Acabant de revisar el capítol de Programari.
--- a/doc/Makefile Fri Nov 16 23:55:09 2007 +0100
+++ b/doc/Makefile Tue Nov 20 12:23:47 2007 +0100
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bwlines.pdf \
escalat422fancy.pdf \
escalat420fancy.pdf \
+ lumscaler422.pdf \
+ lumscaler420.pdf \
+ co-inter-situats422.pdf \
cadena.pdf
memoria.pdf: memoria.tex $(INCLUDES)
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--- a/doc/memoria.tex Fri Nov 16 23:55:09 2007 +0100
+++ b/doc/memoria.tex Tue Nov 20 12:23:47 2007 +0100
@@ -37,7 +37,7 @@
\caption{#3}
\end{figure}
}
-
+\newcommand{\reg}{$^\text{\textregistered}$}
\makeindex
\begin{document}
@@ -137,7 +137,8 @@
personals actuals. Tampoc hi ha implementacions en maquinari per part dels
fabricants de càmeres digitals. Tanmateix, per posar un exemple popular, el
% ref http://lists.brouhaha.com/pipermail/tumble-devel/2004q4/000007.html
-programari Adobe Acrobat des de la versió 6 suporta la codificació JPEG2000 dins
+programari Adobe Acrobat\reg des de la versió 6 suporta la
+codificació JPEG2000 dins
el seu format PDF 1.5. La majoria d'aplicacions d'Adobe, en la seva versió
actual, suporten el format. D'acord amb experts en el camp de fotografia, per
això, per a densitats d'informació similars, opinen que JPEG encara els dóna
@@ -534,9 +535,9 @@
l'interval.
\begin{equation}
z'_i = \begin{cases}
- (\hat y_i - 0.5) Q_i & z_i < (\hat y_i - 0.5) Q_i \\
- (\hat y_i + 0.5) Q_i & z_i > (\hat y_i + 0.5) Q_i \\
- z_i & \textrm{altrament}
+ (\hat y_i - 0.5) Q_i & \text{si} \, z_i < (\hat y_i - 0.5) Q_i \\
+ (\hat y_i + 0.5) Q_i & \text{si} \, z_i > (\hat y_i + 0.5) Q_i \\
+ z_i & \text{altrament}
\end{cases}
\end{equation}
@@ -649,7 +650,7 @@
definits pels conjunts convexes involucrats. Amb la tècnica de MAP el que es
busca és la minimització d'una funció.
-En general l'objectiu és minimitzar una funció, sempre i quan mentenim els
+En general l'objectiu és minimitzar la funció sempre i quan mentenim els
coeficients dins els intervals de quantització. Si $\hat z$ és la nostra imatge
estimada a la descodificació, i $Z$ és el conjunt d'imatges amb coeficients dins
el QCS,
@@ -693,11 +694,11 @@
Com hem vist a l'apartat anterior, trobem nombrosos articles sobre la millora de
la descompressió JPEG. Malauradament, no trobem els algorismes implementats en
-cap mena d'aplicació per a l'usuari final. GIMP i Adobe Photoshop
-\textregistered, possiblement els processadors de mapes de bits més populars,
+cap aplicació popular. GIMP i Adobe
+Photoshop\reg, possiblement els processadors de mapes de bits més populars,
només suporten la descodificació convencional. A la última versió (6b) de la
\texttt{libjpeg} tampoc hi trobem res d'especial, tot i que a la documentació
-fan una declaració d'intencions per incorporar mètodes de restauració a la
+hi trobem una declaració d'intencions per incorporar mètodes de restauració a la
versió 7, però sembla que el desenvolupament d'aquesta llibreria es va aturar
precisament a la 6b el 1998.
@@ -707,24 +708,25 @@
la codificació JPEG es continua utilitzant activament, i per tant molts usuaris
es poden beneficiar d'una iniciativa com aquesta.
