Análise multivariada de imagem para monitorização avançada de processos e produtos

Strelet, Eugeniu
Análise multivariada de imagem para monitorização avançada de processos e produtos

Author: Strelet, Eugeniu
Year: 2019
Source: https://estudogeral.uc.pt/bitstream/10316/86689/1/Dissertacao_AMICAPP_final_corrigida.pdf
/* vim: set shiftwidth=2 tabstop=2 autoindent cindent expandtab filetype=css: */
/*!
* Base CSS for pdf2htmlEX
* Copyright 2012,2013 Lu Wang
* https://github.com/pdf2htmlEX/pdf2htmlEX/blob/master/share/LICENSE
*/
/* Part 1: Web Page Layout: Free to modify, except for a few of them which are required by pdf2htmlEX.js, see the comments */
#sidebar { /* Sidebar */
position:absolute;
top:0;
left:0;
bottom:0;
width:250px;
padding:0;
margin:0px;
overflow:auto;
}
#page-container { /* PDF container */
position:absolute; /* required for calculating relative positions of pages in pdf2htmlEX.js */
top:0;
left:0px;
margin:0;
padding:0;
border:0; /* required for lazy page loading in pdf2htmlEX.js (page visibility test) */
}
@media screen {
/* for sidebar */
#sidebar.opened + #page-container { left:250px; }
#page-container {
/* `bottom' and `right' are required for lazy page loading in pdf2htmlEX.js (page visibility test)
* alternatively you may set width and height
*/
bottom:0;
right:0;
overflow:auto;
}
.loading-indicator_c00000 {
display:none;
}
.loading-indicator_c00000.active {
display:block;
position:absolute;
width:64px;
height:64px;
top:50%;
left:50%;
margin-top:-32px;
margin-left:-32px;
}
.loading-indicator_c00000 img {
position:absolute;
top:0;
left:0;
bottom:0;
right:0;
}
}
@media print {
@page { margin:0; }
html { margin:0; }
body {
margin:0;
-webkit-print-color-adjust:exact; /* enable printing background images for WebKit */
}
#sidebar { display:none; }
#page-container {
width:auto;
height:auto;
overflow:visible;
background-color:transparent;
}
.d_c00000 { display:none; }
}
/* Part 2: Page Elements: Modify with caution
* The followings are base classes, some of which are meant to be override by PDF specific classes
* So do not increase the specificity (e.g. ".classname_c00000" -> "#page-container .classname_c00000")
*/
.pf_c00000 { /* page */
position:relative;
background-color:white;
overflow: hidden;
margin:0;
border:0; /* required by pdf2htmlEX.js for page visibility test */
}
.pc_c00000 { /* content of a page */
position:absolute;
border:0;
padding:0;
margin:0;
top:0;
left:0;
width:100%;
height:100%;
overflow:hidden;
display:block;
/* set transform-origin for scaling */
transform-origin:0% 0%;
-ms-transform-origin:0% 0%;
-webkit-transform-origin:0% 0%;
}
.pc_c00000.opened { /* used by pdf2htmlEX.js, to show/hide pages */
display:block;
}
.bf_c00000 { /* images that occupies the whole page */
position:absolute;
border:0;
margin:0;
top:0;
bottom:0;
width:100%;
height:100%;
-ms-user-select:none;
-moz-user-select:none;
-webkit-user-select:none;
user-select:none;
}
.bi_c00000 { /* images that cover only a part of the page */
position:absolute;
border:0;
margin:0;
-ms-user-select:none;
-moz-user-select:none;
-webkit-user-select:none;
user-select:none;
}
@media print {
.pf_c00000 {
margin:0;
box-shadow:none;
page-break-after:always;
page-break-inside:avoid;
}
@-moz-document url-prefix() {
/* fix page truncation for FireFox */
.pf_c00000 {
overflow:visible;
border:1px solid #FFFFFF;
}
.pc_c00000 {overflow:visible;}
}
}
.c_c00000 { /* clip box */
position:absolute;
border:0;
padding:0;
margin:0;
overflow:hidden;
display:block;
}
.t_c00000 { /* text line */
position:absolute;
white-space:pre;
font-size:1px;
transform-origin:0% 100%;
-ms-transform-origin:0% 100%;
-webkit-transform-origin:0% 100%;
unicode-bidi:bidi-override;/* For rtl languages, e.g. Hebrew, we don't want the default Unicode behaviour */
-moz-font-feature-settings:"liga" 0;/* We don't want Firefox to recognize ligatures */
}
.t_c00000:after { /* webkit #35443 */
content: '';
}
.t_c00000:before { /* Workaround Blink(up to 41)/Webkit bug of word-spacing with leading spaces (chromium #404444 and pdf2htmlEX #412) */
content: '';
display: inline-block;
}
.t_c00000 span { /* text blocks within a line */
/* Blink(up to 41)/Webkit have bug with negative word-spacing and inline-block (pdf2htmlEX #416), so keep normal span inline. */
position:relative;
unicode-bidi:bidi-override; /* For rtl languages, e.g. Hebrew, we don't want the default Unicode behaviour */
}
.__c00000 { /* text shift */
/* Blink(up to 41)/Webkit have bug with inline element, continuous spaces and word-spacing. Workaround by inline-block. */
display: inline-block;
color: transparent;
z-index: -1;
}
/* selection background should not be opaque, for fallback mode */
::selection{
background: rgba(127,255,255,0.4);
}
::-moz-selection{
background: rgba(127,255,255,0.4);
}
.pi_c00000 { /* info for Javascript */
display:none;
}
.l_c00000 { /* annotation links */
}
/* transparent color - WebKit */
.d_c00000 { /* css drawing */
position:absolute;
transform-origin:0% 100%;
-ms-transform-origin:0% 100%;
-webkit-transform-origin:0% 100%;
}
/* for the forms */
.it_c00000 {
border: none;
background-color: rgba(255, 255, 255, 0.0);
}

.ir_c00000:hover {
cursor: pointer;
}

/* Base CSS END */

/* vim: set shiftwidth=2 tabstop=2 autoindent cindent expandtab filetype=css: */
/*!
* Fancy styles for pdf2htmlEX
* Copyright 2012,2013 Lu Wang
* https://github.com/pdf2htmlEX/pdf2htmlEX/blob/master/share/LICENSE
*/
@keyframes fadein { from { opacity:0;} to { opacity:1;} }
@-webkit-keyframes fadein { from { opacity:0;} to { opacity:1;} }
@keyframes swing {
0% { transform: rotate(0deg); }
10% { transform: rotate(0deg); }
90% { transform: rotate(720deg); }
100%{ transform: rotate(720deg); }
}
@-webkit-keyframes swing {
0% { -webkit-transform: rotate(0deg); }
10% { -webkit-transform: rotate(0deg); }
90% { -webkit-transform: rotate(720deg); }
100%{ -webkit-transform: rotate(720deg); }
}
@media screen {
#sidebar {
background-color:#2f3236;
/* modified from http://philbit.com/svgpatterns/#crossstripes */
background-image:url("data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI0IiBoZWlnaHQ9IjQiPgo8cmVjdCB3aWR0aD0iNCIgaGVpZ2h0PSI0IiBmaWxsPSIjNDAzYzNmIj48L3JlY3Q+CjxwYXRoIGQ9Ik0wIDBMNCA0Wk00IDBMMCA0WiIgc3Ryb2tlLXdpZHRoPSIxIiBzdHJva2U9IiMxZTI5MmQiPjwvcGF0aD4KPC9zdmc+");
}
#outline {
font-family:Georgia,Times,"Times New Roman",serif;
font-size:13px;
margin:2em 1em;
}
#outline ul {
padding:0;
}
#outline li {
list-style-type:none;
margin:1em 0;
}
#outline li > ul {
margin-left: 1em;
}
#outline a,
#outline a:visited,
#outline a:hover,
#outline a:active {
line-height:1.2;
color:#e8e8e8;
text-overflow:ellipsis;
white-space:nowrap;
text-decoration:none;
display:block;
overflow:hidden;
outline:0;
}
#outline a:hover {
color:rgb(0,204,255);
}
#page-container {
background-color:#9e9e9e;
/* http://philbit.com/svgpatterns/#thinstripes */
background-image: url("data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI1IiBoZWlnaHQ9IjUiPgo8cmVjdCB3aWR0aD0iNSIgaGVpZ2h0PSI1IiBmaWxsPSIjOWU5ZTllIj48L3JlY3Q+CjxwYXRoIGQ9Ik0wIDVMNSAwWk02IDRMNCA2Wk0tMSAxTDEgLTFaIiBzdHJva2U9IiM4ODgiIHN0cm9rZS13aWR0aD0iMSI+PC9wYXRoPgo8L3N2Zz4=");
-webkit-transition:left 500ms;
transition:left 500ms;
}
.pf_c00000 {
margin: 13px auto;
box-shadow: 1px 1px 3px 1px #333;
/* Needed by IE to make box-shadow works * https://developer.mozilla.org/en-US/docs/Web/CSS/box-shadow */
border-collapse: separate;
}
.pc_c00000.opened { /* used by pdf2htmlEX.js, to show/hide pages */
-webkit-animation: fadein 100ms;
animation: fadein 100ms;
}
.loading-indicator_c00000.active {
/*
* use 0.01s instead of 0s,
* since YUI Compressor will change 0s to 0,
* which is not recognized by Firefox
*/
-webkit-animation: swing 1.5s ease-in-out 0.01s infinite alternate none;
animation: swing 1.5s ease-in-out 0.01s infinite alternate none;
}
.checked_c00000 {
background: no-repeat url(data:image/png;base64,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);
}
}
/* Fancy CSS END */

