lectures/Komp_obr/07-iproc_2.tex

\documentclass[10pt,pdf,hyperref={unicode}]{beamer}
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\usepackage{lect}

\title[ëÏÍÐØÀÔÅÒÎÁÑ ÏÂÒÁÂÏÔËÁ. ìÅËÃÉÑ 7.2.]{ëÏÍÐØÀÔÅÒÎÁÑ ÏÂÒÁÂÏÔËÁ ÒÅÚÕÌØÔÁÔÏ× ÉÚÍÅÒÅÎÉÊ}
\subtitle{ìÅËÃÉÑ 7.2. ïÂÒÁÂÏÔËÁ ÉÚÏÂÒÁÖÅÎÉÊ}
\date{1 ÁÐÒÅÌÑ 2021 ÇÏÄÁ}

\begin{document}
% ôÉÔÕÌ
\begin{frame}
\maketitle
\end{frame}
% óÏÄÅÒÖÁÎÉÅ
\begin{frame}
\tableofcontents
\end{frame}

\section{÷ÅÊ×ÌÅÔÙ}
\begin{frame}{÷ÅÊ×ÌÅÔÙ}
\only<1>{\img[0.6]{pyramid}
\begin{block}{ðÉÒÁÍÉÄÁ ÉÚÏÂÒÁÖÅÎÉÊ}
ðÉÒÁÍÉÄÁ ÐÒÉÂÌÉÖÅÎÉÊ (ÁÐÐÒÏËÓÉÍÉÒÕÀÝÉÅ ËÏÜÆÆÉÃÉÅÎÔÙ), ÐÉÒÁÍÉÄÁ ÏÛÉÂÏË (ÄÅÔÁÌÉÚÉÒÕÀÝÉÅ ËÏÜÆÆÉÃÉÅÎÔÙ).
ðÉÒÁÍÉÄÁ ìÁÐÌÁÓÁ (ÔÏÌØËÏ ÐÉÒÁÍÉÄÁ ÏÛÉÂÏË, ËÏÍÐÒÅÓÓÉÑ); ÇÁÕÓÓÏ×Á ÐÉÒÁÍÉÄÁ (ÔÏÌØËÏ ÐÒÉÂÌÉÖÅÎÉÑ, ÓÉÎÔÅÚ
ÔÅËÓÔÕÒ).\end{block}}
\only<2>{\img[0.7]{lappyramid}}
\only<3>{\img[0.5]{orapple}\centerline{
ïÂßÅÄÉÎÅÎÉÅ ÐÉÒÁÍÉÄ ìÁÐÌÁÓÁ.}}
\end{frame}

\begin{frame}{÷ÅÊ×ÌÅÔÙ}
\only<1>{\img[0.6]{2d-haar-basis}}
\only<2>{\img[0.8]{wvpyramid01}}
\only<3>{\img[0.8]{wvpyramid02}}
\only<4>{\img[0.8]{wvpyramid}}
\only<5>{\img[0.8]{wvpyramid03}}
\end{frame}

\begin{frame}{ðÁËÅÔÙ ×ÅÊ×ÌÅÔÏ×}
\only<1>{\img[0.95]{wpack01}}
\only<2>{\img[0.95]{wpack02}}
\only<3>{\img[0.7]{wpack03}}
\only<4>{\img[0.8]{wpack04}\tiny (a) normal brain; (b) 2-level DWT of normal brain; (c) 2-level
DWPT of normal brain; (d) AD brain; (e) 2-level DWT of AD brain; (f) 2-level DWPT of AD brain.}
\end{frame}