-Quan hem buscat implementacions dels algorismes, n'hem trobat molt poques,
-i la majoria d'aquestes poques estaven escrites en Matlab. Els interprets de
+Quan hem buscat implementacions dels algorismes de restauració analitzats,
+n'hem trobat molt poques,
+i la majoria d'aquestes poques estaven escrites en Matlab. Els intèrprets de
Matlab els trobem pràcticament només a les universitats o dins departaments
-d'investigació d'empreses, però la majoria de professionals de la imatge ni el
-posseiran ni el sabran utilitzar. Nosaltres hem desenvolupat tota l'aplicació i
+d'investigació d'empreses, però la majoria de professionals de la imatge ni els
+posseiran ni els sabran utilitzar. Nosaltres hem desenvolupat tota l'aplicació i
els algorismes en C i C++, ja que ens semblen els llenguatges més populars i a
l'abast de qualsevol gràcies a diversos compiladors i enllaçadors lliures
disponibles. Aquí tenim un llistat de les principals característiques
del programa:
\begin{itemize}
-\item Només permet manipular un JPEG alhora, junt amb versions
+\item Només permet manipular una imatge JPEG alhora, junt amb versions
recuperades o que teníem guardades a disc.
\item Tot el procés i emmagatzematge intern de la informació de les imatges
-es realitza en punt flotant (\texttt{float} en C), per evitar pèrdues per
+es realitza en coma flotant (\texttt{float} en C), per evitar pèrdues per
arrodoniment als càlculs.
\item El programa requereix que l'usuari entengui la part de descodificació JPEG
que hem explicat al primer apartat, ja que
-és l'usuari qui determinarà com es realitzaran diversos passos d'aquesta
+l'usuari determinarà com es realitzaran diversos passos d'aquesta
descodificació.
\end{itemize}
@@ -737,10 +739,12 @@
\item No ens importa la complexitat de l'algorisme en temps de computació o
memòria. No tractarem vídeo, sino imatges estàtiques. Alguns articles presenten
novetats exclusivament en el camp de la restauració ràpida, tot i que no
-aconsegueixen recuperacions tan bones com els algorismes lents.
+aconsegueixen recuperacions tan bones com alguns algorismes més lents.
\item Hem considerat que els exemples d'imatge presentats al mateix article
-ofereixen una bona idea del millor que pot assolir l'algorisme. Creiem que
-alguns articles presenten molt poca millora com per a tenir-los en compte en una
+ofereixen una bona idea del millor resultat que l'algorisme permet assolir.
+Creiem que
+alguns articles presenten molt poca millora (valorant subjectivament a ull nu)
+com per a tenir-los en compte en una
implementació.
\item L'algorisme ha de permetre millorar imatges en general. Alguns només
milloren les zones de baixes freqüències, o fins i tot només serveixen per a
@@ -748,9 +752,9 @@
\item L'efecte de l'algorisme s'ha de caracteritzar per pocs paràmetres, i
aquests han de tenir una relació monòtona amb els seus efectes.
En la majoria de casos l'usuari no
-entendrà internament algorisme, i variarà intuitivament els paràmetres. Si
+entendrà internament algorisme, i en variarà intuitivament els paràmetres. Si
l'usuari no pot entendre l'efecte que té cada paràmetre, segurament refusarà
-manipular-lo.
+manipular-lo, o fins i tot utilitzar-lo.
\end{itemize}
Podem classificar els algorismes segons la seva funció. A la nostra aplicació
@@ -762,7 +766,7 @@
\end{itemize}
A qualsevol imatge que haguem carregat dins de l'aplicació li podem aplicar els
-algorismes de mesura, i obtindrem els resultats en un nou quadre de
+algorismes de mesura, i obtindrem els resultats en un nou quadre flotant de
texte. Per a les mesures referencials haurem d'escollir les dues imatges a
comparar, en comptes de només una.