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D E P A R TA M E N T O D E E NGENHARIA Q UÍMICA
Análise Multivariada de Imagem para
Controlo A vançado de Processos e
Produtos
Autor
Eugeniu Str elet
Orientador
Pr of. Dr . Mar co P . Seabra
dos Reis
Setembr o de 2018

ii

Resumo
Este trabalho de dissertação abor da um tema de importância crescente na ár ea de Enge-
nharia Química que é a Análise e Pr ocessamento de Imagens para efeitos de Controlo
de Pr ocessos e Produtos. O objetivo essencial é extrair das imagens a informação r ele-
vante e usá-la de forma cr escente na monitorização de um conjunto de parâmetros de
um dado pr ocesso e/ou produto. Assim, torna-se possível implementar o contr olo es-
tatístico multivariado do pr ocesso ( MSPC ) ou supervisionar a qualidade de produtos
em tempo r eal.
Nesta dissertação pr ocessam-se as imagens recolhidas, usando determinadas me-
todologias, para obter a informação relevante para os fins em vista. Entr e as metodo-
logias usadas incluem-se: Análise aos Componentes Principais ( PCA ); Mínimos Qua-
drados Par ciais ( PLS ); Metodologias de Classificação; Análise e Pr ocessamento Clás-
sico das Imagens; Análise das T ransformadas de Onduletas ( WT A ); Cartas de Contr olo
(nomeadamente, Hotelling’ s T 2 e Q ).
O pr esente trabalho é dividido em três partes. Cada uma corr esponde a um objetivo
distinto e logo as estratégias e metodologias são funcionalmente distintas. Os objeti-
vos são: (i) a construção de um modelo que permita monitorizar , a partir de tomografia
elétrica, o comportamento de um parâmetr o (altura da interface de dois líquidos imis-
cíveis num tubo), sem que para tal seja necessário r econstruir a imagem em causa; (ii)
desenvolvimento de um algoritmo que permita a análise simultânea de cor e forma;
(iii) desenvolvimento de um algoritmo que permita o contr olo estatístico multivariado
de pr ocessos a partir de análise e processamento de textura e de cor simultaneamente.
Para atingir o primeir o objetivo, r ecorreu-se à r egr essão usando a metodologia PLS ,
após uma análise prévia dos dados através de PCA . T al permitiu explorar o sistema em
causa (dois líquidos imiscíveis, óleo e água num tubo) e construir um modelo que per -
mitiu a monitorização da altura central da interface com uma boa pr ecisão e robustez.
O segundo objetivo foi atingido com o desenvolvimento do algoritmo de Deteção
e Classificação de Objetos (DCO), que empr ega a análise e processamento clássico das
imagens, para detetar e separar objetos do fundo e extrair algumas características/pa-
râmetr os relevantes para a sua posterior identificação. Empr ega também abordagens
de classificação aliadas a PCA para determinar a cor e a forma dos objetos em causa.
Finalmente, testou-se uma estratégia r ecentemente pr oposta, que cruzava WT A e
MSPC , para a monitorização em tempo r eal de produtos texturados: Multiscale and
Multivariate Image Analysis . Com este algoritmo foi possível detetar todas as falhas
(de tamanho, forma e cor) do pr ocesso simulado neste trabalho, cumprindo assim o
ter ceiro objetivo.
No final deste trabalho, foi possível constatar que as imagens constituem uma fonte
rica de informação. O pr ocessamento e análise digital de imagens em conjunto com as
estratégias e metodologias exploradas nesta dissertação r evelaram-se uma combinação
com grande potencial para a ár ea da Engenharia Química, nomeadamente no controlo
de pr ocesso e/ou produtos.
iii

iv RESUMO
Palavras-chave: Pr ocessamento de Imagens Digitais; Análise A vançada de Dados;
Análise Multivariada de Imagens ( MIA ); Análise Multiescalar e Multivariada de Ima-
gens ( MSMIA ); Contr olo Estatístico Multivariado de Processos ( MSPC ).

Abstract
In this dissertation strategies ar e presented that allow to extract useful information fr om images
in r eal time. That information can be ther e used for monitoring a set of product or pr ocess
parameters and implement image-based Multivariate Statistical Pr ocess Control.
The main goal of Multivariate Image Analysis for Pr ocess and Product Monitoring is to
"squeeze"the images to obtain, by applying proper methodologies, the information r equired to
pr ocess monitoring and control. Acording with, ar e: Principal Component Analysis; Partial
Least Squar es; Classifiers; Classical Digital Image Pr ocessing; W avelets T ransforms; Contr ol
Charts (e.g. Hotelling’ s T 2 & Q).
This work is divided into thr ee parts. Each one correspond to a differ ent goal: (i) derive a mo-
del for monitoring the interface heights using Electrical T omography; (ii) develop an algorithm
that enables the identification of objects using simultaneously spectral and shape information
extracted fr om images; (iii) to implement on-line, for the first time, a recently pr oposed algo-
rithm for image-based pr ocess monitoring, called Multiscale and Multivariate Image Analysis
(MSMIA).
T o r each the first goal, a PLS Regr ession modelling approach was developed after PCA
analysis. W ith this approach it was possible to build a model to monitor this interface height
with good accuracy and r obustness.
The second goal was r eached by building an algorithm, that combines classical digital image
pr ocessing and Multivariate Image Analysis approaches. This appr oach was able to detect the
color and shape of objects.
In the scope of third goal, Multiscale and Multivariate Image Analysis was implemented
on-line and tested. With this strategy , it was possible to detect all simulated process faults (size,
shape & color).
W ith this work, it was possible to demonstrate that images are a rich sour ce of information.
Digital Image Pr ocessing allied with advanced data analysis and modelling is a powerful com-
bination to use in Chemical Engineering, namely for pr ocess and/or product contr ol.
Keywords: Digital Image Pr ocessing; Advanced Data Analysis; Multivariate Image Analy-
sis (MIA); Multiscale and Multivariate Image Analysis (MSMIA); Multivariate Statistical
Pr ocess Control (MSPC).
v

