More on scaling.
--- a/doc/Makefile Thu Nov 15 18:47:08 2007 +0100
+++ b/doc/Makefile Thu Nov 15 19:24:24 2007 +0100
@@ -6,6 +6,7 @@
house-bleeding.pdf \
lena-blocking.pdf \
bwlines.pdf \
+ escalat422fancy.pdf \
cadena.pdf
memoria.pdf: memoria.tex $(INCLUDES)
--- a/doc/cited.bib Thu Nov 15 18:47:08 2007 +0100
+++ b/doc/cited.bib Thu Nov 15 19:24:24 2007 +0100
@@ -356,3 +356,11 @@
journal = "IEEE International Conference on Image Processing (ICIP),
Singapore"
}
+
+@manual{jfif,
+ title = "JPEG File Interchange Format, Version 1.02",
+ author = "Eric Hamilton",
+ note = "Version 1.02",
+ month = "September",
+ year = "1992"
+}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
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--- a/doc/memoria.tex Thu Nov 15 18:47:08 2007 +0100
+++ b/doc/memoria.tex Thu Nov 15 19:24:24 2007 +0100
@@ -1,4 +1,4 @@
-\documentclass[catalan,a4paper,titlepage,12pt]{article}
+\documentclass[catalan,a4paper,titlepage,12pt]{report}
\usepackage{graphicx}
\usepackage{ucs}
\usepackage[utf8x]{inputenc}
@@ -44,9 +44,9 @@
\maketitle
-\section{Planetjament del problema}
+\chapter{Planetjament del problema}
-\subsection{La codificació JPEG}
+\section{La codificació JPEG}
\revisar{Això ve de la Wikipedia. Cal citar-la? Ja la referencio un altre cop
més tard, pels dibuixos}
@@ -100,7 +100,7 @@
tècniques que pretenen aprofitar millor la informació del JPEG per a reconstruir
una versió més agradable de la imatge original codificada.
-\subsection{Popularitat}
+\section{Popularitat}
Des de l'establiment de l'estàndard JPEG com a norma ISO (10918-1) el 1994, i de
la donació al domini públic de la implementació coneguda amb el nom de
@@ -161,7 +161,7 @@
procurat que l'usuari no necessiti coneixements experts de JPEG o de programació
per a dur a terme les descodificacions.
-\subsection{Les pèrdues al JPEG}
+\section{Les pèrdues al JPEG}
\label{sec:perdues}
% TODO: mal sangrat
@@ -203,7 +203,7 @@
\end{enumerate}
-\subsubsection{Plans de color i delmat}
+\subsection{Plans de color i delmat}
\label{sec:plans-color}
Les nostres pantalles solen utilitzar tres plans per a determinar la imatge a
@@ -260,7 +260,31 @@
plans, però sense delmar els plans de color. Ja no s'hi aprecia tant el
vessament.}
-\subsubsection{Blocs i quantització dels coeficients}
+\begin{table}[!htp]
+\centering
+\begin{tabular}{|c|c|p{9cm}|}
+%\hline
+%{\bfseries 4:x:y} & {\bfseries Y,Cb,Cr} &
+%{\bfseries Significat} \\
+%\hline
+\hline
+4:4:4 & 1x1,1x1,1x1 & Igual resolució de lluminositat i color \\
+\hline
+4:2:2 & 2x1,1x1,1x1 & La meitat de punts de color en horitzontal \\
+\hline
+4:2:0 & 2x2,1x1,1x1 & La meitat de punts de color en horitzontal, i la meitat
+en vertical \\
+\hline
+4:1:1 & 4x1,1x1,1x1 & Un quart de punts de color en horitzontal \\
+\hline
+\end{tabular}
+\caption{\label{tab:notacions}Notacions pels delmats dels canals de color
+per a les components YCbCr. La segona és típica de les càmeres digitals, i la
+tercera, el delmat per defecte al guardar imatges a diversos programes
+informàtics.}
+\end{table}
+
+\subsection{Blocs i quantització dels coeficients}
La imatge es parteix en blocs de 8x8 pícsels, i cada bloc es codifica de manera
independent. La informació que es llença s'escull exclusivament en
@@ -359,7 +383,7 @@
superfícies de lluminositat similar. Al mig, el mateix tall de la imatge
original, per comparar.}
-\section{Qualitat de les imatges}
+\chapter{Qualitat de les imatges}
En aquest treball ens proposem millorar la descompressió d'imatges JPEG. Per
tant, cal que definim la qualitat de la imatge resultant d'una manera
@@ -467,7 +491,7 @@
llavors en la majoria dels casos $1 < S < 10$.