\section{íÏÒÆÏÌÏÇÉÞÅÓËÉÅ ÏÐÅÒÁÃÉÉ}
\begin{frame}{íÏÒÆÏÌÏÇÉÞÅÓËÉÅ ÏÐÅÒÁÃÉÉ}
\only<1>{
\begin{block}{ïÓÎÏ×ÎÙÅ ÐÏÎÑÔÉÑ}
\begin{itemize}
\item ðÕÓÔØ $A$~-- ÎÅËÏÔÏÒÁÑ ÏÂÌÁÓÔØ ÎÁ ÂÉÎÁÒÎÏÍ ÉÚÏÂÒÁÖÅÎÉÉ, $a=(a_1,a_2)\in A$~-- ÔÏÞËÁ, ÅÊ
ÐÒÉÎÁÄÌÅÖÁÝÁÑ; ÉÎÔÅÎÓÉ×ÎÏÓÔØ × ÔÏÞËÅ $a$ ÏÂÏÚÎÁÞÉÍ ËÁË $v(a)$.
\item {\bf ïÂßÅËÔ}: $A=\{a\;|\;v(a)==1, \forall a \text{ 4/8-connected}\}$.
\item {\bf æÏÎ}: $B=\{b\;|\;b==0 \cup b\text{ not connected}\}$.
\item {\bf óÄ×ÉÇ}: $A_x=\{c\;|\;c=a+x, \forall a\in A\}$.
\item {\bf ïÔÒÁÖÅÎÉÅ}: $\hat A=\{c \;|\; c=-a, \forall a\in A\}$.
\item {\bf äÏÐÏÌÎÅÎÉÅ}: $A^C=\{c \;|\; c\notin A\}$.
\item {\bf óÕÍÍÁ}: $A+B=\{c \;|\; c\in (A\cup B)\}=A\cup B$.
\item {\bf òÁÚÎÏÓÔØ}: $A-B=\{c \;|\; c\in A, c\notin B\}=A \cap B^C$.
\end{itemize}
\end{block}}
\only<2>{\img[0.8]{baseimop}}
\end{frame}

\begin{frame}{üÒÏÚÉÑ (ÕÓÅÞÅÎÉÅ)}
\begin{block}{}
$$A\ominus B=\{x \;|\; B_x\subseteq A\}\text{ ÉÌÉ }
A\ominus B=\{x \;|\; B_x\cap A^C=\varnothing\}\text{ ÉÌÉ }
A\ominus B=\bigcap_{b\in B}A_b
$$
\end{block}
\only<1>{\img[0.7]{erosion}}
\only<2>{\img[0.7]{erosion01}}
\only<3>{\img{erosion02}}
\end{frame}

\begin{frame}{äÉÌÁÔÁÃÉÑ (ÎÁÒÁÝÉ×ÁÎÉÅ)}
\begin{block}{}
$$A\oplus B = \{x \;|\; \hat B_z\cap A \ne\varnothing\} \text{ ÉÌÉ }
A\oplus B = \bigcup_{b\in B}A_b=\bigcup_{a\in A}B_a
$$
\end{block}
\only<1>{\img[0.7]{dilation}}
\only<2>{\img{dilation01}}
\end{frame}

\begin{frame}{ó×ÏÊÓÔ×Á}
\begin{block}{}
\centerline{ëÏÍÍÕÔÁÔÉ×ÎÏÓÔØ:}
$$A\oplus B = B\oplus A\qquad A\ominus B \ne B\ominus A$$
\centerline{áÓÓÏÃÉÁÔÉ×ÎÏÓÔØ:}
$$A\oplus (B\cup C)=(A\oplus B)\cup(A\oplus C)\qquad A\ominus (B\cup C)=(A\ominus B)\cap(A\ominus
C)$$
$$(A\ominus B)\ominus C = A\ominus(B\oplus C)$$
\centerline{ä×ÏÊÓÔ×ÅÎÎÏÓÔØ:}
$$(A\ominus B)^C=A^C\oplus\hat B\qquad
(A\oplus B)^C =A^C\ominus\hat B$$
\end{block}
\end{frame}

\begin{frame}{ïÔËÒÙÔÉÅ (ÒÁÚÍÙËÁÎÉÅ)}
\begin{block}{}$$A\circ B = (A\ominus B)\oplus B$$\end{block}
\img{opening01}
\end{frame}

\begin{frame}{úÁËÒÙÔÉÅ (ÚÁÍÙËÁÎÉÅ)}
\begin{block}{}
$$A\bullet B = (A\oplus B)\ominus B$$
\img{closing01}
\end{block}
\end{frame}

\begin{frame}{}
\img{morph01}
\end{frame}

\begin{frame}{<<Top hat>> É <<Bottom hat>>}
\begin{block}{}
$$A\hat\circ B = A\backslash (A\circ B), \qquad
A\hat\bullet B = (A\bullet B)\backslash A$$
\end{block}
\only<1>{\img[0.8]{tophat}}
\only<2>{\img[0.8]{bottomhat}}
\end{frame}