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left:0;
bottom:0;
width:250px;
padding:0;
margin:0px;
overflow:auto;
}
#page-container { /* PDF container */
position:absolute; /* required for calculating relative positions of pages in pdf2htmlEX.js */
top:0;
left:0px;
margin:0;
padding:0;
border:0; /* required for lazy page loading in pdf2htmlEX.js (page visibility test) */
}
@media screen {
/* for sidebar */
#sidebar.opened + #page-container { left:250px; }
#page-container {
/* `bottom' and `right' are required for lazy page loading in pdf2htmlEX.js (page visibility test)
* alternatively you may set width and height
*/
bottom:0;
right:0;
overflow:auto;
}
.loading-indicator_c00001 {
display:none;
}
.loading-indicator_c00001.active {
display:block;
position:absolute;
width:64px;
height:64px;
top:50%;
left:50%;
margin-top:-32px;
margin-left:-32px;
}
.loading-indicator_c00001 img {
position:absolute;
top:0;
left:0;
bottom:0;
right:0;
}
}
@media print {
@page { margin:0; }
html { margin:0; }
body {
margin:0;
-webkit-print-color-adjust:exact; /* enable printing background images for WebKit */
}
#sidebar { display:none; }
#page-container {
width:auto;
height:auto;
overflow:visible;
background-color:transparent;
}
.d_c00001 { display:none; }
}
/* Part 2: Page Elements: Modify with caution
* The followings are base classes, some of which are meant to be override by PDF specific classes
* So do not increase the specificity (e.g. ".classname_c00001" -> "#page-container .classname_c00001")
*/
.pf_c00001 { /* page */
position:relative;
background-color:white;
overflow: hidden;
margin:0;
border:0; /* required by pdf2htmlEX.js for page visibility test */
}
.pc_c00001 { /* content of a page */
position:absolute;
border:0;
padding:0;
margin:0;
top:0;
left:0;
width:100%;
height:100%;
overflow:hidden;
display:block;
/* set transform-origin for scaling */
transform-origin:0% 0%;
-ms-transform-origin:0% 0%;
-webkit-transform-origin:0% 0%;
}
.pc_c00001.opened { /* used by pdf2htmlEX.js, to show/hide pages */
display:block;
}
.bf_c00001 { /* images that occupies the whole page */
position:absolute;
border:0;
margin:0;
top:0;
bottom:0;
width:100%;
height:100%;
-ms-user-select:none;
-moz-user-select:none;
-webkit-user-select:none;
user-select:none;
}
.bi_c00001 { /* images that cover only a part of the page */
position:absolute;
border:0;
margin:0;
-ms-user-select:none;
-moz-user-select:none;
-webkit-user-select:none;
user-select:none;
}
@media print {
.pf_c00001 {
margin:0;
box-shadow:none;
page-break-after:always;
page-break-inside:avoid;
}
@-moz-document url-prefix() {
/* fix page truncation for FireFox */
.pf_c00001 {
overflow:visible;
border:1px solid #FFFFFF;
}
.pc_c00001 {overflow:visible;}
}
}
.c_c00001 { /* clip box */
position:absolute;
border:0;
padding:0;
margin:0;
overflow:hidden;
display:block;
}
.t_c00001 { /* text line */
position:absolute;
white-space:pre;
font-size:1px;
transform-origin:0% 100%;
-ms-transform-origin:0% 100%;
-webkit-transform-origin:0% 100%;
unicode-bidi:bidi-override;/* For rtl languages, e.g. Hebrew, we don't want the default Unicode behaviour */
-moz-font-feature-settings:"liga" 0;/* We don't want Firefox to recognize ligatures */
}
.t_c00001:after { /* webkit #35443 */
content: '';
}
.t_c00001:before { /* Workaround Blink(up to 41)/Webkit bug of word-spacing with leading spaces (chromium #404444 and pdf2htmlEX #412) */
content: '';
display: inline-block;
}
.t_c00001 span { /* text blocks within a line */
/* Blink(up to 41)/Webkit have bug with negative word-spacing and inline-block (pdf2htmlEX #416), so keep normal span inline. */
position:relative;
unicode-bidi:bidi-override; /* For rtl languages, e.g. Hebrew, we don't want the default Unicode behaviour */
}
.__c00001 { /* text shift */
/* Blink(up to 41)/Webkit have bug with inline element, continuous spaces and word-spacing. Workaround by inline-block. */
display: inline-block;
color: transparent;
z-index: -1;
}
/* selection background should not be opaque, for fallback mode */
::selection{
background: rgba(127,255,255,0.4);
}
::-moz-selection{
background: rgba(127,255,255,0.4);
}
.pi_c00001 { /* info for Javascript */
display:none;
}
.l_c00001 { /* annotation links */
}
/* transparent color - WebKit */
.d_c00001 { /* css drawing */
position:absolute;
transform-origin:0% 100%;
-ms-transform-origin:0% 100%;
-webkit-transform-origin:0% 100%;
}
/* for the forms */
.it_c00001 {
border: none;
background-color: rgba(255, 255, 255, 0.0);
}

.ir_c00001:hover {
cursor: pointer;
}

/* Base CSS END */

/* vim: set shiftwidth=2 tabstop=2 autoindent cindent expandtab filetype=css: */
/*!
* Fancy styles for pdf2htmlEX
* Copyright 2012,2013 Lu Wang
* https://github.com/pdf2htmlEX/pdf2htmlEX/blob/master/share/LICENSE
*/
@keyframes fadein { from { opacity:0;} to { opacity:1;} }
@-webkit-keyframes fadein { from { opacity:0;} to { opacity:1;} }
@keyframes swing {
0% { transform: rotate(0deg); }
10% { transform: rotate(0deg); }
90% { transform: rotate(720deg); }
100%{ transform: rotate(720deg); }
}
@-webkit-keyframes swing {
0% { -webkit-transform: rotate(0deg); }
10% { -webkit-transform: rotate(0deg); }
90% { -webkit-transform: rotate(720deg); }
100%{ -webkit-transform: rotate(720deg); }
}
@media screen {
#sidebar {
background-color:#2f3236;
/* modified from http://philbit.com/svgpatterns/#crossstripes */
background-image:url("data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI0IiBoZWlnaHQ9IjQiPgo8cmVjdCB3aWR0aD0iNCIgaGVpZ2h0PSI0IiBmaWxsPSIjNDAzYzNmIj48L3JlY3Q+CjxwYXRoIGQ9Ik0wIDBMNCA0Wk00IDBMMCA0WiIgc3Ryb2tlLXdpZHRoPSIxIiBzdHJva2U9IiMxZTI5MmQiPjwvcGF0aD4KPC9zdmc+");
}
#outline {
font-family:Georgia,Times,"Times New Roman",serif;
font-size:13px;
margin:2em 1em;
}
#outline ul {
padding:0;
}
#outline li {
list-style-type:none;
margin:1em 0;
}
#outline li > ul {
margin-left: 1em;
}
#outline a,
#outline a:visited,
#outline a:hover,
#outline a:active {
line-height:1.2;
color:#e8e8e8;
text-overflow:ellipsis;
white-space:nowrap;
text-decoration:none;
display:block;
overflow:hidden;
outline:0;
}
#outline a:hover {
color:rgb(0,204,255);
}
#page-container {
background-color:#9e9e9e;
/* http://philbit.com/svgpatterns/#thinstripes */
background-image: url("data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI1IiBoZWlnaHQ9IjUiPgo8cmVjdCB3aWR0aD0iNSIgaGVpZ2h0PSI1IiBmaWxsPSIjOWU5ZTllIj48L3JlY3Q+CjxwYXRoIGQ9Ik0wIDVMNSAwWk02IDRMNCA2Wk0tMSAxTDEgLTFaIiBzdHJva2U9IiM4ODgiIHN0cm9rZS13aWR0aD0iMSI+PC9wYXRoPgo8L3N2Zz4=");
-webkit-transition:left 500ms;
transition:left 500ms;
}
.pf_c00001 {
margin: 13px auto;
box-shadow: 1px 1px 3px 1px #333;
/* Needed by IE to make box-shadow works * https://developer.mozilla.org/en-US/docs/Web/CSS/box-shadow */
border-collapse: separate;
}
.pc_c00001.opened { /* used by pdf2htmlEX.js, to show/hide pages */
-webkit-animation: fadein 100ms;
animation: fadein 100ms;
}
.loading-indicator_c00001.active {
/*
* use 0.01s instead of 0s,
* since YUI Compressor will change 0s to 0,
* which is not recognized by Firefox
*/
-webkit-animation: swing 1.5s ease-in-out 0.01s infinite alternate none;
animation: swing 1.5s ease-in-out 0.01s infinite alternate none;
}
.checked_c00001 {
background: no-repeat url(data:image/png;base64,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);
}
}
/* Fancy CSS END */

.ff0_c00001{font-family:sans-serif;visibility:hidden;}
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vi ABSTRACT

