Add image processing - 2

Komp_obr_SFedU/07-iproc_2.tex

@@ -0,0 +1,509 @@
+\documentclass[10pt,pdf,hyperref={unicode}]{beamer}
+\hypersetup{pdfpagemode=FullScreen}
+\usepackage{lect}
+
+\title[ëÏÍÐØÀÔÅÒÎÁÑ ÏÂÒÁÂÏÔËÁ. ìÅËÃÉÑ 7.]{ëÏÍÐØÀÔÅÒÎÁÑ ÏÂÒÁÂÏÔËÁ ÒÅÚÕÌØÔÁÔÏ× ÉÚÍÅÒÅÎÉÊ}
+\subtitle{ìÅËÃÉÑ 7. ïÂÒÁÂÏÔËÁ ÉÚÏÂÒÁÖÅÎÉÊ, ÞÁÓÔØ 2}
+\date{}
+
+\def\pair#1#2{\ensuremath{\langle #1, #2\rangle}}
+
+\begin{document}
+% ôÉÔÕÌ
+\begin{frame}
+\maketitle
+\end{frame}
+% óÏÄÅÒÖÁÎÉÅ
+\begin{frame}
+\tableofcontents
+\end{frame}
+
+\section{÷ÅÊ×ÌÅÔÙ}
+\begin{frame}{÷ÅÊ×ÌÅÔÙ}
+\only<1>{ \begin{block}{òÁÚÌÏÖÅÎÉÅ ÆÕÎËÃÉÉ ÐÏ ÂÁÚÉÓÕ}
+ðÒÅÏÂÒÁÚÏ×ÁÎÉÅ æÕÒØÅ É ÌÀÂÙÅ ÄÒÕÇÉÅ ÐÒÅÏÂÒÁÚÏ×ÁÎÉÑ $f(x)$ ÐÏ ÂÁÚÉÓÕ $r(x,u)$ × 1-ÍÅÒÎÏÍ ×ÁÒÉÁÎÔÅ
+ÍÏÖÎÏ ÐÒÅÄÓÔÁ×ÉÔØ ×ÙÒÁÖÅÎÉÅÍ
+$$T(u)=\sum_{x=0}^{N-1}f(x)r(x,u),\qquad
+f(x)=\sum_{u=0}^{N-1}T(u)s(x,u).$$
+÷ ÍÁÔÒÉÞÎÏÍ ×ÉÄÅ: $\B{t}=\B{Rf}$ É $\B{f}=\B{St}$. ïÞÅ×ÉÄÎÏ, ÞÔÏ $\B{S}=\B{R}^{-1}$ É ÏÂÒÁÔÎÏ.
+åÓÌÉ ÂÁÚÉÓ $\B{S}$ ÏÒÔÏÎÏÒÍÉÒÏ×ÁÎ ($\B{S}^T\B{S}=\B{I}$), ÔÏ $\B{R}=\B{S}^T$.
+
+÷ Ä×ÕÍÅÒÎÏÍ ×ÉÄÅ $s=s(x,y,u,v)$, ÐÏÌÏÖÉÍ, ÞÔÏ ÑÄÒÏ~--- ÒÁÚÄÅÌÑÅÍÏÅ É ÓÉÍÍÅÔÒÉÞÎÏÅ, Ô.Å.
+$s=s(x,y)\cdot s(u,v)$. ÷ ÜÔÏÍ ÓÌÕÞÁÅ ÑÄÒÏ ÍÏÖÎÏ ÚÁÐÉÓÁÔØ × ×ÉÄÅ Ä×ÕÍÅÒÎÏÊ ÍÁÔÒÉÃÙ:
+$$\B{T}=\B{SFS}^T, \qquad \B{F}=\B{S}^T\B{FS}.$$
+\end{block}
+}\only<2>{
+\begin{block}{}
+òÁÓÓÍÏÔÒÉÍ ÐÒÏÓÔÅÊÛÉÊ ÂÁÚÉÓ:
+$$\B{s}_0=\frac{1}{\sqrt{2}}\begin{pmatrix}1\\1\end{pmatrix},\quad
+\B{s}_1=\frac{1}{\sqrt{2}}\begin{pmatrix}1\\-1\end{pmatrix};\qquad
+\B{A}=(\B{s}_0 \B{s}_1)^{T}=\frac{1}{\sqrt{2}}\begin{pmatrix}1 & 1\\ 1 & -1\end{pmatrix}.$$
+íÏÖÎÏ ÐÒÏ×ÅÒÉÔØ, ÞÔÏ ÄÁÎÎÙÊ ÂÁÚÉÓ~--- ÏÒÔÏÎÏÒÍÁÌØÎÙÊ.
+
+äÌÑ ÐÒÑÍÏÕÇÏÌØÎÙÈ ÉÚÏÂÒÁÖÅÎÉÊ ÒÁÚÍÅÒÏÍ $M\times N$ ($M$~ÓÔÒÏË É $N$~ÓÔÏÌÂÃÏ×) ÐÉËÓÅÌÅÊ ÑÄÒÁ ÂÕÄÕÔ
+ÉÍÅÔØ ÒÁÚÍÅÒÙ $M\times M$ É
+$N\times N$:
+$$\B{T}=\B{A}_M\B{FA}^T_N,\qquad \B{F}=\B{A}_M^T\B{TA}_N.$$