\end{itemize}
-\section{Tècniques}
+\chapter{Tècniques}
\label{sec:tecniques}
A la l'apartat \ref{sec:perdues} hem explicat quines pèrdues de senyal
@@ -478,7 +502,7 @@
el convencional. Hem procurat estudiar l'estat de l'art del JPEG, i classificar
els mètodes més interessants segons les tècniques en què es basen.
-\subsection{Projecció sobre l'espai de quantització}
+\section{Projecció sobre l'espai de quantització}
Aquesta tècnica no millora les imatges en si, però sí que la utilitzen a molts
mètodes. Podem diferenciar els mètodes en dos grans grups: els de \emph{dins la
@@ -531,7 +555,7 @@
0,5]$ al voltant del centre de l'interval de quantització. A \cite{liew2004},
per exemple, consideren millors els resultats amb un marge de $[-0,3, 0,3]$.
-\subsection{Coeficients com a variables aleatòries}
+\section{Coeficients com a variables aleatòries}
La descodificació convencional d'agafar el punt mig de l'interval de
quantització per cada coeficient compleix la \emph{no destrucció}. Aquest cas
@@ -548,7 +572,7 @@
descodificar. El segon, basant-la amb estadístiques d'altres
imatges.\revisar{Com ho fa exactament el primer?}
-\subsection{Segmentació i suavitzat}
+\section{Segmentació i suavitzat}
Un dels efectes que més es distingeixen a les imatges codificades amb una
relació de compressió alta (més denses) és el de blocs. A les zones de baixes
@@ -575,7 +599,7 @@
poc pes dels punts del voltant; i a \cite{alfahoum2001}, \cite{pham2005} i
\cite{trianta2003} fan servir filtres direccionals.
-\subsection{\index{POCS}POCS - Projecció sobre conjunts convexos}
+\section{\index{POCS}POCS - Projecció sobre conjunts convexos}
Els mètodes basats en POCS solen donar molts bons resultats, i apareixen a la
literatura des dels inicis de l'ús del JPEG. Malauradament l'algorisme és lent,
@@ -618,7 +642,7 @@
fins a sis conjunts per eliminar \emph{l'efecte de blocs} i amb especial
incís \emph{l'efecte d'ones}.
-\subsection{\index{MAP}Maximum A Posteriori}
+\section{\index{MAP}Maximum A Posteriori}
Aquesta tècnica és similar a la de POCS, ja que és iterativa, i té projeccions
sobre conjunts convexes. Estrictament, a POCS els mètodes venen
@@ -637,7 +661,7 @@
aleatori de Huber-Màrkov. A \cite{froment2005} utilitzen una versió adaptada
de la norma de Variació Total (TV).
-\subsection{Altres mètodes de recuperació de plans}
+\section{Altres mètodes de recuperació de plans}
Alguns mètodes (\cite{jung1998}, \cite{kwon2002})
utilitzen transformacions d'ondetes, ja que aquestes aporten
@@ -649,23 +673,23 @@
versions desplaçades de la imatge descodificada de manera convencional, fent una
mitjana de les múltiples versions de les imatges desplaçades descodificades.
-\subsection{Recuperació del color basada en lluminància}
+\section{Recuperació del color basada en lluminositat}
Tal com hem vist a l'apartat \ref{sec:plans-color},
el JPEG aïlla tota la informació de color en dos
-plans que es codifiquen a menys qualitat que el de lluminància. Totes les
+plans que es codifiquen a menys qualitat que el de lluminositat. Totes les
tècniques que hem presentat fins ara es poden utilitzar per recuperar qualsevol
dels plans del JPEG, però a la literatura també trobem tècniques que utilitzen
-la correlació entre lluminància i color per a recuperar millor els plans
+la correlació entre lluminositat i color per a recuperar millor els plans
cromàtics.
-A \cite{coudoux2004} detecten les cantonades del pla de lluminància, i les
+A \cite{coudoux2004} detecten les cantonades del pla de lluminositat, i les
utilitzen amb un algorisme adaptatiu
per corregir els vessaments de color deguts a l'escalat. A \cite{sugita2006}
ponderen els canvis d'intensitat dels plans de color d'acord amb els canvis
-d'intensitat del pla de lluminància.