Agradecimentos
Quer o deixar aqui a minha gratidão e r econhecimento a todas as pessoas que estiveram
dir eta ou indir etamente envolvidos na elaboração desta dissertação. Principalmente,
um obrigado especial aos meus pais, V eaceslav e V ioleta Str elet, e irmão, Dmitrii Stre-
let, que sempr e me apoiaram nesta ascensão dos degraus do conhecimento. É a eles
que se atribui o mérito de ser a pessoa que sou hoje em dia, um orgulhoso estudante
do Mestrado Integrado em Engenharia Química e da Universidade de Coimbra.
Expr esso aqui um enorme agradecimento a toda comunidade do Departamento
de Engenharia Química, onde passei cinco anos que me enriqueceram não apenas pelo
conhecimento, mas também pela sabedoria absorvida dentro das par edes deste grande
departamento. Ao meu orientador , Prof. Dr . Marco Reis, um enorme obrigado pelo
dir ecionamento sábio para atingir os objetivos da pr esente dissertação e de r evelar
novas oportunidades de evolução. Á Pr of. Dra. Maria da Graça Rasteir o pelo todo o
apoio na ár ea de tomografia elétrica, um enorme obrigado também. Não podia deixar
de agradecer ao Pr of. Dr . Lino Santos pelas lar gas horas pr opor cionadas a enriquecer
e fomentar o nosso conhecimento, não apenas na ár ea da Engenharia Química.
Um outr o agradecimento especial é dedicado à minha namorada, Catarina Peralta,
que ajudou bastante em alturas mais apertadas dos trabalhos e que me deu muita for ça
e ener gia, através do mais belo e mágico sentimento que partilhamos, o amor .
Como já dizia V oltair e, "A amizade de um grande homem é um benefício dos deu-
ses", neste sentido posso dizer que tenho os Deuses todos do meu lado. Fui abençoado
pela dádiva divina de ter como amigos grandes homens e mulher es, grandes camara-
das. Entr e os quais, estão Nélson de Assunção, Joel Sansana, Adriano Dias, Beatriz Ba-
naco, Inês Inocêncio, Maria Leonor e muitos outr os que não foram mencionados aqui,
mas que não deixaram de ter valor por isso. Certamente foi o Baco que nos cruzou,
mas foi a Minerva que nos uniu. Ao camarada Nélson de Assunção, que pr ontamente
me apoiou nos trabalhos laboratoriais, um especial obrigado. Não posso deixar de
parte a Andr eia Per eira, com o seu dom de fazer panados que nos enchia as energias
em alturas apertadas de trabalhos.
Ao Deividson Silveira quer o agradecer pela ajuda pr estada com o equipamento de
tomografia elétrica.
Um enorme e mais sincer o obrigado a todos!
vii

viii AGRADECIMENT OS

Conteúdo
Resumo iii
Abstract v
Agradecimentos vii
1 Introdução 1
2 Metodologias e Ferramentas Usadas 3
2.1 Análise e Pr ocessamento de Imagem . . . . . . . . . . . . . . . . . . . . . 3
2.2 Análise dos Componentes Principais . . . . . . . . . . . . . . . . . . . . . 5
2.3 Metodologias de Classificação . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.4 Regr essão pelo método dos Mínimos Quadrados Par ciais . . . . . . . . . 7
2.5 T ransformada de Onduleta . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.6 Contr olo Estatístico dos Pr ocessos . . . . . . . . . . . . . . . . . . . . . . 9
2.7 Softwar es u s a d o s ................................. 1 0
3 T omografia Elétrica 13
3.1 Estudo dos dados iniciais . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3 . 2 E x p e r i ê n c i a 1 ................................... 2 0
3 . 3 E x p e r i ê n c i a 2 ................................... 2 7
3 . 4 C o n c l u s õ e s .................................... 3 2
4 Deteção e Classificação de Objetos 35
4.1 Análise e Pr ocessamento de Objetos em Imagens Digitais . . . . . . . . . 36
4.2 Análise e Pr ocessamento de Cor . . . . . . . . . . . . . . . . . . . . . . . . 39
4.3 T r eino dos Classificador es . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.3.1 Classificador para a Forma . . . . . . . . . . . . . . . . . . . . . . 41
4.3.2 Classificador para a Cor . . . . . . . . . . . . . . . . . . . . . . . . 42
4.4 Algoritmo de Classificação . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4 . 5 N o t a s fi n a i s ................................... 4 7
4 . 6 C o n c l u s õ e s .................................... 4 7
5 Aplicação online da Análise Multiescala e Multivariada de Imagens ( MSMIA ) 49
5 . 1 P r é - p r o c e s s a m e n t o ............................... 5 0
5 . 2 F a s e I : T r e i n o d o M o d e l o ............................ 5 2
5 . 3 F a s e I I : T e s t e d o M o d e l o ............................ 5 4
5 . 3 . 1 F a l h a s d e T a m a n h o ........................... 5 4
5 . 3 . 2 F a l h a s d e F o r m a ............................ 5 7
5 . 3 . 3 F a l h a s d e C o r .............................. 5 9
5 . 3 . 4 F a l h a s S i m u l t â n e a s........................... 6 0
ix

x CONTEÚDO
5 . 4 C o n c l u s õ e s .................................... 6 2
6 Conclusões Finais 65
6.1 Pr oposta de T rabalhos futur os . . . . . . . . . . . . . . . . . . . . . . . . . 67
Bibliografia 69
Lista de Figuras 71
Lista de T abelas 75
Glossário 77
Siglas 79
Ferramentas M A T L A B ® Mencionadas 81
Anexos 83

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/* Blink(up to 41)/Webkit have bug with negative word-spacing and inline-block (pdf2htmlEX #416), so keep normal span inline. */
position:relative;
unicode-bidi:bidi-override; /* For rtl languages, e.g. Hebrew, we don't want the default Unicode behaviour */
}
.__c00002 { /* text shift */
/* Blink(up to 41)/Webkit have bug with inline element, continuous spaces and word-spacing. Workaround by inline-block. */
display: inline-block;
color: transparent;
z-index: -1;
}
/* selection background should not be opaque, for fallback mode */
::selection{
background: rgba(127,255,255,0.4);
}
::-moz-selection{
background: rgba(127,255,255,0.4);
}
.pi_c00002 { /* info for Javascript */
display:none;
}
.l_c00002 { /* annotation links */
}
/* transparent color - WebKit */
.d_c00002 { /* css drawing */
position:absolute;
transform-origin:0% 100%;
-ms-transform-origin:0% 100%;
-webkit-transform-origin:0% 100%;
}
/* for the forms */
.it_c00002 {
border: none;
background-color: rgba(255, 255, 255, 0.0);
}

.ir_c00002:hover {
cursor: pointer;
}

/* Base CSS END */

/* vim: set shiftwidth=2 tabstop=2 autoindent cindent expandtab filetype=css: */
/*!
* Fancy styles for pdf2htmlEX
* Copyright 2012,2013 Lu Wang
* https://github.com/pdf2htmlEX/pdf2htmlEX/blob/master/share/LICENSE
*/
@keyframes fadein { from { opacity:0;} to { opacity:1;} }
@-webkit-keyframes fadein { from { opacity:0;} to { opacity:1;} }
@keyframes swing {
0% { transform: rotate(0deg); }
10% { transform: rotate(0deg); }
90% { transform: rotate(720deg); }
100%{ transform: rotate(720deg); }
}
@-webkit-keyframes swing {
0% { -webkit-transform: rotate(0deg); }
10% { -webkit-transform: rotate(0deg); }
90% { -webkit-transform: rotate(720deg); }
100%{ -webkit-transform: rotate(720deg); }
}
@media screen {
#sidebar {
background-color:#2f3236;
/* modified from http://philbit.com/svgpatterns/#crossstripes */
background-image:url("data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI0IiBoZWlnaHQ9IjQiPgo8cmVjdCB3aWR0aD0iNCIgaGVpZ2h0PSI0IiBmaWxsPSIjNDAzYzNmIj48L3JlY3Q+CjxwYXRoIGQ9Ik0wIDBMNCA0Wk00IDBMMCA0WiIgc3Ryb2tlLXdpZHRoPSIxIiBzdHJva2U9IiMxZTI5MmQiPjwvcGF0aD4KPC9zdmc+");
}
#outline {
font-family:Georgia,Times,"Times New Roman",serif;
font-size:13px;
margin:2em 1em;
}
#outline ul {
padding:0;
}
#outline li {
list-style-type:none;
margin:1em 0;
}
#outline li > ul {
margin-left: 1em;
}
#outline a,
#outline a:visited,
#outline a:hover,
#outline a:active {
line-height:1.2;
color:#e8e8e8;
text-overflow:ellipsis;
white-space:nowrap;
text-decoration:none;
display:block;
overflow:hidden;
outline:0;
}
#outline a:hover {
color:rgb(0,204,255);
}
#page-container {
background-color:#9e9e9e;
/* http://philbit.com/svgpatterns/#thinstripes */
background-image: url("data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI1IiBoZWlnaHQ9IjUiPgo8cmVjdCB3aWR0aD0iNSIgaGVpZ2h0PSI1IiBmaWxsPSIjOWU5ZTllIj48L3JlY3Q+CjxwYXRoIGQ9Ik0wIDVMNSAwWk02IDRMNCA2Wk0tMSAxTDEgLTFaIiBzdHJva2U9IiM4ODgiIHN0cm9rZS13aWR0aD0iMSI+PC9wYXRoPgo8L3N2Zz4=");
-webkit-transition:left 500ms;
transition:left 500ms;
}
.pf_c00002 {
margin: 13px auto;
box-shadow: 1px 1px 3px 1px #333;
/* Needed by IE to make box-shadow works * https://developer.mozilla.org/en-US/docs/Web/CSS/box-shadow */
border-collapse: separate;
}
.pc_c00002.opened { /* used by pdf2htmlEX.js, to show/hide pages */
-webkit-animation: fadein 100ms;
animation: fadein 100ms;
}
.loading-indicator_c00002.active {
/*
* use 0.01s instead of 0s,
* since YUI Compressor will change 0s to 0,
* which is not recognized by Firefox
*/
-webkit-animation: swing 1.5s ease-in-out 0.01s infinite alternate none;
animation: swing 1.5s ease-in-out 0.01s infinite alternate none;
}
.checked_c00002 {
background: no-repeat url(data:image/png;base64,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);
}
}
/* Fancy CSS END */