+
+÷ ÓÌÕÞÁÅ ËÏÍÐÌÅËÓÎÏÇÏ ÂÁÚÉÓÁ $\B{T}=\B{AFA}^T$, ÎÏ $\B{F}=\B{A}^{*T}\B{TA}^*$.
+\end{block}
+}\only<3>{
+\begin{block}{ìÏËÁÌÉÚÁÃÉÑ}
+äÅÌØÔÁ-ÆÕÎËÃÉÑ ÌÏËÁÌÉÚÏ×ÁÎÁ ÐÏ ×ÒÅÍÅÎÉ, ÎÏ ÎÅ ÉÍÅÅÔ ÌÏËÁÌÉÚÁÃÉÉ ÐÏ ÞÁÓÔÏÔÅ; ËÏÍÐÌÅËÓÎÁÑ
+ÓÉÎÕÓÏÉÄÁ~--- ÎÁÏÂÏÒÏÔ.\Ö ÷ÅÊ×ÌÅÔ\Î ÉÍÅÅÔ ÌÏËÁÌÉÚÁÃÉÀ ËÁË ÐÏ ÞÁÓÔÏÔÅ, ÔÁË É ÐÏ ×ÒÅÍÅÎÉ.
+\end{block}
+\img{tfloc}
+}\only<4>{
+\begin{block}{÷ÅÊ×ÌÅÔ}
+éÍÅÑ\Ö ÍÁÔÅÒÉÎÓËÉÊ ×ÅÊ×ÌÅÔ\Î $\psi(t)$, ÚÁÄÁÄÉÍ\Ö ÂÁÚÉÓ ×ÅÊ×ÌÅÔÏ×\Î ËÁË
+$$\psi_{s,\tau}=2^{s/2}\psi(2^st-\tau).$$
+äÌÑ ÄÉÓËÒÅÔÎÙÈ ÉÚÏÂÒÁÖÅÎÉÊ ÐÏÌÕÞÁÅÍ ÎÁÂÏÒ\Ö ÍÁÓÛÔÁÂÉÒÕÀÝÉÈ ÆÕÎËÃÉÊ\Î:
+$$\phi_{j,k}=2^{j/2}\phi(2^jx-k),$$
+$k$~ÚÁÄÁÅÔ ÓÍÅÝÅÎÉÅ ×ÅÊ×ÌÅÔÁ, $j$~-- ÅÇÏ ÍÁÓÛÔÁÂ.
+
+âÁÚÉÓ ×ÅÊ×ÌÅÔÏ× É ÍÁÓÛÔÁÂÉÒÕÀÝÉÈ ÆÕÎËÃÉÊ ÐÏÚ×ÏÌÑÅÔ ÐÒÏÉÚ×ÅÓÔÉ ÄÅËÏÍÐÏÚÉÃÉÀ ÉÚÏÂÒÁÖÅÎÉÊ.
+
+ïÄÎÏÍÅÒÎÙÊ ÓÌÕÞÁÊ:
+$$f(x)=\frac{1}{2}\left\{T_\phi(0,0)\phi(x)+T_\psi(0,0)\psi_{0,0}(x)+T_\psi(1,0)\psi_{1,0}(x)\cdots\right\}.$$
+\end{block}
+}\only<5>{
+íÁÓÛÔÁÂÉÒÕÀÝÁÑ ÆÕÎËÃÉÑ èÁÁÒÁ: $\phi(x)=1$ ÐÒÉ $0\le x\le 1$.
+\img{haarw}
+}\only<6>{
+÷ÅÊ×ÌÅÔ èÁÁÒÁ:
+$$\psi(x)=\begin{cases}
+1, & 0\le x< 0.5;\\
+-1, & 0.5\le x < 1;\\
+0, & \text{× ÏÓÔÁÌØÎÙÈ ÓÌÕÞÁÑÈ.}
+\end{cases}$$
+\img{haarx2}
+}\only<7>{
+ðÉÒÁÍÉÄÁ ÐÒÅÏÂÒÁÚÏ×ÁÎÉÊ
+\img{wpiramid}
+}\only<8>{
+\img[0.6]{wpiram}
+}
+\end{frame}
+
+\begin{frame}{}
+\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}: $A-B=\{c \;|\; c\in A, c\notin B\}=A \cap B^C$.
+\item {\bf óÔÒÕËÔÕÒÎÙÊ ÜÌÅÍÅÎÔ}: ÐÏÄÏÂßÅËÔ, ÐÏ ËÏÔÏÒÏÍÕ ÐÒÏ×ÏÄÑÔÓÑ ÍÏÒÆÏÌÏÇÉÞÅÓËÉÅ ÏÐÅÒÁÃÉÉ.
+\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}{}
+\only<1>{\img{opclos}}
+\only<2>{\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}
+
+
+\section{äÅËÏÎ×ÏÌÀÃÉÑ}
+\begin{frame}{äÅËÏÎ×ÏÌÀÃÉÑ}
+    \only<1>{
+        \begin{block}{}
+            $$I(x,y) = P(x,y)*O(x,y)+N(x,y),\quad\text{$P$~-- PSF}\quad\text{ÉÌÉ}$$
