tasks in machine
  47 vision is to find the contours of objects in a complex scene. Yet,
  48 state-of-the-art edge detection techniques do not differentiate
  49 between object contours --- these are the actual primitives needed in
  50 most applications --- and edges originating from textured
  51 regions. There is evidence that the human visual system makes such a
  52 difference in its early stages of visual information processing, and
  53 that isolated edges, on one hand, and edges in a group, on the other
  54 hand, are perceived in different ways.  In this chapter we propose two
  55 biologically motivated models for contour detection and show their
  56 applicability in contour detection in natural images.
  57
  58 \bigskip
  59
  60 An important finding in the neurophysiology of the visual system of
  61 monkeys and cats, made in the beginning of the 1960s --- i.e. before
  62 the development of edge detection algorithms for digital image
  63 processing --- was that the majority of neurons in the primary visual
  64 cortex respond to a line or an edge of a certain orientation in a
  65 given position of the visual field. Initially, two types of
  66 orientation selective neuron were found, one that was sensitive to the
  67 contrast polarity of lines and edges, called simple cell, and another
  68 that was not, called complex cell \cite{Hubel62,Hubel74}.
  69 \index{Complex cell!response}
  70
  71 \index{Gabor functions!used in applications} These computational
  72 models gave the basis for biologically motivated edge detection
  73 algorithms in image processing. In particular, a family of two
  74 dimensional Gabor functions was proposed as a model of the linear
  75 filtering properties of simple cells
  76 \cite{Daugman80,Daugman85}.
  77
  78 %%% Example figure %%%
  79
  80 \begin{figure}[tpb]
  81   \begin{center} \includegraphics[width=0.45\textwidth]{./chapter_3/png/tobin-blakemore.png}
  82     \caption{The effect of orientation contrast in non-CRF inhibition: the
  83     plot shows the response of a neuron to a stimulus composed of a single bar
  84     of optimal orientation in the CRF (central circle) and a grating of
  85     varying orientation outside the CRF. The inhibition by the surrounding
  86     grating is strongest when its orientation coincides with the optimal
  87     stimulus. (Courtesy of C. Blakemore and Exp. Brain Res.).}
  88     \label{fig:Blakemore} \end{center}
  89 \end{figure}
  90
  91 %%% Example table %%%
  92
  93 \index{Performance!contour detection}
  94 \begin{table}[htpb]
  95   \begin{center}
  96     \footnotesize
  97     \begin{tabular}{llcccccc}
  98 \hline
  99 \textbf{Goat 3}
 100       & Gabor energy & $2.0$ & $0.1$ &       & $0.72$ & $0.38$ & $0.25$ \\
 101       & Canny        & $2.4$ & $0.1$ &       & $0.83$ & $0.55$ & $0.14$ \\
 102       & Anisotropic  & $2.4$ & $0.1$ & $1.2$ & $0.36$ & $0.60$ & $0.32$ \\
 103       & Isotropic    & $2.0$ & $0.1$ & $1.0$ & $0.46$ & $0.51$ & $0.34$\\ \hline
 104 \textbf{Elephant 2}
 105       & Gabor energy & $2.0$ & $0.1$ &       & $0.59$ & $0.36$ & $0.32$ \\
 106       & Canny        & $2.4$ & $0.1$ &       & $0.71$ & $0.50$ & $0.23$ \\
 107       & Anisotropic  & $2.4$ & $0.1$ & $1.2$ & $0.36$ & $0.45$ & $0.40$ \\
 108       & Isotropic    & $2.0$ & $0.1$ & $1.0$ & $0.31$ & $0.49$ & $0.42$\\ \hline
 109 \textbf{Hyena}
 110       & Gabor energy & $2.0$ & $0.1$ &       & $0.52$ & $0.32$ & $0.39$ \\
 111       & Canny        & $2.2$ & $0.1$ &       & $0.59$ & $0.50$ & $0.28$ \\
 112       & Anisotropic  & $2.4$ & $0.1$ & $1.2$ & $0.37$ & $0.25$ & $0.51$ \\
 113       & Isotropic    & $2.0$ & $0.1$ & $1.0$ & $0.22$ & $0.35$ & $0.55$\\ \hline
 114 \textbf{Gazelle 2}
 115       & Gabor energy & $2.0$ & $0.1$ &       & $0.61$ & $0.48$ & $0.32$ \\
 116       & Canny        & $1.6$ & $0.2$ &       & $0.72$ & $0.38$ & $0.23$ \\
 117       & Anisotropic  & $1.6$ & $0.2$ & $1.0$ & $0.51$ & $0.42$ & $0.36$ \\
 118       & Isotropic    & $1.6$ & $0.2$ & $1.0$ & $0.44$ & $0.46$ & $0.38$ \\
 119     \end{tabular}
 120   \caption{Operator parameters, errors, and performances for the images
 121     presented in Fig.~\protect\ref{Fig:Images}.}
 122   \label{tab:performance}
 123   \end{center}
 124 \end{table}
 125
 126