.ff0_c00002{font-family:sans-serif;visibility:hidden;}
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Aos meus pais e irmão.

xii CONTEÚDO

Capítulo 1
Introdução
"A pintura deve par ecer uma coisa
natural vista num grande espelho."
Leonardo Da V inci
Polímata italiano, 1452 - 1519
Ao longo dos últimos três séculos a indústria passou por várias fases que foram
mar cadas pela mudança de um paradigma para outr o. Começando pela mecaniza-
ção usando a for ça motriz do movimento natural da água, passando pela massificação
potenciada pela for ça do vapor , combustíveis fósseis e eletricidade e posteriormente
pr odução automática e apoiada por sistemas computacionais, estamos agora perante o
paradigma da Indústria 4.0: digitalização das indústrias e integração (Lu 2017). Adici-
onalmente, regista-se a r ecolha em massa de dados que servirão posteriormente para
análise e pr ocessamento, por forma a alcançar melhor desempenho das unidades in-
dustriais. Essa r ecolha de dados ocorr e com ajuda de múltiplos sensor es (de tempera-
tura, de pr essão, concentração, altura, pr ofundidade, etc) e novas tecnologias de medi-
ção que estão a ser colocadas dir etamente nos pr ocessos (espectr oscopia, imagiologia,
cr omatografia, etc.).
Neste contexto, os sistemas de aquisição automática de imagens digitais, estão entr e
as fontes de informação que têm r egistado uma evolução mais significativa, apresentan-
do-se hoje em dia como soluções industriais acessíveis, robustas e informativas. No
entanto, não obstante o seu potencial informativo e o acesso atual a meios computaci-
onais poder osos bem como a pr eços compatíveis com as possibilidades das empr esas,
esta fonte de informação ainda não está a ser convenientemente explorada na indús-
tria química (ao contrário do que já sucede com a indústria de manufactura de com-
ponentes mecânicos e electrónicos e sua montagem) e os seus benefícios tar dam a ser
r ecolhidos e traduzidos em mais-valias para as empr esas.
Com o avanço da tecnologia que se pode verificar hoje em dia, torna-se possível,
r ecorr endo a equipamentos de aquisição de imagens e computador es, fazer todo o tipo
de análise que o ser humano consegue fazer com r ecurso à sua visão. Desta forma, as
tar efas r epetidas de monitorização e interpr etação são executadas de uma forma mais
rápida, objectiva, estável e r obusta. Assim, estas tarefas deixam de depender dos fato-
r es humanos como o cansaço, estados psicológicos, de saúde ou boa visão. Algumas
destas tar efas estão ligadas à inspeção da qualidade do pr oduto, inspeção das fases
do pr ocesso, etc. Muitas destas são feitas em modo offline , com atrasos significativos
r elativamente ao momento de r ecolha das amostras. Os dispositivos de aquisição de
imagens e computador es permitem, hoje em dia, a execução online das tare fas anteri-
ormente mencionadas, sem as desvantagem r eferidas (Reis 2014).
1

2 CAPÍTULO 1. INTRODUÇÃO
As imagens que são r ecolhidas pelas câmaras ou outr os dispositivos de aquisição,
não são mais do que matrizes or ganizadas de dados. O pr ocessamento ocorr e "des-
montando"as imagens em dados (píxeis) e tratando-os estatisticamente com PCA, PLS
e estatísticas multivariadas, ou ainda, transformando-as com r ecurso a transformadas
de onduletas ou de Fourier , por exemplo (Reis 2015).
Com o objectivo geral de demonstrar a utilidade potencial da utilização de siste-
mas de análise de imagem em Engenharia Química para condução de tar efas de alto
nível, como a monitorização avançada de pr ocessos, abor dam-se nesta dissertação vá-
rios casos de estudo onde as mais valias destes sistemas são exploradas. Em particular ,
r eportam-se três aplicações com objetivos, metodologias e estratégias de análise distin-
tas:
• Construção de um modelo que permita monitorizar , a partir de dados em br uto
de tomografia elétrica, o comportamento de um parâmetro (altura da interface
entr e dois líquidos imiscíveis num tubo), sem necessidade de reconstr uir a ima-
gem em causa;
• Desenvolvimento de um algoritmo de classificação baseado em imagens, que
permita a análise e pr ocessamento de cor , objetos e a geometria dos mesmos,
simultaneamente;
• Desenvolvimento de um algoritmo que permita o controlo estatístico multivari-
ado de pr ocessos a partir de análise e pr ocessamento de textura e de cor , simul-
taneamente.
V isão Geral da Dissertação
Nos próximos capítulos serão apr esentadas várias metodologias usadas na análise e
pr ocessamento de imagens, consoante os objetivos a atingir . No Capítulo 2, serão
abor dadas de uma forma r esumida as ferramentas e metodologias usadas ao longo
do pr esente trabalho. No Capítulo 3, será feita uma análise exploratória de dados, com
possível r edução da dimensão dos mesmos e posterior extração de um modelo que
permite a monitorização de um parâmetr o r elevante para o pr ocesso onde esta análise
é aplicada (altura da interface). A análise de objetos e monitorização dos r espetivos
parâmetr os geométricos e espetr o/cor dos mesmos é explorada no Capítulo 4. O algo-
ritmo para o contr olo estatístico multivariado de pr ocesso a partir de pr ocessamento
simultâneo de cor/espetr o e textura (padrão), simultaneamente, é apr esentada no Ca-
pítulo 5. No Capítulo 6 apr esentam-se as conclusões gerais do trabalho desenvolvido.
Os perigos associados a r ealização dos trabalhos da pr esente dissertação encontram-
se nos Anexos.