+            $$\FT{I}=\FT{O}\cdot\FT{P}+\FT{N}\quad\Arr\quad
+            \FT{O}=\frac{\FT{I} - \FT{N}}{\FT{P}}$$
+            $$\text{îÁÉÍÅÎØÛÉÅ Ë×ÁÄÒÁÔÙ:}\quad
+            \FT{O}=\frac{\FT{P}^*\FT{I}}{|\FT{P}|^2}$$
+            $$\text{òÅÇÕÌÑÒÉÚÁÃÉÑ ôÉÈÏÎÏ×Á, $\min(J_T)$ ($H$~-- HPF):}\quad
+            \quad J_T=||I-P*O|| - \lambda||H*O||,$$
+            $$\FT{O}=\frac{\FT{P}^*\FT{I}}{|\FT{P}|^2+\lambda|\FT{H}|^2}$$
+        \end{block}
+    }\only<2>{
+        \begin{block}{òÅÇÕÌÑÒÉÚÁÃÉÑ ÐÏ âÁÊÅÓÕ}
+            $$p(O|I)=\frac{p(I|O)\cdot p(O)}{p(I)}$$
+            $$\text{Maximum likelihood:}\quad \mathrm{ML}(O)=\max_O p(I|O)$$
+            $$\text{Maximum-a-posteriori solution:}\quad
+            \mathrm{MAP}(O)=\max_O p(I|O)\cdot p(O)$$
+        \end{block}
+        \begin{block}{}
+            \begin{itemize}
+                \item éÔÅÒÁÃÉÏÎÎÁÑ ÒÅÇÕÌÑÒÉÚÁÃÉÑ
+                \item ÷ÅÊ×ÌÅÔ-ÒÅÇÕÌÑÒÉÚÁÃÉÑ
+                \item \dots
+            \end{itemize}
+        \end{block}
+    }
+\end{frame}
+
+\begin{frame}{æÕÎËÃÉÑ ÒÁÓÓÅÑÎÉÑ ÔÏÞËÉ}
+    \only<1>{\img[0.6]{moffat}}
+    \only<2>{\begin{block}{}
+            \begin{itemize}
+                \item çÁÕÓÓ: $f(x) = f_0\exp\Bigl(\dfrac{-(x-x_0)^2}{2\sigma^2}\Bigr)$,
+                $\FWHM\approx2.355\sigma$
+                \item íÏÆÆÁÔ: $f(x) = f_0\Bigl(1+\dfrac{(x-x_0)^2}{\alpha^2}\Bigr)^{-\beta}$,
+                $\FWHM\approx2\alpha\sqrt{2^{1/\beta}-1}$
+                \item æÒÉÄ: $\FT{f} \propto \exp\Bigl[-(bu)^{5/3}\Bigr]$,
+                $\FWHM\approx 2.921 b$ (íÏÆÆÁÔ Ó $\beta=4.765$, ÔÉÐÉÞÎÙÅ ÖÅ $\beta=2.5\cdots4.5$).
+            \end{itemize}
+        \end{block}
+    }
+\end{frame}
+
+\section{ïÂÎÁÒÕÖÅÎÉÅ}
+\begin{frame}{ïÂÎÁÒÕÖÅÎÉÅ}