\begin{frame}{Hit-and-miss}
\only<1,2>{\begin{block}{}$$A \circledast B = (A\ominus B_1)\cap(A^C\ominus B_2),\quad\text{ÇÄÅ}$$
$$B_1=\{b \;|\; b\in B, b=1\},\; B_2=\{\tilde b \;|\; b\in B, b=0\}$$
\end{block}}
\only<1>{\img[0.8]{hitamiss01}}
\only<2>{\img[0.8]{hitamiss02}}
\only<3>{\img[0.8]{hit_and_miss_skel}$$S=A\backslash \bigcup_{i}(A\circledast B_i)$$}
\only<4>{\img{skel01}}
\only<5>{\img{skel02}}
\end{frame}

\section{óÅÇÍÅÎÔÁÃÉÑ ÉÚÏÂÒÁÖÅÎÉÊ}
\begin{frame}{óÅÇÍÅÎÔÁÃÉÑ ÉÚÏÂÒÁÖÅÎÉÊ}
\begin{block}{ïÓÎÏ×Ù}
\begin{itemize}
\item óÅÇÍÅÎÔÁÃÉÑ: $\cup_{i=1}^n R_i \,\cup\, \cup_{i=1}^n B_i= R$, ×ÓÅ $R_i$ Ó×ÑÚÎÙÅ, $B_i$~--
ÆÏÎ.
\item $R_i\cap R_j=\varnothing$ $\forall i\ne j$.
\item $Q(R_i) = 1$, $i=\overline{1,n}$, $Q$~-- ÌÏÇÉÞÅÓËÉÊ ÐÒÅÄÉËÁÔ.
\item $Q(R_i\cup R_j)=0$ $\forall i\ne j$.
\end{itemize}
\end{block}
\begin{block}{ðÒÏÉÚ×ÏÄÎÙÅ}
\begin{itemize}
\item $\partder{f}{x}\equiv f'_x=f(x+1)-f(x)$
\item $\dpartder{f}{x}\equiv f''_x = f'_x(x+1)-f'_x(x)=f(x+2)+f(x)-2f(x+1)$
\item $\nabla^2f(x,y) = f''_x(x,y)+f''_y(x,y) \Arr$
 $\nabla^2 f(x,y)=f(x+1,y)+f(x-1,y)+f(x,y+1)+f(x,y-1)-4f(x,y)$
\end{itemize}
\end{block}
\end{frame}

\begin{frame}{ðÒÉÍÅÒÙ (M13)}
\only<1>{ïÒÉÇÉÎÁÌ:\\
    \smimg[0.5]{origFull}\;\smimg[0.5]{origCrop}
}
\only<2>{âÉÎÁÒÉÚÁÃÉÑ ÐÏ ÐÏÓÔÏÑÎÎÏÍÕ ÐÏÒÏÇÕ:\\
    \smimg[0.5]{binFull}\;\smimg[0.5]{binCrop}
}
\only<3>{þÅÔÙÒÅÈËÒÁÔÎÁÑ ÜÒÏÚÉÑ:\\
    \smimg[0.5]{erosion4Full}\;\smimg[0.5]{erosion4Crop}
}
\only<4>{þÅÔÙÒÅÈËÒÁÔÎÏÅ ÒÁÚÍÙËÁÎÉÅ:\\
    \smimg[0.5]{opening4Full}\;\smimg[0.5]{opening4Crop}
}
\only<5>{ïÒÉÇÉÎÁÌ Ó ÐÒÅÄÙÄÕÝÅÊ ÍÁÓËÏÊ:\\
    \smimg[0.5]{objE4D4Full}\;\smimg[0.5]{objE4D4Crop}
}
\only<6>{ä×ÁÄÃÁÔÉÐÑÔÉËÒÁÔÎÁÑ ÜÒÏÚÉÑ:\\
    \smimg[0.5]{erosion25Full}\;\smimg[0.5]{erosion25Crop}
}
\only<7>{íÁÓËÁ (25 ÜÒÏÚÉÊ É 200 ÄÉÌÁÔÁÃÉÊ):\\
    \smimg[0.5]{opE25D200Full}\;\smimg[0.5]{opE25D200Crop}
}
\only<8>{ïÒÉÇÉÎÁÌ Ó ÐÒÅÄÙÄÕÝÅÊ ÍÁÓËÏÊ:\\
    \smimg[0.5]{objE25D200Full}\;\smimg[0.5]{objE25D200Crop}
}
\only<9>{÷ÙÄÅÌÅÎÎÙÅ ÏÂßÅËÔÙ (ÒÁÚÍÙËÁÎÉÅ È4 É È10; 237 É 9 ÏÂßÅËÔÏ× × ÐÏÌÅ ÓÏÏÔ×ÅÔÓÔ×ÅÎÎÏ):\\
    \smimg[0.5]{count4}\;\smimg[0.5]{count10}
}
\end{frame}