Capítulo 2
Metodologias e Ferramentas Usadas
"Os métodos são as ver dadeiras
riquezas."
Friedrich W ilhelm Nietzsche
Filósofo alemão, 1844 - 1900
Os algoritmos desenvolvidos neste trabalho são diversificados, e foram utilizados
de forma flexível, através da sua combinação sinergística de forma a atingir os objetivos
delineados em cada tar efa. Assim, para melhor interpretar os métodos r eferidos nos
capítulos posterior es, é oportuno per ceber os seus fundamentos. Estes são descritos,
de forma r esumida neste Capítulo.
São assim explorados conceitos base para análise multivariada e multiescala de
imagens, como:
• Análise e Processamento de Imagem (Secção 2.1)
• Análise dos Componentes Principais (Secção 2.2)
• Metodologias de Classificação (Secção 2.3)
• Regressão pelo método dos Mínimos Quadrados Parciais (Secção 2.4)
• T ransformada de Onduleta (Secção 2.5)
• Controlo Estatístico dos Processos (Secção 2.6)
T odo o trabalho foi feito com r ecurso a ferramentas informáticas de cálculo, mo-
delação, edição de textos e gráficos. Os mais relevantes são apr esentados na Secção
2.7.
2.1 Análise e Processamento de Imagem
As imagens são funções f ( x , y ) , onde x e y são coordenadas espaciais. A(s) ampli-
tude(s) de f correspondente(s) a um par de coor denadas ( x , y ) , pixel, é(são) intensi-
dade(s) de uma determinada cor . Os termos em plural ou singular dependem se f é
apenas um valor ou um vetor . Caso este seja um valor , trata-se de uma imagem na
escala dos cinzentos, caso seja um vetor de intensidades, tratam-se de imagens a cores,
espetrais, multi-espetrais ou hiper-espetrais, dependendo a designação das componen-
tes do vetor (Gonzalez et al. 2009).
3

/* vim: set shiftwidth=2 tabstop=2 autoindent cindent expandtab filetype=css: */
/*!
* Base CSS for pdf2htmlEX
* Copyright 2012,2013 Lu Wang
* https://github.com/pdf2htmlEX/pdf2htmlEX/blob/master/share/LICENSE
*/
/* Part 1: Web Page Layout: Free to modify, except for a few of them which are required by pdf2htmlEX.js, see the comments */
#sidebar { /* Sidebar */
position:absolute;
top:0;
left:0;
bottom:0;
width:250px;
padding:0;
margin:0px;
overflow:auto;
}
#page-container { /* PDF container */
position:absolute; /* required for calculating relative positions of pages in pdf2htmlEX.js */
top:0;
left:0px;
margin:0;
padding:0;
border:0; /* required for lazy page loading in pdf2htmlEX.js (page visibility test) */
}
@media screen {
/* for sidebar */
#sidebar.opened + #page-container { left:250px; }
#page-container {
/* `bottom' and `right' are required for lazy page loading in pdf2htmlEX.js (page visibility test)
* alternatively you may set width and height
*/
bottom:0;
right:0;
overflow:auto;
}
.loading-indicator_c00003 {
display:none;
}
.loading-indicator_c00003.active {
display:block;
position:absolute;
width:64px;
height:64px;
top:50%;
left:50%;
margin-top:-32px;
margin-left:-32px;
}
.loading-indicator_c00003 img {
position:absolute;
top:0;
left:0;
bottom:0;
right:0;
}
}
@media print {
@page { margin:0; }
html { margin:0; }
body {
margin:0;
-webkit-print-color-adjust:exact; /* enable printing background images for WebKit */
}
#sidebar { display:none; }
#page-container {
width:auto;
height:auto;
overflow:visible;
background-color:transparent;
}
.d_c00003 { display:none; }
}
/* Part 2: Page Elements: Modify with caution
* The followings are base classes, some of which are meant to be override by PDF specific classes
* So do not increase the specificity (e.g. ".classname_c00003" -> "#page-container .classname_c00003")
*/
.pf_c00003 { /* page */
position:relative;
background-color:white;
overflow: hidden;
margin:0;
border:0; /* required by pdf2htmlEX.js for page visibility test */
}
.pc_c00003 { /* content of a page */
position:absolute;
border:0;
padding:0;
margin:0;
top:0;
left:0;
width:100%;
height:100%;
overflow:hidden;
display:block;
/* set transform-origin for scaling */
transform-origin:0% 0%;
-ms-transform-origin:0% 0%;
-webkit-transform-origin:0% 0%;
}
.pc_c00003.opened { /* used by pdf2htmlEX.js, to show/hide pages */
display:block;
}
.bf_c00003 { /* images that occupies the whole page */
position:absolute;
border:0;
margin:0;
top:0;
bottom:0;
width:100%;
height:100%;
-ms-user-select:none;
-moz-user-select:none;
-webkit-user-select:none;
user-select:none;
}
.bi_c00003 { /* images that cover only a part of the page */
position:absolute;
border:0;
margin:0;
-ms-user-select:none;
-moz-user-select:none;
-webkit-user-select:none;
user-select:none;
}
@media print {
.pf_c00003 {
margin:0;
box-shadow:none;
page-break-after:always;
page-break-inside:avoid;
}
@-moz-document url-prefix() {
/* fix page truncation for FireFox */
.pf_c00003 {
overflow:visible;
border:1px solid #FFFFFF;
}
.pc_c00003 {overflow:visible;}
}
}
.c_c00003 { /* clip box */
position:absolute;
border:0;
padding:0;
margin:0;
overflow:hidden;
display:block;
}
.t_c00003 { /* text line */
position:absolute;
white-space:pre;
font-size:1px;
transform-origin:0% 100%;
-ms-transform-origin:0% 100%;
-webkit-transform-origin:0% 100%;
unicode-bidi:bidi-override;/* For rtl languages, e.g. Hebrew, we don't want the default Unicode behaviour */
-moz-font-feature-settings:"liga" 0;/* We don't want Firefox to recognize ligatures */
}
.t_c00003:after { /* webkit #35443 */
content: '';
}
.t_c00003:before { /* Workaround Blink(up to 41)/Webkit bug of word-spacing with leading spaces (chromium #404444 and pdf2htmlEX #412) */
content: '';
display: inline-block;
}
.t_c00003 span { /* text blocks within a line */
/* Blink(up to 41)/Webkit have bug with negative word-spacing and inline-block (pdf2htmlEX #416), so keep normal span inline. */
position:relative;
unicode-bidi:bidi-override; /* For rtl languages, e.g. Hebrew, we don't want the default Unicode behaviour */
}
.__c00003 { /* text shift */
/* Blink(up to 41)/Webkit have bug with inline element, continuous spaces and word-spacing. Workaround by inline-block. */
display: inline-block;
color: transparent;
z-index: -1;
}
/* selection background should not be opaque, for fallback mode */
::selection{
background: rgba(127,255,255,0.4);
}
::-moz-selection{
background: rgba(127,255,255,0.4);
}
.pi_c00003 { /* info for Javascript */
display:none;
}
.l_c00003 { /* annotation links */
}
/* transparent color - WebKit */
.d_c00003 { /* css drawing */
position:absolute;
transform-origin:0% 100%;
-ms-transform-origin:0% 100%;
-webkit-transform-origin:0% 100%;
}
/* for the forms */
.it_c00003 {
border: none;
background-color: rgba(255, 255, 255, 0.0);
}

.ir_c00003:hover {
cursor: pointer;
}

/* Base CSS END */

/* vim: set shiftwidth=2 tabstop=2 autoindent cindent expandtab filetype=css: */
/*!
* Fancy styles for pdf2htmlEX
* Copyright 2012,2013 Lu Wang
* https://github.com/pdf2htmlEX/pdf2htmlEX/blob/master/share/LICENSE
*/
@keyframes fadein { from { opacity:0;} to { opacity:1;} }
@-webkit-keyframes fadein { from { opacity:0;} to { opacity:1;} }
@keyframes swing {
0% { transform: rotate(0deg); }
10% { transform: rotate(0deg); }
90% { transform: rotate(720deg); }
100%{ transform: rotate(720deg); }
}
@-webkit-keyframes swing {
0% { -webkit-transform: rotate(0deg); }
10% { -webkit-transform: rotate(0deg); }
90% { -webkit-transform: rotate(720deg); }
100%{ -webkit-transform: rotate(720deg); }
}
@media screen {
#sidebar {
background-color:#2f3236;
/* modified from http://philbit.com/svgpatterns/#crossstripes */
background-image:url("data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI0IiBoZWlnaHQ9IjQiPgo8cmVjdCB3aWR0aD0iNCIgaGVpZ2h0PSI0IiBmaWxsPSIjNDAzYzNmIj48L3JlY3Q+CjxwYXRoIGQ9Ik0wIDBMNCA0Wk00IDBMMCA0WiIgc3Ryb2tlLXdpZHRoPSIxIiBzdHJva2U9IiMxZTI5MmQiPjwvcGF0aD4KPC9zdmc+");
}
#outline {
font-family:Georgia,Times,"Times New Roman",serif;
font-size:13px;
margin:2em 1em;
}
#outline ul {
padding:0;
}
#outline li {
list-style-type:none;
margin:1em 0;
}
#outline li > ul {
margin-left: 1em;
}
#outline a,
#outline a:visited,
#outline a:hover,
#outline a:active {
line-height:1.2;
color:#e8e8e8;
text-overflow:ellipsis;
white-space:nowrap;
text-decoration:none;
display:block;
overflow:hidden;
outline:0;
}
#outline a:hover {
color:rgb(0,204,255);
}
#page-container {
background-color:#9e9e9e;
/* http://philbit.com/svgpatterns/#thinstripes */
background-image: url("data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI1IiBoZWlnaHQ9IjUiPgo8cmVjdCB3aWR0aD0iNSIgaGVpZ2h0PSI1IiBmaWxsPSIjOWU5ZTllIj48L3JlY3Q+CjxwYXRoIGQ9Ik0wIDVMNSAwWk02IDRMNCA2Wk0tMSAxTDEgLTFaIiBzdHJva2U9IiM4ODgiIHN0cm9rZS13aWR0aD0iMSI+PC9wYXRoPgo8L3N2Zz4=");
-webkit-transition:left 500ms;
transition:left 500ms;
}
.pf_c00003 {
margin: 13px auto;
box-shadow: 1px 1px 3px 1px #333;
/* Needed by IE to make box-shadow works * https://developer.mozilla.org/en-US/docs/Web/CSS/box-shadow */
border-collapse: separate;
}
.pc_c00003.opened { /* used by pdf2htmlEX.js, to show/hide pages */
-webkit-animation: fadein 100ms;
animation: fadein 100ms;
}
.loading-indicator_c00003.active {
/*
* use 0.01s instead of 0s,
* since YUI Compressor will change 0s to 0,
* which is not recognized by Firefox
*/
-webkit-animation: swing 1.5s ease-in-out 0.01s infinite alternate none;
animation: swing 1.5s ease-in-out 0.01s infinite alternate none;
}
.checked_c00003 {
background: no-repeat url(data:image/png;base64,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);
}
}
/* Fancy CSS END */