+    \begin{block}{ðÒÏÓÔÅÊÛÉÊ ÁÌÇÏÒÉÔÍ}
+        \begin{enumerate}
+            \item ÷ÙÞÉÓÌÅÎÉÅ É ×ÙÞÉÔÁÎÉÅ ÆÏÎÁ
+            \item ó×ÅÒÔËÁ Ó ÍÁÓËÏÊ É ÂÉÎÁÒÉÚÁÃÉÑ
+            \item ïÂÎÁÒÕÖÅÎÉÅ Ó×ÑÚÎÙÈ ÏÂÌÁÓÔÅÊ
+            \item õÔÏÞÎÅÎÉÅ ÆÏÎÁ, goto 1
+            \item ëÌÁÓÓÉÆÉËÁÃÉÑ, ÆÏÔÏÍÅÔÒÉÑ É Ô.Ð.
+        \end{enumerate}
+    \end{block}
+\end{frame}
+
+\begin{blueframe}{}
+    \img{objdet}
+\end{blueframe}
+
+\begin{blueframe}{éÚÏÆÏÔÙ}
+    \only<1>{\begin{block}{íÅÔÏÄ ÛÁÇÁÀÝÉÈ Ë×ÁÄÒÁÔÏ×}
+            âÉÎÁÒÉÚÕÅÍ ÉÚÏÂÒÁÖÅÎÉÅ ÐÏ ÚÁÄÁÎÎÏÍÕ ÐÏÒÏÇÕ. ðÏ ÓÏÓÅÄÑÍ ËÁÖÄÏÇÏ ÐÉËÓÅÌÑ ×ÙÞÉÓÌÑÅÍ
+            ÂÉÔÏ×ÕÀ ÍÁÓËÕ
+            ($0\div15$). ïÔ ÔÏÞËÉ $1\div14$ ÓÔÒÏÉÍ ÉÚÏÌÉÎÉÀ, ÓÏÏÔ×ÅÔÓÔ×ÅÎÎÏ ÍÅÎÑÑ ÚÎÁÞÅÎÉÑ ×
+            ÐÉËÓÅÌÑÈ ÍÁÓËÉ. ëÁÖÄÙÊ ÕÚÅÌ
+            ÉÚÏÌÉÎÉÉ~--- ÌÉÎÅÊÎÁÑ ÉÌÉ ÄÒÕÇÁÑ ÉÎÔÅÒÐÏÌÑÃÉÑ ÉÎÔÅÎÓÉ×ÎÏÓÔÉ × ÐÉËÓÅÌÑÈ ÏÒÉÇÉÎÁÌÁ.
+        \end{block}
+        \img[0.5]{isophotes}
+    }
+    \only<2>{\img{Marching_squares_algorithm}}
+\end{blueframe}
+
+\begin{frame}{WCS-ÐÒÉ×ÑÚËÁ}
+    \only<1>{
+        \img[0.6]{WCS_triangles}
+        \centerline{A.~P\'al, G.\'A.~Bakos. PASP {\bf 118}: 1474--1483, 2006. }}
+    \only<2>{
+        \img[0.65]{WCS_quad}
+        \centerline{\url{astrometry.net}}}
+    \only<3>{\begin{block}{}
+            \begin{itemize}
+                \item ðÏÌÏÖÅÎÉÅ ÎÅÓËÏÌØËÉÈ Ú×ÅÚÄ ÈÁÒÁËÔÅÒÉÚÕÅÔÓÑ ÐÁÒÁÍÅÔÒÏÍ, ÉÎ×ÁÒÉÁÎÔÎÙÍ Ë
+                ÚÅÒËÁÌÉÒÏ×ÁÎÉÀ, ÍÁÓÛÔÁÂÉÒÏ×ÁÎÉÀ,
+                ×ÒÁÝÅÎÉÀ É ÐÅÒÅÎÏÓÕ. õÓÔÏÊÞÉ×ÙÍ Ë ÛÕÍÕ.
+                \item ë×ÁÄÒÁÔÕ ABCD ÓÏÏÔ×ÅÔÓÔ×ÕÅÔ ÞÅÔÙÒÅÈÍÅÒÎÙÊ ËÏÄ × ÏÔÎÏÓÉÔÅÌØÎÙÈ ËÏÏÒÄÉÎÁÔÁÈ
+                ÔÏÞÅË C É D.
+                \item ðÒÏÂÌÅÍÁ ×ÙÒÏÖÄÅÎÉÑ: ÐÒÉ ÓÍÅÎÅ ÐÏÒÑÄËÁ A, B ÉÌÉ C, D ËÏÄ <<ÏÔÒÁÖÁÅÔÓÑ>>.
+                \item îÁ ÎÅÂÅ ÓÔÒÏÉÔÓÑ ÓÅÔËÁ Ó ÍÁÓÛÔÁÂÉÒÕÅÍÙÍ ÛÁÇÏÍ, ÐÏ ËÁÔÁÌÏÖÎÙÍ ÄÁÎÎÙÍ × ÅÅ