@@ -786,13 +790,14 @@
baules (amb el contorn més gruixut) on hi podem col·locar diversos
algorismes. Les línies de punts separen els diferents tipus d'algorismes
acceptats. D'esquerra a dreta: \emph{desquantitzador i IDCT2D},
-\emph{restaurador de pla}, \emph{escalador}, \emph{canvi de plans de color}.}
+\emph{restauradors de pla}, \emph{escalador}, \emph{canvis de plans de color}.}
-L'aplicació posarà a la disposició de l'usuari uns quants algorismes de cada
-tipus, i aquest podrà col·locar els que cregui adients a la cadena, en forma de
-baula. Alguns dels algorismes que col·locarem a les baules són configurables.
+L'aplicació posarà a disposició de l'usuari uns quants algorismes de cada
+tipus, i aquest podrà col·locar els que cregui adients a la cadena, com si es
+tractéssin de baules.
+Alguns dels algorismes que col·locarem a les baules són configurables.
Això vol dir que el resultat que donin dependrà tant de l'entrada de
-l'algorisme (de la baula anterior) com de la configuració dels seus
+l'algorisme (provinent de la baula anterior) com de la configuració dels seus
paràmetres interns.
\subsection{Desquantització i IDCT 2D de cada pla}
@@ -811,7 +816,7 @@
convencional de JPEG escollint el punt mig dels intervals. I el segon considera
la informació dels coeficients AC (tots menys la component contínua DC, el
primer coeficient de cada bloc) com variables aleatòries exponencials d'igual
-mitjana, com a \cite{trianta2003}. L'usuari pot configurar la mitjana.
+mitjana, com a \cite{trianta2003}. L'usuari pot configurar-ne la mitjana.
\subsection{Restaurador de pla}
@@ -823,13 +828,13 @@
La majoria d'algorismes de restauració de JPEGs que hem trobat encaixen dins
aquesta categoria. Partint d'un pla inicial (als articles sol ser una
-descompressió convencional) utilitzen diverses tècniques per obtenir una versió
+descodificació convencional) utilitzen diverses tècniques per obtenir una versió
millor del mateix pla. A l'apartat \ref{sec:tecniques} ja hem parlat d'aquest
tipus d'algorismes.
Cal destacar que als articles utilitzen imatges d'escala de grisos ja que
exclusivament intenten millorar un pla de la imatge. A la nostra aplicació podem
-utilitzar els algorismes a qualsevol dels plans del JPEG. Igualment, podem
+utilitzar aquests algorismes a qualsevol dels plans del JPEG. Igualment, podem
encadenar tants algorismes d'aquests tipus com volguem, on cada un determinarà
la imatge inicial del seu successor.
@@ -841,28 +846,29 @@
projecció com a algorisme independent. A part de les
propostes d'articles, inclou un
senzill algorisme de millora de les zones amb textura desenvolupat per nosaltres
-mateixos que aprofita la naturalesa de l'aplicació: combinar i encadenar
+mateixos que aprofita la naturalesa del programa: combinar i encadenar
tècniques. L'explicarem més endavant a l'apartat \ref{sec:hcontrast}.
Finalment, la implementació actual també inclou uns mòduls especials
que ens permeten alterar els
plans mitjançant una altra aplicació informàtica. Són els següents:
\begin{itemize}
-\item \emph{salvar pla a disc}. Si l'usuari col·loca aquesta funció dins una baula de
+\item \emph{salvar pla a disc}. Si l'usuari col·loca aquesta funció dins
+'duna baula de
restauració de pla, al aplicar la descodificació definida per la cadena, el pla
d'entrada de la baula s'escriurà a disc. Llavors l'usuari pot utilitzar el seu
-programa preferit de manipulació fotogràfica amb les tècniques que cregui
-convenients, i guardar-les a disc, utilitzant després la funció que ve a
-continuació.
+programa preferit de manipulació fotogràfica aplicant les tècniques que cregui
+convenients al pla, i guardar els canvis per a reincorporar-los a la cadena amb
+la funció que descrivim a continuació.