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4 CAPÍTULO 2. MET ODOLOGIAS E FERRAMENT AS USADAS
As imagens podem ter o formato RGB , CMYK , escala de cinzentos, etc. Neste tra-
balho, foram usados imagens na escala de cinzento e imagens RGB . Estes formatos
de imagens são os mais difundidos no mundo e os mais baratos de adquirir pois não
exigem nenhuma instrumentação sofisticada (Gonzalez et al. 2009).
As coor denadas convencionais das imagens estão pr esentes na Figura 2.1(a). Con-
tudo as coor denadas usadas no pr esente trabalho são as da Figura 2.1(b). Isto deve-se
ao facto de se ter r ecorrido ao M A TLAB ® para analisar e pr ocessar as imagens e imple-
mentar os algoritmos (Gonzalez et al. 2009).
(a) Coor denadas convencionais. (b) Coor denadas M A TLAB ® .
Figura 2.1: Coor denadas das imagens.
Desta forma, as imagens podem ser vistas como matrizes, equação 2.1, em que f
pode ser um valor ou um vetor de valor es para cada x e y .
f ( x , y ) = 




f ( 1, 1 ) f ( 1, 2 ) . . . f ( 1, N )
f ( 2, 1 ) f ( 2, 2 ) . . . f ( 2, N )
.
.
. .
.
. . . . .
.
.
f ( M , 1 ) f ( M , 2 ) . . . f ( M , N )




 (2.1)
O pr ocessamento digital de imagens é o termo usado para designar qualquer ope-
ração, b
O , aplicada aos pixeis da mesma imagem, f ( x , y ) , equação 2.2. Estas operações
podem consistir na aplicação de filtr os, eliminação de ruído, r edimensionamento, seg-
mentação, corr eção de intensidade de luz, etc. (Gonzalez et al. 2009).
g ( x , y ) = b
O ( f ( x , y ) ) (2.2)
A análise e pr ocessamento digital de imagens pode ser implementada a vários ní-
veis: básico, intermédio e avançado. O nível básico r efer e-se apenas ao pr ocessamento
simples das imagens com o objetivo de as melhorar (otimizar contraste, eliminar ruído,
etc.). A segmentação, identificação de objetos, descrição e classificação dos mesmos
já são operações que se enquadram no nível intermédio. O nível avançado de pr o-
cessamento corr esponde à aplicação de algoritmos com desempenho semelhantes ao
pr ocessamento e funções cognitivas da visão humana (Gonzalez et al. 2009). Os algo-
ritmos desenvolvidos e testados neste trabalho situam-se entr e o nível intermédio e o
nível avançado.

2.2. ANÁLISE DOS COMPONENTES PRINCIP AIS 5
2.2 Análise dos Componentes Principais
A análise de componentes principais, ou em inglês, Principal Component Analysis ( PCA ),
é uma ferramenta importante em várias ár eas, como por exemplo a quimiometria de
pr ocessos (Gur den et al. 1998). Esta análise permite diminuir o espaço de análise dos
dados originais, constituído por um grande númer o de variáveis, usualmente correla-
cionadas. PCA pode ser interpr etado como uma pr ojeção dos dados do espaço original
das variáveis para um novo sub-espaço de novas variáveis designadas de componen-
tes principais, ou em inglês, Principal Component ( PC ).
Antes da aplicação do algoritmo PCA , os dados normalmente são pré-pr ocessados.
O pré-pr ocessamento mais comum é conhecido por autoscaling , equação2.3. Este con-
siste em subtrair a cada variável original ( x i , j ) a média correspondente ( x j ) seguido
da divisão dos mesmos pelo desvio padrão corr espondente ( s x j ), em que os índices
i e j corr espondem a observações (linhas) e variáveis (colunas) r espetivamente (com
i = 1, ..., I e j = 1, ..., J ). O sobrescrito a s indica que os dados do X sofreram o pr ocesso
de autoscaling (Br o & Smilde (2014); Jollif fe (2002)).
x a s
i , j = x i , j − x j
s x j
(2.3)
O autoscaling implica transformar as variáveis originais de forma que estas apr esen-
tem a mesma dispersão de valor es e, portanto, a mesma importância para o algoritmo
PCA. A matriz de dados originais X é decomposta numa combinação entre scor e s ( T ) e
loading s ( L ) e r esíduos ( E ), como se pode observar na equação 2.4. E corr esponde à por -
ção da variabilidade de X que as componentes principais consideradas não conseguem
explicar .
X = T PCA · L T
PCA + E (2.4)
Sendo X uma matriz I por J ; T PCA I por P ; L PCA J por P e E I por J . P , neste caso, é o
númer o máximo de componentes principais a ter em consideração que, normalmente,
é muito inferior ao númer o de variáveis originais ( P < < J ) (Br o & Smilde (2014); Jol-
lif fe (2002)).
Os scor e s dos componentes principais são determinados de forma a que os score s do
primeir o PC , T 1 PCA , consiga captar a maior parte da variabilidade dos dados originais.
Os scor e s do segundo PC , T 2 PCA , conseguem descr ever a maior parte da variabilidade
r emanescente que não foi explicada pela primeira componente e assim sucessivamente
até ao T P PCA (Bro & Smilde (2014); Jollif fe (2002)).
Desta forma, r esultam os scor e s ( T I × P
PCA ) e os loading s ( L J × P
PCA ). Cada componente prin-
cipal consegue descr ever a parte da variabilidade dos dados originais que os pr ece-
dentes não conseguem descr ever , ficando as tendências importantes captadas logo nas
primeiras componentes principais, enquanto o ruído é captado pelas r estantes compo-
nentes. Assim, os dados originais são projetados num sub-espaço de variáveis, PC s,
não corr elacionadas (Br o & Smilde (2014); Jollif fe (2002)).
Analisando os scor e s pode-se identificar padrões e tendências dos dados, enquanto
a análise dos loading s permite inferir a importância de cada variável para a r econstru-
ção dos espaço original dos dados bem como as corr elações dominantes (Br o & Smilde
(2014); Jollif fe (2002)).
Normalmente, as primeiras duas a dez componentes principais conseguem descre-
ver quase toda a variabilidade dos dados. Contudo, a escolha do número de PC deve
ser objecto de uma análise cuidada. Existem vários critérios, como é o caso do Scr ee
T est , critério de Kaiser , validação cruzada, a fração da variabilidade explicada, etc. (Br o