+                ÑÞÅÊËÁÈ ÏÐÒÅÄÅÌÑÀÔÓÑ Ë×ÁÄÒÁÔÙ
+                Ó ÎÉÓÐÁÄÁÀÝÅÊ ÑÒËÏÓÔØÀ Ú×ÅÚÄ.
+                \item ðÏÌÕÞÅÎÎÙÊ ÎÁÂÏÒ ËÏÄÏ× ÐÏÚ×ÏÌÑÅÔ ÉÄÅÎÔÉÆÉÃÉÒÏ×ÁÔØ ÕÞÁÓÔËÉ ÎÅÂÁ ×ÐÌÏÔØ ÄÏ
+                ÓÁÍÙÈ ÍÅÌËÉÈ ÍÁÓÛÔÁÂÏ× (ÎÕÖÎÙ
+                ÈÏÔÑ ÂÙ ÞÅÔÙÒÅ Ú×ÅÚÄÙ × ËÁÄÒÅ).
+                \item þÅÍ ÂÏÌØÛÅ Ú×ÅÚÄ ÎÁ ËÁÄÒÅ, ÔÅÍ ÎÁÄÅÖÎÅÊ ÂÕÄÅÔ ÉÄÅÎÔÉÆÉËÁÃÉÑ.
+            \end{itemize}
+        \end{block}
+    }
+\end{frame}
+
+\begin{blueframe}{ôÒÉÁÎÇÕÌÑÃÉÑ äÅÌÏÎÅ}
+    \img[0.6]{delaunay}
+\end{blueframe}
+
+\begin{blueframe}{äÉÁÇÒÁÍÍÙ ÷ÏÒÏÎÏÇÏ}
+    \only<1>{\img[0.6]{voronoi}}
+    \only<2>{\img[0.6]{delvor}}
+\end{blueframe}
+
+\begin{frame}{ó×ÏÊÓÔ×Á ÔÒÉÁÎÇÕÌÑÃÉÉ äÅÌÏÎÅ}
+    \begin{block}{}
+        \begin{itemize}
+            \item ôä ×ÚÁÉÍÎÏ ÏÄÎÏÚÎÁÞÎÏ ÓÏÏÔ×ÅÔÓÔ×ÕÅÔ ÄÉÁÇÒÁÍÍÅ ÷ÏÒÏÎÏÇÏ ÄÌÑ ÔÏÇÏ ÖÅ ÍÎÏÖÅÓÔ×Á
+            ÔÏÞÅË.
+            ëÁË ÓÌÅÄÓÔ×ÉÅ: ÅÓÌÉ ÎÉËÁËÉÅ ÞÅÔÙÒÅ ÔÏÞËÉ ÎÅ ÌÅÖÁÔ ÎÁ ÏÄÎÏÊ ÏËÒÕÖÎÏÓÔÉ, ôä ÅÄÉÎÓÔ×ÅÎÎÁ.
+            \item ôä ÍÁËÓÉÍÉÚÉÒÕÅÔ ÍÉÎÉÍÁÌØÎÙÊ ÕÇÏÌ ÓÒÅÄÉ ×ÓÅÈ ÕÇÌÏ× ×ÓÅÈ ÐÏÓÔÒÏÅÎÎÙÈ
+            ÔÒÅÕÇÏÌØÎÉËÏ×, ÔÅÍ
+            ÓÁÍÙÍ ÉÚÂÅÇÁÀÔÓÑ <<ÔÏÎËÉÅ>> ÔÒÅÕÇÏÌØÎÉËÉ.
+            \item ôä ÍÁËÓÉÍÉÚÉÒÕÅÔ ÓÕÍÍÕ ÒÁÄÉÕÓÏ× ×ÐÉÓÁÎÎÙÈ ÏËÒÕÖÎÏÓÔÅÊ.
+            \item ôä ÍÉÎÉÍÉÚÉÒÕÅÔ ÍÁËÓÉÍÁÌØÎÙÊ ÒÁÄÉÕÓ ÍÉÎÉÍÁÌØÎÏÇÏ ÏÂßÅÍÌÀÝÅÇÏ ÛÁÒÁ.
+            \item ôä  ÎÁ ÐÌÏÓËÏÓÔÉ ÏÂÌÁÄÁÅÔ ÍÉÎÉÍÁÌØÎÏÊ ÓÕÍÍÏÊ ÒÁÄÉÕÓÏ× ÏËÒÕÖÎÏÓÔÅÊ, ÏÐÉÓÁÎÎÙÈ ÏËÏÌÏ
+            ÔÒÅÕÇÏÌØÎÉËÏ×, ÓÒÅÄÉ ×ÓÅÈ ×ÏÚÍÏÖÎÙÈ ÔÒÉÁÎÇÕÌÑÃÉÊ.
+        \end{itemize}
+    \end{block}
+\end{frame}
+
+\begin{blueframe}{K-nearest}
+    \begin{columns}
+        \column{0.5\textwidth}
+        \begin{block}{}
+            ëÌÁÓÓÉÆÉËÁÃÉÑ ÏÂßÅËÔÁ ÐÏ $k$~ÂÌÉÖÁÊÛÉÍ ÓÏÓÅÄÑÍ. ÷ ÓÌÕÞÁÅ ÐÅÒ×ÏÊ ×ÙÂÏÒËÉ~---
+            ÔÒÅÕÇÏÌØÎÉË, × ÓÌÕÞÁÅ ×ÔÏÒÏÊ~---