\item \emph{carregar pla de disc}. El pla d'entrada d'aquest algorisme
s'ignorarà completament, i el pla de sortida vindrà determinat per un fitxer
guardat a disc.
\end{itemize}
Aquestes dues funcions les hem utilitzat a la pràctica per millorar els plans
amb un filtre del GIMP\footnote{GNU Image Manipulation Program
-\url{http://www.gimp.org/}}, el suavitzat Gaussià sel·lectiu.
+\url{http://www.gimp.org/}}:, el suavitzat Gaussià sel·lectiu.
Aquesta tècnica també la utilitzen
combinada amb altres a \cite{queiroz1998} i \cite{kim1999}, i alguns manuals de
-GIMP la recomanen per a eliminar part del soroll d'algunes imatges JPEG.
+GIMP la recomanen per eliminar part del soroll d'algunes imatges JPEG.
Si utilitzem les funcions de \emph{salvar el
pla}, apliquem el filtre amb el GIMP, \emph{el carreguem a la cadena}, i després
hi apliquem una \emph{projecció sobre l'espai de quantització}, obtenim
@@ -873,44 +879,49 @@
\begin{description}
\item[entrada] $n$ plans independents, possiblement alguns delmats
-\item[sortida] $n$ plans de color
+\item[sortida] $n$ plans, tots de la mateixa mida
\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
+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
+independentment 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.
+els plans de color de la mateixa mida. Per això al descodificar
+ens cal interpolar els plans delmats, de manera que adquireixin les
+seves dimensions originals. Cal recordar que el codificador delmarà els plans
+dividint
+les dimensions originals per un número enter, i els delmats més comuns són 4:2:2
+i 4:2:0.
Al programa hem implementat tres tipus d'escaladors. El primer simplement
-replica els punts per aconseguir les dimensions desitjades. Per exemple, si
+duplica 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
+El segon escalador, provinent també de la \texttt{libjpeg}
+(on l'anomenen \emph{fancy upsampler}), interpola
+linealment 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
+delmats a la meitat en 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 el valor d'un punt d'una línia final,
-$p_1$ és el del punt més proper a
-$\hat p_o$
-de la línia delmada, i $p_2$ el del segon punt més proper. La Figura
+on $\hat p_o$ és el valor d'un punt d'una fila final,
+$p_1$ és el del punt de la fila delmada més proper a
+$\hat p_o$, i $p_2$ el del segon punt més proper. La Figura
\ref{fig:fancy422} representa visualment el procés.
-\figuraw{10cm}{escalat422fancy.pdf}{\label{fig:fancy422}Reescalat d'una línia
+\figuraw{10cm}{escalat422fancy.pdf}{\label{fig:fancy422}Reescalat d'una fila
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
+En el cas 4:2:0 el segon escalador interpola cada punt final mitjançant
els quatre punts més propers:
\[ \hat p_o = \frac{9}{16} p_1 + \frac{3}{16} (p_2 + p_3) + \frac{1}{16} p_4 \]
on $\hat p_o$ és el valor d'un punt del pla final, $p_2$ i $p_3$
@@ -921,7 +932,27 @@
\figuraw{10cm}{escalat420fancy.pdf}{\label{fig:fancy420}Reescalat d'una porció
de la component de color de delmat 4:2:0 (en forma de creu dreta)
a la mida final determinada per la lluminositat (en forma de cercles),
-mitjançant interpolació entre els quatre punts més propers.}
+mitjançant interpolació linial entre els quatre punts més propers.}
+
+Finalment, hem implementat un tercer escalador, basat en \cite{sugita2006},
+on utilitzem una tècnica similar a la interpolació linial,
+però a més d'obtenir el
+color de cada punt final basant-nos amb els quatre punts de color més propers,
+ho ponderem segons les variacions de llum del pla de lluminositat (quan no ha
+estat delmat). A
+l'Annexe \ref{sec:colorponderat} expliquem l'algorisme en detall.
