Adding some images exemplifying the restorations.
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/doc/images/lena-10-froment-12-1-f-trianta-2-2,5-1-5-500-qcs.pgm Sun Nov 25 19:43:48 2007 +0100
@@ -0,0 +1,4 @@
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000
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\ No newline at end of file
Binary file doc/images/sailing1top.png has changed
--- a/doc/memoria.tex Tue Nov 20 18:08:18 2007 +0100
+++ b/doc/memoria.tex Sun Nov 25 19:43:48 2007 +0100
@@ -19,6 +19,9 @@
\author{Lluís Batlle}
\date{\today}
+% For in-paragraph lists of a), b), c).
+\newcommand{\subcite}[1]{\emph{#1)}}
+
\newcommand{\decimal}[1]{\sepnum{,\!}{.}{}{#1}}
\newcommand{\revisar}[1]{\marginpar{\scriptsize #1}}
@@ -44,6 +47,8 @@
\maketitle
+\tableofcontents
+
\chapter{Planetjament del problema}
\section{La codificació JPEG}
@@ -376,11 +381,13 @@
\figura{lena-blocking.pdf}{
\label{fig:quant-problems} A l'esquerra, pla de lluminositat de la Lena de 256x256 píxels, a
-qualitat 40 segons la \texttt{libjpeg}. A l'esquerra, tall on podem veure els efectes a) d'ones
+qualitat 40 segons la \texttt{libjpeg}. A l'esquerra, tall on podem veure els
+efectes
+\subcite{a}d'ones
(\index{ringing}\emph{ringing})
-als blocs que tenen un canvi brusc d'intensitat pel mig, b)
-d'escala (\index{staircase}\emph{staircase})
-i c) de blocs \index{blocking}\emph{blocking}, entre blocs a les
+als blocs que tenen un canvi brusc d'intensitat pel mig,
+\subcite{b}d'escala (\index{staircase}\emph{staircase}) i
+\subcite{c}de blocs \index{blocking}\emph{blocking}, entre blocs a les
superfícies de lluminositat similar. Al mig, el mateix tall de la imatge
original, per comparar.}
@@ -506,6 +513,7 @@
\section{Projecció sobre l'espai de quantització}
+\label{sec:qcsproject}
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
cadena de descodificació}, i els de {post-processat}. Els primers consideren
@@ -964,8 +972,9 @@
Aquests algorismes transformen els plans de color codificats del JPEG als plans
exigits pel sistema gràfic del nostre ordinador. La nostra aplicació ara mateix
-necessita que les imatges finals tinguin a) un
-pla de lluminositat o b) tres plans vermell-ved-blau. Segurament la majoria dels
+necessita que les imatges finals tinguin \subcite{a}un
+pla de lluminositat o \subcite{b}tres plans vermell-ved-blau.
+Segurament la majoria dels
nostres JPEG a color estaran codificats amb lluminositat-blavor-vermellor, i per
tant, per a mostrar-los correctament a l'aplicació,
necessitarem un algorisme conversor de YCbCr a RGB.
@@ -978,12 +987,203 @@
\chapter{Anàlisi dels mètodes implementats}
-\section{Suavitzat excessiu}
+Al programa hem donat uns noms als algorismes que hem implementat. A la Taula
+\ref{tab:algnames} els teniu tots llistats, i permetran seguir millor els
+comentaris dels seus resultats.
+
+\begin{table}[!htp]
+\centering
+\begin{tabular}{ll}
+IDCTFloat & Descodificació convencional per a un pla \\
+IDCTFExp & Coeficients com v.a. exponencials, de \cite{trianta2003} \\
+Froment & \cite{froment2005} \\
+O'Rourke & \cite{orourke1995} \\
+Robertson & \cite{robertson2004} \\
+Trianta & \cite{trianta2003} \\
+Nosratinia & \cite{nosratinia2002} \\
+HP & \cite{hp2004} \\
+QCS Projection & Apartat \ref{sec:qcsproject} \\
+HContrast & Annexe \ref{sec:hcontrast} \\
+QCSKeepHF & XXXXXXXXXXXXXX \\
+LoadPlane & Carregar pla de disc \\
+SavePlane & Salvar pla a disc \\
+IntScaler & Escalador que duplica els punts delmats \\
+FancyScaler & Escalador interpolador lineal \\
+LumScaler & \cite{sugita2006}, Annexe \ref{sec:colorponderat} \\
+\end{tabular}
+\caption{\label{tab:algnames}}
+\end{table}
+
+En aquest anàlisi no ens hem basat gaire amb mesures matemàtiques, ja que
+precisament un dels objectius que ens havíem proposat a l'hora de fer aquest
+programari consisteix en pemetre a l'usuari comparar resultats variant
+paràmetres manualment. L'usuari dels algorismes, en aquest cas, provarà
+d'aplicar diversos mètodes i a anar variant els paràmetres, fins a obtenir
+una imatge que el contenti pel seu objectiu.