6 CAPÍTULO 2. MET ODOLOGIAS E FERRAMENT AS USADAS
& Smilde 2014). Como este trabalho tem um objetivo mais exploratório, geralmente
serão consideradas apenas as primeiras três componentes principais, pois essa escolha
permite visualizar os dados em gráficos a uma, a duas e a três dimensões.
2.3 Metodologias de Classificação
Segundo Alpaydin (2010) e Hastie et al. (2001), a função de um classificador é atribuir
um determinado conjunto de dados/observações a uma determinada categoria ( label )
de entr e um conjunto finito de possibilidades. Uma das classes de metodologias de
classificação mais comum, consiste em determinar as funções discriminantes, que r e-
pr esentam a fr onteira entr e duas ou mais r egiões corr espondentes a difer entes classes.
Essas fr onteiras podem ser linear es ou não.
Na prática, um classificador corr esponde a uma função, f cl ass , que faz uso de um
conjunto de featur e s (pr editor es) ( b
x ) , com base nos quais determina a classe/rótulo
k = f cl ass ( b
x ) da observação, x . O classificador é estimado a partir de um conjunto de
dados de tr eino, x tr a i n , cujas classes são conhecidas. Posteriormente este classificador
é sujeito a uma validação com os dados de validação, x v a l , cujas classes também são
conhecidas para avaliar o seu desempenho efetivo em condições de pr evisão.
Figura 2.2: Algoritmo para o tr eino e validação do classificador .
O desempenho do classificador pode ser avaliado com um conjunto de dados in-
dependente para validação (validação externa) ou através da validação cruzada (vali-
dação interna), em que o conjunto de tr eino é dividido em subconjuntos e uma parte
destes conjuntos é sucessivamente usada para tr eino e outra para validação. Os clas-
sificador es podem ser de vários tipos, como por exemplo (Hastie et al. (2001); Michie
et al. (2009)):
• Discriminantes linear es de Fisher ( Fisher ’ s linear discriminants );
• Árvor es de decisão e métodos baseados em r egras ( Decision tr ee and Rule-based
methods One );
• V izinho mais próximo k ( k-Near est-Neighbour );
• Redes neur onais ( Neural Networks );
• Máquinas de vetor es de suporte e discriminantes flexíveis ( Support V ector Machi-
nes and Flexible Discriminants );

2.4. REGRESSÃO PELO MÉT ODO DOS MÍNIMOS QUADRADOS P ARCIAIS 7
• Apr endizagem não supervisionada ( Unsupervised Learning );
• Flor estas aleatórias ( Random For ests );
• etc.
Neste trabalho foi usado um classificador discriminante linear cujo desempenho foi
avaliado com validação cruzada (Per eira et al. 2009).
2.4 Regressão pelo método dos Mínimos Quadrados Par -
ciais
A r egr essão pelo método dos mínimos quadrados par ciais, ou em inglês, Partial Least
Squar es ( PLS ) Regr ession , é uma ferramenta de r egressão multivariada especialmente
útil em situações em que os pr editor es são em elevado númer o e apr esentam fortes
corr elações entr e si. PLS é assim capaz de extrair um modelo com múltiplas variáveis
em X , mas também em Y .
Os dados, antes de ser em sujeitos ao tratamento PLS , são usualmente sujeitos a um
um pré-pr ocessamento. O pré-pr ocessamento a usar depende da situação em apreço.
Quando as unidades das variáveis difer em, o processamento normalmente usado é o
autoscaling . Aplicando o modelo PLS ocorr e a pr ojeção dos dados originais, tanto de
X como de Y , num novo subespaço, semelhante à aplicação de PCA . Contudo, essa
pr ojeção ocorr e de forma difer ente, dado que tem em conta, neste caso, a r esposta, Y .
Em suma, PLS estima as combinações linear es das variáveis X e Y que apr esentam
sucessivamente covariância máxima entr e si.
O significado de scor e s e dos loading s em PLS é semelhante ao do significado na
metodologia PCA . Contudo, em PLS , os score s de X são influenciados pelos pesos, W .
Estes pesos têm a informação sobr e o peso de cada variável de X na predição de Y ,
equação 2.5 (Här dle (2011); W old et al. (2001)).
T PLS = X · W ∗ (2.5)
Onde,
W ∗ = W · ( P T · W ) − 1 (2.6)
Sendo W os pesos ( W eights ) de X baseados nos r esíduos e P os loading s. Caso Y
seja composto por mais do que um tipo de r esposta, ou seja, Y tem as dimensões I por
H , em que H > 1, este pode ser expresso pela combinação de scor e s, T , loading s ( C ) e
r esíduos ( F ) equação 2.7. Assim os score s de X são usados para a previsão de Y (Här dle
(2011); W old et al. (2001)).
Y = T PLS · C + F (2.7)
Onde, C são pesos ( weights ) de Y e F a matriz de resíduos de pr evisão de Y . Subs-
tituindo T PLS da equação 2.7 pela expressão da equação 2.5, obtém-se a equação 2.8
(Här dle (2011); W old et al. (2001)).
Y = X · W · C + F = X · B + F (2.8)
B r epr esenta os coeficientes do modelo a aplicar aos pr editor es ( X ) para obter a
r esposta ( Y ). B tem dimensões I × H . O algoritmo usado para estimar os parâmetros

8 CAPÍTULO 2. MET ODOLOGIAS E FERRAMENT AS USADAS
do modelo linear pelo método PLS é o algoritmo Nonlinear Iterative Partial Least Squar es
( NIP ALS ) (Sarkodie & Adom 2018).
2.5 T ransformada de Onduleta
Na análise e pr ocessamento de imagem, as transformadas de onduletas, ou em inglês,
W avelet T ransform ( WT ), são referidas por Gonzalez et al. (2009) e Reis (2015) como
ferramenta adequada para análise de texturas. A WT permite a extração de várias
featur e s da imagem r elativa à sua textura, a partir de transformadas duas dimensões
(2D) aplicadas a cada imagem. Normalmente, as transformadas de onduletas per se
não conseguem fazer a análise e pr ocessamento de textura e cor , simultaneamente, de
uma imagem. Contudo, podem-se adotar estratégias r eferidas neste trabalho para o
conseguir (Reis 2015).
As WT transforma o sinal original f i segundo a equação 2.9.
f i =
J dec
∑
j = 1
a j φ j +
J dec
∑
j = 1
d j ψ j (2.9)
Onde, j é o nível de decomposição, J dec é a pr ofundidade de decomposição máxima,
a j é a matriz de apr oximação de r esolução mais gr osseira, d j é a matriz de detalhes cor -
r espondente a um determinado nível de decomposição, φ j bases ortogonais de versões
apr oximadas da função f i e ψ j onduletas ortogonais correspondentes ao nível de deta-
lhe j .
É possível aplicar WT a um sinal 2D r ecorr endo à WT a 2D. Assim, pode-se aplicar
as transformadas de onduleta às imagens. Da aplicação das WT às imagens r esulta
uma matriz de apr oximação de r esolução mais gr osseira a j e três matrizes de detalhe
d k
j por cada nível de decomposição j , com k = 1, 2, 3. Estes corr espondem a combi-
nações de operações de decomposição aplicadas de forma vertical ( d 1
j ), diagonal ( d 2
j )
e horizontal( d 3
j ) no sinal original, a imagem a 2D. Desta forma obtém-se um conjunto
de decomposição como r epr esentado no exemplo da Figura 2.3, com o J dec = 3 (Reis &
Bauer 2009).
W avelets T extur e Analysis ( WT A ) possibilita a extração featur e s a partir de coefici-
entes r esultantes da decomposição da imagem original. Estes coeficientes captam a
informação das várias fr equências espaciais corr espondentes a cada nível de decom-
posição. Como exemplos de WT A featur e s temos a ener gia, entr opia, desvio padrão de
cada bloco de coeficientes, etc. No presente trabalho utilizou-se a ener gia, E k
j , que não
é mais do que o desvio padrão dos coeficientes da WT A , equação 2.10 (Reis & Bauer
2009).
E k
j = σ ( d k
j ) (2.10)
O algoritmo para a aplicação de WT A é apr esentado na Figura ?? . Primeir o a ima-
gem é adquirida ou carr egada. Posteriormente, esta sofr e um pré-pr ocessamento, que
pode consistir em eliminar ruído, corrigir a luminosidade, redimensionar , etc. De se-
guida, é aplicada WT e extraídos os coeficientes para cada bloco (definido por um ní-
vel de decomposição e uma dir eção) e calculadas as featur e s em questão (Reis & Bauer
2009).

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