+            Ë×ÁÄÒÁÔ.
+
+            $k$ ÍÏÖÅÔ ÂÙÔØ ÄÒÏÂÎÙÍ, ÅÓÌÉ ÐÒÉÍÅÎÑÔØ ×Ú×ÅÛÅÎÎÙÅ ÒÁÓÓÔÏÑÎÉÑ.
+        \end{block}
+        \column{0.5\textwidth}
+        \img{knearest}
+    \end{columns}
+\end{blueframe}
+
+\begin{frame}{ðÒÏÇÒÁÍÍÎÏÅ ÏÂÅÓÐÅÞÅÎÉÅ}
+    \begin{block}{\url{http://heasarc.gsfc.nasa.gov/docs/heasarc/astro-update/}}
+        \begin{itemize}
+            \item ASTROPY: A single core package for Astronomy in Python
+            \item Aladin: An interactive software sky atlas
+            \item CFITSIO: FITS file access subroutine library
+            \item GSL: GNU Scientific Library
+            \item IDLAUL: IDL Astronomical Users Library
+            \item IRAF: Image Reduction and Analysis Facility
+            \item MIDAS: Munich Image Data Analysis System
+            \item PyRAF: Run IRAF tasks in Python
+            \item SAOImage ds9: FITS image viewer and analyzer
+            \item SEXTRACTOR: Builds catalogue of objects from an astronomical image
+            \item WCSLIB: World Coordinate System software library
+            \item \dots~\url{http://tdc-www.harvard.edu/astro.software.html}
+        \end{itemize}
+    \end{block}
+\end{frame}
+
+\begin{frame}{ìÉÔÅÒÁÔÕÒÁ}
+    \begin{itemize}
+        \item W. Romanishin. An Introduction to Astronomical Photometry Using CCDs.
+        \item Jean-Luc Starck and Fionn Murtagh. Handbook of Astronomical Data Analysis.
+        \item Gonzalez \& Woods. Digital Image Processing, 4th edition. 2018. ISBN 10: 1-292-22304-9
+        \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{frame}
+
+
+\begin{frame}{óÐÁÓÉÂÏ ÚÁ ×ÎÉÍÁÎÉÅ!}
+\centering
+\begin{minipage}{5cm}
+\begin{block}{mailto}
+eddy@sao.ru\\
+edward.emelianoff@gmail.com
+\end{block}\end{minipage}
+\end{frame}
+\end{document}