\begin{frame}{ïÂÎÁÒÕÖÅÎÉÅ ÌÉÎÉÊ, ÔÏÞÅË É ÐÅÒÅÐÁÄÏ×}
\only<1>{\centerline{ôÏÞËÉ --- ÌÁÐÌÁÓÉÁÎ, ÌÉÎÉÉ, ÐÅÒÅÐÁÄÙ --- ÇÒÁÄÉÅÎÔ}\img[0.8]{prewitt}
\centerline{Prewitt}}
\only<2>{\img[0.7]{compmask}}
\only<3>{\begin{block}{çÒÁÄÉÅÎÔ}
$$\nabla \vec f = (f'_x, f'_y) = \bigl(f(x+1,y)-f(x,y), f(x,y+1)-f(x,y)\bigr)$$
\end{block}\img[0.8]{imgrad}}
\end{frame}

\begin{frame}{÷ÙÄÅÌÅÎÉÅ ÇÒÁÎÉÃ}
\only<1>{\begin{block}{íÏÒÆÏÌÏÇÉÞÅÓËÉÊ ÇÒÁÄÉÅÎÔ}
$$\beta(A)=A\backslash(A\ominus B)\qquad
\beta'(A)=(A\oplus B)\backslash A\qquad
\beta''(A)=(A\oplus B)\backslash(A\ominus B)$$
\end{block}\img{morphgrad}}
\only<2>{\begin{block}{Canny}
\begin{enumerate}
\item òÁÚÍÙ×ÁÎÉÅ ÉÚÏÂÒÁÖÅÎÉÑ ÇÁÕÓÓÏ×ÙÍ ÆÉÌØÔÒÏÍ.
\item ÷ÙÞÉÓÌÅÎÉÅ ÞÁÓÔÎÙÈ ÐÒÏÉÚ×ÏÄÎÙÈ $I'_x$ É $I'_y$ (òÏÂÅÒÔÓ, óÏÂÅÌØ, ðÒÀÉÔÔ, LoG, DoG\dots) É
ËÏÍÐÏÎÅÎÔÏ× ÇÒÁÄÉÅÎÔÁ: $M=\sqrt{(I'_x)^2+(I'_y)^2}$, $\theta=\arctg\frc{I'_y}{I'_x}$.
\item ðÏÒÏÇÏ×ÏÅ ÐÒÅÏÂÒÁÚÏ×ÁÎÉÅ $M$: $M_T = M$, ÅÓÌÉ $M>T$, ÉÎÁÞÅ $M_T=0$.
\item ïÂÎÕÌÅÎÉÅ ÎÅÍÁËÓÉÍÁÌØÎÙÈ $M_T$ ÐÏ ÎÁÐÒÁ×ÌÅÎÉÀ $\theta$ (ÐÏ Ä×ÕÍ ÓÏÓÅÄÑÍ).
\item ðÏÌÕÞÅÎÉÅ Ä×ÕÈ ÐÏÒÏÇÏ×ÙÈ ÚÎÁÞÅÎÉÊ: $M_{T_1}$ É $M_{T_2}$; $T_1<T_2$.
\item úÁÐÏÌÎÅÎÉÅ ÐÒÏÐÕÓËÏ× × $M_{T_2}$ ÐÏ ÓÏÓÅÄÎÉÍ ÚÎÁÞÅÎÉÑÍ × $M_{T_1}$.
\end{enumerate}
\end{block}}
\only<3>{\img[0.6]{canny01}\centerline{ïÂÒÁÚÅÃ}}
\only<4>{\img[0.6]{canny02}\centerline{Sobel}}
\only<5>{\img[0.6]{canny03}\centerline{Prewitt}}
\only<6>{\img[0.6]{canny04}\centerline{DoG}}
\only<7>{\img[0.6]{canny05}\centerline{Canny, $\sigma=5$, $T_1=0.8$, $T_2=0.95$}}
\end{frame}