+Als articles que ofereixen mesures objectives dels
+resultats de diversos algorismes, i no sempre hi ha una correspondència clara
+entre aquestes mesuers i l'opinió d'individuals. A l'avaluació hi
+prenen part almenys: el contingut de la imatge (persones, dibuixos,
+paisatges), la
+resolució (de quina distància es miraran els punts de la imatge), i
+l'objectiu de la restauració (impressió, postprocessat). Les mesures objectives
+que hem analitzat no tenen en consideració aquests paràmetres, i per tant no ens
+són suficients per avaluar els resultats dels algorismes. I és amb això que
+justifiquem l'existència d'una aplicació informàtica com la que presentem. En
+aquest apartat, quan comparem algorismes, ens referirem a les opinions
+d'uns pocs individus després d'haver escollit manualment tant els algorismes com
+els paràmetres de la cadena de descodificació.
+
+\section{Plans a molt poca qualitat}
+
+Aquest tipus d'imatges (qualitat$<40$ a \texttt{libjpeg})
+es caracteritzen per efectes de bloc molt importants
+i poc detall de textures.
+Partint d'una descodificació convencional, els algorismes iteratius no-adaptatius de Froment, O'Rourke,
+i Robertson són els que produeixen millors resultats.
+El de Trianta, com que funciona de manera
+adaptativa segons informació espacial, no distingeix bé els blocs de
+cantondes reals de la imatge. Els de Nosratinia i HP suavitzen excesivament la
+imatge, comparat amb els tres primers que hem mencionat. Podeu veure un exemple
+de baixa qualitat a la Figura \ref{fig:lena40g}
+
+\begin{figure}[!htp]
+\centering
+\begin{tabular}{cc}
+\includegraphics[width=6cm]{images/lena.png} &
+\includegraphics[width=6cm]{images/lena-40-jpg.png} \\
+a) & b) \\
+\includegraphics[width=6cm]{images/lena-40-froment-8-1-f-sharp30.png} &
+\includegraphics[width=6cm]{images/lena-40-jp2.png} \\
+c) & d)
+\end{tabular}
+\caption{\label{fig:lena40g}Codificació/descodificació de la imatge Lena de 256x256
+pícsels:
+\subcite{a}original,
+\subcite{b}JPEG qualitat 40 - PSNR 44,09 dB,
+\subcite{c}descodificació amb
+Froment \cite{froment2005} (pesos de Froment, 8 iteracions,
+mida inicial de pas 1) i posterior esmolat amb GIMP
+(Filtre ``afila'', amb afilament 30) - PSNR 44,99 dB, i
+\subcite{d}versió JPEG2000 (amb \texttt{jasper} versió 1.701.0) amb la mateixa
+relació de compressió que la JPEG - PSNR 68,89 dB.}
+\end{figure}
+
+L'algorisme de Trianta, però, si l'encadanem després d'algun dels altres
+algorismes que suavitzen la imatge, permet recuperar bé moltes cantonades
+accentuant-les. Cal mencionar que aquest algorisme no manté els coeficients dins
+l'espai de quantització, i per això després d'aplicar-lo, recomanem una
+projecció sobre el QCS. Podeu veure un exemple de compressió a molt baixa
+qualitat a la Figura \ref{fig:lena10g}.