Komp_obr_SFedU/Materials4Pract/04/F.m

@@ -0,0 +1,4 @@
+function F = F(x)
+    F(1) = exp(-exp(-(x(1)+x(2)))) - x(2)*(1+x(1).^2);
+    F(2) = x(1).*cos(x(2)) + x(2).*sin(x(1)) - 0.5;
+endfunction

Komp_obr_SFedU/Materials4Pract/04/i1.m

@@ -0,0 +1,3 @@
+function y = i1 (x)
+    y = x .* sin (1./x) .* sqrt (abs (1 - x));
+endfunction

Komp_obr_SFedU/Materials4Pract/04/ode1.m

@@ -0,0 +1,3 @@
+function xdot = ode1(x, t)
+    xdot = -exp(-t)*x^2;
+endfunction

Komp_obr_SFedU/Materials4Pract/04/vdp1.m

@@ -0,0 +1,4 @@
+% Initialisation of Van der Pol with mu=1
+function dydt = vdp1(t,y)
+    dydt = [y(2); (1-y(1)^2)*y(2)-y(1)];
+endfunction

Komp_obr_SFedU/Materials4Pract/04ans/test.m

@@ -0,0 +1,5 @@
+function A = test(x)
+    A(1) = 2*(x(1) - 4).^2 + 7*(x(2)-8).^2 - x(3).^2;
+    A(2) = 5*(x(1) - 1).^2 - 4*(x(2)+3).^2 + 2* x(3).^2 + 1;
+    A(3) = x(1).^2 + x(2)^2 + x(3)^2;
+endfunction

Komp_obr_SFedU/Materials4Pract/04ans/testans

@@ -0,0 +1 @@
+9.54, 3.44, -7.91