+d'intensitat del pla de lluminositat.
-\section{Programari}
+\chapter{Programari}
Com hem vist a l'apartat anterior, trobem nombrosos articles sobre la millora de
la descompressió JPEG. Malauradament, no trobem els algorismes implementats en
@@ -742,7 +766,7 @@
texte. Per a les mesures referencials haurem d'escollir les dues imatges a
comparar, en comptes de només una.
-\subsection{La cadena de descodificació}
+\section{La cadena de descodificació}
Un cop l'usuari hagi determinat quina imatge JPEG vol recuperar, li caldrà
decidir com es descodificarà. L'aplicació li donarà un esquema de la
@@ -771,7 +795,7 @@
l'algorisme (de la baula anterior) com de la configuració dels seus
paràmetres interns.
-\subsubsection{Desquantització i IDCT 2D de cada pla}
+\subsection{Desquantització i IDCT 2D de cada pla}
\begin{description}
\item[entrada] els intervals de quantització d'un pla de la imatge ocdificada
@@ -789,7 +813,7 @@
primer coeficient de cada bloc) com variables aleatòries exponencials d'igual
mitjana, com a \cite{trianta2003}. L'usuari pot configurar la mitjana.
-\subsubsection{Restaurador de pla}
+\subsection{Restaurador de pla}
\begin{description}
\item[entrada] els intervals de quantització d'un pla de la imatge ocdificada
@@ -845,15 +869,50 @@
resultats competitius amb altres algorismes, segons el tipus de imatge i el
tipus de codificació JPEG.
-\subsubsection{Escalador dels plans}
+\subsection{Escalador dels plans}
\begin{description}
\item[entrada] $n$ plans independents, possiblement alguns delmats
\item[sortida] $n$ plans de color
\end{description}
+Tal com hem explicat a l'apartat \ref{sec:plans-color}, alguns dels plans de color de la imatge poden haver estat delmats abans de codificar independent els
+plans (DCT 2D i quantització). La imatge final descodificada ha de tenir tots
+els plans de color de la mateixa mida. Per això, ens cal interpolar els plans
+que hem descodificat, que havien set delmats, de manera que adquireixin les
+seves dimensions originals. Cal recordar que els delmats sempre seran dividint
+les dimensions originals per un número enter.
-\subsubsection{Canvi de plans de color}
+Al programa hem implementat tres tipus d'escaladors. El primer simplement
+replica els punts per aconseguir les dimensions desitjades. Per exemple, si
+tenim els valors per punt en una fila $1,5,3,2,6$, i ens cal doblar la seva
+mida horitzontal, l'algorisme ens donarà $1,1,5,5,3,3,2,2,6,6$. La
+\texttt{libjpeg} també inclou una implementació d'aquest escalador.
+
+El segon escalador, provinent també de la \texttt{libjpeg}, interpola
+els punts del pla final a partir de la versió delmada descodificada, tot i que
+només funciona pels delmats 4:2:2 i 4:2:0. \marginpar{Cal citar on explico la
+notació 4:x:y?}. En el cas de 4:2:2, interpola cada punt final amb els dos punts
+més propers del pla delmat. Hem de recordar que segons l'especificació JFIF
+\cite{jfif}, els plans
+delmats a la meitat horitzontal, no tindran punts coincidents amb els del pla
+final. Així doncs, obtenim els punts de color per les posicions dels punts de
+lluminositat de la següent manera:
+\[ \hat p_o = \frac{3}{4} p_1 + \frac{1}{4} p_2 \]
+on $\hat p_o$ és un punt d'una línia final, $p_1$ és el punt més proper a
+$\hat p_o$
+de la línia delmada, i $p_2$ el segon punt més proper. La Figura
+\ref{fig:fancy422} representa visualment el procés.
+
+\figuraw{10cm}{escalat422fancy.pdf}{\label{fig:fancy422}Reescalat d'una línia
+de la component de color de delmat 4:2:2 (a dalt)
+a la mida final determinada per la lluminositat (a baix), mitjançant
+interpolació dels dos punts més propers.}
+
+En el cas 4:2:0 l'escalador interpola cada punt final mitjançant
+els quatre punts més propers.
+
+\subsection{Canvi de plans de color}
\begin{description}
\item[entrada] $n$ plans de color