\begin{frame}{ïÂÎÁÒÕÖÅÎÉÅ ÐÒÑÍÙÈ É ÏËÒÕÖÎÏÓÔÅÊ}
\only<1>{\begin{block}{ðÒÅÏÂÒÁÚÏ×ÁÎÉÅ èÁÆÁ}
$$r = x\cos\theta + y\sin\theta$$
\end{block}
\img[0.5]{R_theta_line}}
\only<2>{\img{htdiagram}}
\only<3>{\img[0.7]{htexample}}
\only<4>{\img{htEx}}
\only<5>{\includegraphics[width=0.48\textwidth]{h01}\hfil
	\includegraphics[width=0.48\textwidth]{h02}}
\only<6>{\begin{block}{ðÒÅÏÂÒÁÚÏ×ÁÎÉÅ èÁÆÁ ÄÌÑ ÐÏÉÓËÁ ÏËÒÕÖÎÏÓÔÅÊ}
$$(x-x_c)^2+(y-y_c)^2=r^2$$
\end{block}\img{htcirc01}}
\only<7>{\img{htcirc02}\centerline{ôÒÅÈÍÅÒÎÙÊ ÍÁÓÓÉ× × ÓÌÕÞÁÅ ÎÅÉÚ×ÅÓÔÎÙÈ ÃÅÎÔÒÁ É ÒÁÄÉÕÓÁ.}}
\end{frame}

\begin{frame}{ðÒÉÍÅÒ: ÄÁÔÞÉË ×ÏÌÎÏ×ÏÇÏ ÆÒÏÎÔÁ}
\img{Hough_ex}
\end{frame}

\begin{frame}{óÅÇÍÅÎÔÁÃÉÑ ÐÏ ÍÏÒÆÏÌÏÇÉÞÅÓËÉÍ ×ÏÄÏÒÁÚÄÅÌÁÍ}
\only<1>{\begin{block}{}
âÉÎÁÒÎÙÅ ÉÚÏÂÒÁÖÅÎÉÑ: ÉÔÅÒÁÔÉ×ÎÙÅ ÄÉÌÁÔÁÃÉÉ Ó ÐÏÓÔÒÏÅÎÉÅÍ ÐÅÒÅÇÏÒÏÄÏË × ÍÅÓÔÁÈ
ÏÂÒÁÚÏ×Á×ÛÉÈÓÑ ÐÅÒÅÓÅÞÅÎÉÊ.
\end{block}}
\only<2,3>{\begin{block}{}âÉÎÁÒÎÙÅ ÉÚÏÂÒÁÖÅÎÉÑ: ÐÒÅÏÂÒÁÚÏ×ÁÎÉÑ ÒÁÓÓÔÏÑÎÉÊ\end{block}}
\only<1>{\img[0.5]{watershed}}
\only<2>{\img[0.4]{wat01}}
\only<3>{\img[0.75]{wat02}}
\only<4>{\begin{block}{}
÷ ÏÂÝÅÍ ÓÌÕÞÁÅ: ÒÁÚÌÉÞÎÙÅ ÁÌÇÏÒÉÔÍÙ ÚÁÐÏÌÎÅÎÉÑ.
\end{block}
\img[0.7]{watershed01}}
\end{frame}

\begin{frame}{óÐÁÓÉÂÏ ÚÁ ×ÎÉÍÁÎÉÅ!}
\centering
\begin{minipage}{5cm}
\begin{block}{mailto}
eddy@sao.ru\\
edward.emelianoff@gmail.com
\end{block}\end{minipage}
\begin{block}{ìÉÔÅÒÁÔÕÒÁ}
\begin{itemize}
\item Gonzalez \& Woods. Digital Image Processing, 3rd edition. 2008.
\item Gonzalez \& Woods \& Eddins. Digital Image Processing Using MATLAB, 2nd edition. 2009.
\item \url{http://www.imageprocessingplace.com/root_files_V3/tutorials.htm}
\end{itemize}
\end{block}

\end{frame}
\end{document}