-\section{Pèrdua de contrast}
+\begin{figure}[!htp]
+\centering
+\begin{tabular}{cc}
+\includegraphics[width=6cm]{images/lena.png} &
+\includegraphics[width=6cm]{images/lena-10-jpg.png} \\
+a) & b) \\
+\includegraphics[width=6cm]{images/lena-10-froment-12-1-f.png} &
+\includegraphics[width=6cm]{images/lena-10-froment-12-1-f-trianta-2-2,5-1-5-500-qcs.png} \\
+c) & d)
+\end{tabular}
+\caption{\label{fig:lena10g}Codificació/descodificació de la imatge Lena de
+256x256 pícsels a molt baixa qualitat:
+\subcite{a}original,
+\subcite{b}JPEG qualitat 10 - PSNR 26,04 dB,
+\subcite{c}descodificació amb
+Froment \cite{froment2005} (pesos de Froment, 12 iteracions,
+mida inicial de pas 1) - PSNR 28,92 dB, i
+\subcite{d}descodificació amb Froment (com abans) seguit de Trianta \cite{trianta2002}
+($\sigma_{lf}=2, \sigma_{hf}=2,5, \sigma_{\text{WSMM}}=1, \mu = 5, T=500$) i projecció sobre QCS - PSNR 27,90 dB}
+\end{figure}
+
+Respecte als plans de color, que en el cas de poca qualitat segurament hauran
+estat delmats i codificats amb unes taules de quantització de valors molt alts,
+donaran grans blocs diferenciats de color a la imatge. El que ens ha semblat més
+correcte ha estat utilitzar algorismes que suavitzin molt, com els de
+Nosratinia i HP. Utilitzant l'escalador ponderat per lluminositat ens disminuirà
+els vessaments de color importants que podem trobar en un cas com aquest.
+
+Si l'ús excessiu d'algorismes suavitzants ens ha reduït el contrast de la
+imatge, podem arreglar-ho a la imatge final mitjançant un programa de retoc
+fotogràfic.
+
+\section{Efecte d'ones superior al de blocs}
+
+Quan els plans es codifiquen a la qualitat sovint oferta per defecte als
+programes de manipulació gràfica ($\approx 75$ a la \texttt{libjpeg}), els
+efectes d'ones sovint superen els de blocs. En aquests casos, Nosratinia i HP no
+els eliminen del tot, i els algorismes iteratius de Froment, O'Rourke i
+Robertson ofereixen bons resultats, tot i que amb masses iteracions o passos
+per iteració massa grans (més de
+10) suavitzarem la imatge més del compte. Per exemple, quan apliquem
+excessivament O'Rourke o Robertson (molt similars), els gradients d'intensitat
+de la imatge sofriran una mena de reducció de color. Les petites diferències de
+tonalitat desapareixeran, deixant només les cantonades més marcades.
+
+També hem comprovat l'efectivitat de restaurar el pla de lluminositat amb el
+\emph{filtre Gaussià selectiu} del GIMP, i involucrar el resultat al mig de la
+cadena de descodificació. Si es tracta d'una codificació d'alta qualitat (amb
+intervals de quantització prou petits), aquest algorisme no ens suavitzarà zones
+d'altes freqüències. Això sí, caldrà aplicar una projecció sobre el QCS abans de
+l'escalador per a obtenir una versió possiblement més fidel a la codificació
+original.
-\subsection{Algorisme HContrast}
-\label{sec:hcontrast}
+Respecte als plans de color, l'escalador de color que pondera segons la
+lluminositat ens dóna els millors resultats dels tres que hi ha implementats en
+totes les imatges que hem provat, també en el cas d'alta qualitat si és que hi
+ha delmat de color. Podem veure un exemple a la Figura \ref{fig:nenufar75}
+
+\begin{figure}[!htp]
+\centering
+\begin{tabular}{cc}
+\includegraphics[width=6cm]{images/nenufar.png} &
+\includegraphics[width=6cm]{images/nenufar-75.png} \\
+a) & b) \\
+\includegraphics[width=6cm]{images/nenufar-75-froment-6-fancy.png} &
+\includegraphics[width=6cm]{images/nenufar-75-froment-6-lumscaler.png} \\
+c) & d)
+\end{tabular}
+\caption{\label{fig:nenufar75}Codificació/descodificació d'una fotografia d'un
+nenúfar de 256x256 pícsels, amb la qualitat per defecte de la \texttt{libjpeg}.