+
+Tot i que fins ara hem parlat del cas general de que les imatges JPEG tenen
+unes mides múltiples de la mida de bloc (8 pícsels), en realitat aquesta
+condició no s'exigeix a les imatges a codificar. La mida original de la imatge
+està escrita al contenidor del JPEG, i l'escalador del descodificador és
+l'encarregat de retallar
+els últims blocs en horitzontal i vertical per a aconseguir la imatge final de
+la mida que toca. Així, si una imatge medeix 124 pícsels d'amplada,
+s'haurà codificat amb 16 blocs de 8 pícsels, però de l'últim
+bloc de cada fila (codificada d'esquerra a dreta)
+només tindrem en compte la meitat esquerra descodificada
+de 4 pícsels d'amplada.
\subsection{Canvi de plans de color}
@@ -938,8 +969,111 @@
tant, per a mostrar-los correctament a l'aplicació,
necessitarem un algorisme conversor de YCbCr a RGB.
-Les extensions JFIF permeten codifcar la imatge en varis plans de color. Per
-defecte amb YCbCr, però també s'hi poden indicar codificacions RGB o CMYK.
+Les extensions JFIF permeten anotar en quins plans de color s'ha codificat la
+imatge. Per defecte es codifica amb YCbCr,
+però també s'hi poden indicar codificacions RGB o CMYK. Nosaltres només hem
+implementat el conversor YCbCr a RGB, ja que no ens hem trobat imatges que
+utilitzessin altres configuracions de color.
+
+\chapter{Anàlisi dels mètodes implementats}
+
+\section{Suavitzat excessiu}
+
+\section{Pèrdua de contrast}
+
+\subsection{Algorisme HContrast}
+\label{sec:hcontrast}
+
+\section{Difícil parametrització}
+
+\chapter{Conclusions i treball futur}
+
+\appendix
+
+\chapter{Escalat dels plans de color ponderats amb la lluminositat}
+
+\label{sec:colorponderat}A l'article \cite{sugita2006} proposen el ponderat
+per a imatges que tenen els
+plans de color delmats co-situats (\emph{cosited}). Això vol dir que els punts
+del pla de color delmat coincideixen amb la posició de punts del pla sense
+delmar. A les imatges JPEG, tal com diu l'especificació del JFIF \cite{jfif},
+els plans delmats tenen els
+punts inter-situats (\emph{intersited}) respecte al pla més gran (vegeu la
+Figura \ref{fig:co-inter-situats422}. Això fa una
+mica més complexes els algorismes.
+
+\figuraw{7cm}{co-inter-situats422.pdf}{\label{fig:co-inter-situats422}Diferència entre
+un pla de color delmat co-situat i un d'inter-situat pel cas 4:2:2.}
+
+\section{Delmat 4:2:2}
+Comencem pel cas 4:2:2. El valor de croma del pla delmat, a la
+codificació, ha estat calculat segons la mitjana aritmètica dels dos punts
+originals més propers.
+Aquest algorisme proposa fer el mateix amb el pla de
+lluminositat, com si el delméssim.
+Del pla delmat anomenem $Y_1$ al punt més proper al nostre punt d'interès,
+i $Y_2$ al segon més proper. Com que el pla de lluminància el tenim també
+sense delmar, sabem el valor del punt d'interès $Y_o$. Llavors, podem utilitzar
+la relació
+$\tfrac{Y_o-Y_1}{Y_2-Y_1}$ per a ponderar el pla de color. Podem veure-ho
+gràficament a la Figura \ref{fig:lumscaler422}
+
+\figura{lumscaler422.pdf}{\label{fig:lumscaler422}Escalat de color de 4:2:2 a
+4:4:4 amb ponderació per lluminositat. Calculem la versió delmada de la
+lluminositat, i obtenim $Y_1$ i $Y_2$, on $Y_1$ és el punt delmat més proper a
+$Y_o$, i $Y_2$ el segon més proper. Veiem que la interpolació linial entre $Y_1$
+i $Y_2$ ens donaria un punt inferior a $Y_o$ - i aquesta és la correcció que es
+fa palesa al pla de color. Les creus dretes ens mostren la versió delmada, i
+ponderant el pla de color amb $\tfrac{Y_o-Y_1}{Y_2-Y_1}$ aconseguim també
+l'anàlog a $Y_o$ més alt que si utilitzéssim interpolació linial.}
+
+Ara podem reescriure l'algorisme en funció de cada punt de la imatge (delmat i
+sense delmar), i limitar la ponderació segons un paràmetre $\epsilon_h$.
+En general, per cada fila tenim $1..N$ columnes de pla de color
+i $1..2N$ columnes de pla
+de lluminositat. Llavors, per cada punt $i$ del pla de color obtenim:
+\begin{align}
+Y(2i) &= C(i) + (C(i+1) - C(i)) \, w(Y(2i), Y_m(2i-1), Y_m(2i+1)) \\
+Y(2i+1) &= C(i+1) + (C(i) - C(i+1)) \, w(Y(2i+1), Y_m(2i+1), Y_m(2i-1))
+\end{align}
+on el pes $w(p,n,f)$ i el delmat de lluminositat $Y_m(j)$ els definim així:
+\begin{align}
+w(p,n,f) &= \begin{cases}
+ 0,25 + \epsilon_h & \text{si} \, w'(p,n,f) > 0,25 + \epsilon_h \\
+ 0,25 - \epsilon_h & \text{si} \, w'(p,n,f) < 0,25 - \epsilon_h \\
+ w'(p,n,f) & \text{altrament}
+ \end{cases} \\
+w'(p,n,f) &= \frac{p - n}{f-n} \\
+Y_m(j) &= \frac{Y(j) + Y(j+1)}{2}
+\end{align}
+on l'usuari pot escollir $\epsilon_h$.
+
+\section{Delmat 4:2:0}
+
+L'algorisme de 4:2:2 involucra dos punts $Y_1$ i $Y_2$ per cada punt de la
+imatge final. En canvi, en el cas 4:2:0 tenim quatre punts involucrats, i ens
+cal adaptar l'algorisme a aquests quatre punts. Com bé sabem, tenim tant delmat
+horitzontal com vertical. Així, la nostra adaptació consisteix en primer
+considerar el cas horitzontal i després el vertical, per cada punt de la imatge.
+
+\figuraw{8cm}{lumscaler420.pdf}{\label{fig:lumscaler420}Escalat de color 4:2:0 a
+4:4:4 ponderant segons la lluminositat.}
+
+Seguint l'esquema de la Figura \ref{fig:lumscaler420}, i amb l'objectiu de
+determinar el color al punt $Y_o$, considerem els punts
+$Y_{1\ldots4}$ com els punts ordenats segons el més proper,
+el segon més proper en
+horitzontal, el tercer més proper en vertical, i el quart més proper. Utilitzant
+la tècnica del cas de 4:2:2, considerem el punt temporal $Y_{o1}$
+i en calculem la
+croma ponderada segons $Y_1$ i $Y_2$ (amb els càlculs pertinents de la
+lluminositat) i $\epsilon_h$.
+Fem el mateix amb el punt $Y_{o2}$, $Y_3$, $Y_4$, i la mateixa $\epsilon_h$.
+Finalment, a partir d'aquestes noves cromes dels punts $Y_o1$ i $Y_o2$, i d'unes
+versions de la lluminostat de $Y_{o1}$
+i $Y_{o2}$ (segons la mitjana dels seus punts
+de lluminostiat més propers), fem la ponderació per aconseguir $Y_o$, aquest copsegons un
+paràmetre $\epsilon_v$ també configurable per l'usuari.
\printindex