+\subcite{a}original,
+\subcite{b}JPEG qualitat 75, delmat 4:2:0 - PSNR R/G/B 38,47/47,33/33,87 dB,
+\subcite{c}descodificació amb
+Froment \cite{froment2005} (pesos de Froment, 6 iteracions,
+mida inicial de pas 1) i escalador Fancy - PSNR R/G/B 41,26/46,43/37,52 dB, i
+\subcite{d}descodificació amb Froment (com abans) seguit de
+l'escalador LumScale - PSNR R/G/B 42,12/47,92/39,82 dB}
+\end{figure}
+
+En el cas de que algunes textures es perdin massa pel suavitzat d'alguns
+algorismes, podem utilitzar l'algorisme HContrast (Annexe \ref{sec:hcontrast})
+per a intentar recuperar-les. Podem veure un exemple del seu ús a la Figura
+\ref{fig:masxa}.
+
+\begin{figure}[!htp]
+\centering
+\begin{tabular}{cc}
+\includegraphics[width=6cm]{images/masxa-crop-jpg.png} &
+\includegraphics[width=6cm]{images/masxa-crop-froment-5.png} \\
+a) & b) \\
+\includegraphics[width=6cm]{images/masxa-crop-froment-5-orourke-lum.png} &
+\includegraphics[width=6cm]{images/masxa-crop-froment-5-orourke-lum-hcontrast-0,5.png} \\
+c) & d)
+\end{tabular}
+\caption{\label{fig:masxa}Codificació/descodificació d'una fotografia
+publicada a internet, de 256x256 pícsels.
+\subcite{a}publicació original,
+\subcite{b}descodificació amb Froment \cite{froment2005} (pesos de Froment, 5 iteracions, mida
+inicial de pas 1),
+\subcite{c}descodificació amb Froment com abans, més O'Rourke \cite{orourke1995}
+(10 iteracions, $T=0,1$, mida inical de pas 1) als canals de color, i
+l'escalador LumScaler ($\sigma_h = \sigma_v = 0,25$,
+Annexe \ref{sec:colorponderat}).
+\subcite{d}descodificació amb Froment i O'Rourke com abans, amb HContrast
+(Llindar 0,05 i finestra de 7x7), i LumScaler també com abans.}
+\end{figure}
+
+\section{El color}
\section{Difícil parametrització}
@@ -995,13 +1195,13 @@
\section{Manteniment de textures}
-La majoria dels mètodes de millora de pla estudiats utilitzen alguna mena de
-suavitzat per eliminar, entre altres, els efectes de bloc. Si aquest suavitzat
-s'aplica a zones on hi ha textures d'alta freqüència, el resultat pot
-empitjorar respecte a una descodificació convencional. En la majoria de casos
-això es traduirà en un augment de la PSNR, però ja hem explicat a l'apartat
-\ref{sec:psnr} com la PSNR no ens serveix com a mesura de qualitat en
-zones d'altes freqüències.
+\label{sec:hcontrast} La majoria dels mètodes de millora de pla estudiats
+utilitzen alguna mena de suavitzat per eliminar, entre altres, els efectes de
+bloc. Si aquest suavitzat s'aplica a zones on hi ha textures d'alta freqüència,
+el resultat pot empitjorar respecte a una descodificació convencional. En la
+majoria de casos això es traduirà en un augment de la PSNR, però ja hem explicat
+a l'apartat \ref{sec:psnr} com la PSNR no ens serveix com a mesura de qualitat
+en zones d'altes freqüències.
És per això que hem proposat un mètode adaptatiu per a no empitjorar
aquest tipus de zones. Ens basem en que si suavitzem una
@@ -1010,7 +1210,8 @@
reduit molt el contrast local, val més recuperar el punt de la descompressió
convencional.
Pas per pas, evaluem segons el contrast
-local per cada punt $i,j$ de la imatge. El contrast el valorem segons Michelson:
+local per cada punt $i,j$ de la imatge. El contrast el valorem segons
+Michelson: \revisar{Ho he tret de la wikipedia}
\newcommand{\Itext}[1]{I_{\text{#1}}}
\[ C(i,j) = \frac{\Itext{max}(i,j) - \Itext{min}(i,j)}{\Itext{max}(i,j)
+ \Itext{min}(i,j)} \]
@@ -1080,7 +1281,7 @@
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) &= 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:
