Transcript
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Aplicaes da Digitalizao 3D:Inspeco e Engenharia Inversa
Verificao de Tolerncias de Fabrico e Qualidade do Processo;
Engenharia Inversa, restauro e recuperao;
Inspeco Remota, em ambientes perigosos.
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Digitalizao 3D:Por Contacto
Contacto
Sem Contacto
Medies Directas(rguas, paqumetros, micrmetros, mesas de coordenadas 3D (CMM), AFM)
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Digitalizao 3D :Fotografia estreo ou mltipla
Contacto
Sem Contacto
Activo
PassivoForma-X
(stereo/multi-vistas, silhuetas, focus/defocus, movimento, textura,
etc.)
Medies Directas(rguas, paqumetros, micrmetros, mesas de coordenadas 3D (CMM), AFM)
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Digitalizao 3D:Silhuetas
Contacto
Sem Contacto
Activo
PassivoForma-X
(stereo/multi-vistas, silhuetas, focus/defocus, movimento, textura,
etc.)
Medies Directas(rguas, paqumetros, micrmetros, mesas de coordenadas 3D (CMM), AFM)
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Digitalizao 3D:Focus/Defocus
Contacto
Sem Contacto
Activo
PassivoForma-X
(stereo/multi-vistas, silhuetas, focus/defocus, movimento, textura,
etc.)
Medies Directas(rguas, paqumetros, micrmetros, mesas de coordenadas 3D (CMM), AFM)
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Parallel/Fan-beam Projections
0 50 100 150rotation angle (degrees)
Density Function
Transmissivo
Reflectivo
Computed Tomography (CT)Transmissive Ultrasound
Digitalizao 3D:Computed Tomography (CT)
Contacto
Sem Contacto
Activo
PassivoForma-X
(stereo/multi-vistas, silhuetas, focus/defocus, movimento, textura,
etc.)
Medies Directas(rguas, paqumetros, micrmetros, mesas de coordenadas 3D (CMM), AFM)
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Mtodos no opticos
(reflective ultrasound, radar, sonar, MRI)
Digitalizao 3D:Mtodos no opticos activos
Transmissivo
Reflectivo
Computed Tomography (CT)Transmissive Ultrasound
Contacto
Sem Contacto
Activo
PassivoForma-X
(stereo/multi-vistas, silhuetas, focus/defocus, movimento, textura,
etc.)
Medies Directas(rguas, paqumetros, micrmetros, mesas de coordenadas 3D (CMM), AFM)
http://upload.wikimedia.org/wikipedia/commons/d/db/Structural.gifhttp://upload.wikimedia.org/wikipedia/commons/d/db/Structural.gifhttp://upload.wikimedia.org/wikipedia/commons/f/f3/Embryo_at_14_weeks_profile.JPGhttp://upload.wikimedia.org/wikipedia/commons/f/f3/Embryo_at_14_weeks_profile.JPGhttp://upload.wikimedia.org/wikipedia/en/a/a1/UltrasoundProbe2006a.jpghttp://upload.wikimedia.org/wikipedia/en/a/a1/UltrasoundProbe2006a.jpg7/23/2019 Scan 3D - Laser
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Variantes activas dos mtodos passivos
(stereo/focus/defocus using projected patterns)
Digitalizao 3D:Variantes activas dos mtodos passivos
Mtodos no opticos
(reflective ultrasound, radar, sonar, MRI)
Transmissivo
Reflectivo
Computed Tomography (CT)Transmissive Ultrasound
Contacto
Sem Contacto
Activo
PassivoForma-X
(stereo/multi-vistas, silhuetas, focus/defocus, movimento, textura,
etc.)
Medies Directas(rguas, paqumetros, micrmetros, mesas de coordenadas 3D (CMM), AFM)
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Tempo de Voo
Digitalizao 3D:Tempo de Voo
nssm
m
c
dt 17
103
0.528
Variantes activas dos mtodos passivos
(stereo/focus/defocus using projected patterns)
Mtodos no opticos
(reflective ultrasound, radar, sonar, MRI)
Transmissivo
Reflectivo
Computed Tomography (CT)Transmissive Ultrasound
Contacto
Sem Contacto
Activo
PassivoForma-X
(stereo/multi-vistas, silhuetas, focus/defocus, movimento, textura,
etc.)
Medies Directas(rguas, paqumetros, micrmetros, mesas de coordenadas 3D (CMM), AFM)
http://upload.wikimedia.org/wikipedia/commons/0/0e/Lidar_P1270901.jpghttp://upload.wikimedia.org/wikipedia/commons/0/0e/Lidar_P1270901.jpg7/23/2019 Scan 3D - Laser
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Triangulao(laser striping and structured lighting)
Digitalizao 3D:Triangulao com Laser
Tempo de Voo
Variantes activas dos mtodos passivos
(stereo/focus/defocus using projected patterns)
Mtodos no opticos
(reflective ultrasound, radar, sonar, MRI)
Transmissivo
Reflectivo
Computed Tomography (CT)Transmissive Ultrasound
Contacto
Sem Contacto
Activo
PassivoForma-X
(stereo/multi-vistas, silhuetas, focus/defocus, movimento, textura,
etc.)
Medies Directas(rguas, paqumetros, micrmetros, mesas de coordenadas 3D (CMM), AFM)
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Digitalizao 3D:Triangulao com luz estruturada
Triangulao(laser striping and structured lighting)
Tempo de Voo
Variantes activas dos mtodos passivos
(stereo/focus/defocus using projected patterns)
Mtodos no opticos
(reflective ultrasound, radar, sonar, MRI)
Transmissivo
Reflectivo
Computed Tomography (CT)Transmissive Ultrasound
Contacto
Sem Contacto
Activo
PassivoForma-X
(stereo/multi-vistas, silhuetas, focus/defocus, movimento, textura,
etc.)
Medies Directas(rguas, paqumetros, micrmetros, mesas de coordenadas 3D (CMM), AFM)
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Desafios
S deve existir uma fonte de luz;
As superfcies no devem ser transparentes, nem reflectoras, nemdifusoras;
Tempo de aquisio funo do tipo de objecto.
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Mtodo
Aplicao de
Textura
Alinhamento
3D Point Clouds
Reconstruo
3D Point Cloud(s)
Captura de
Dados
Extrao
Isosurface
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3D Scanners Comerciais
Caractersticas, vantagens e desvantagens:
Normalmente utilizam laser e uma mesa rotativa;
So demasiado caros (NextEngine ~$3,000 USD);
Executam todo o processo de forma automtica.
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Do-It-Yourself (DIY) 3D Scanners
Caractersticas, vantagens e desvantagens : Normalmente utilizam laser e uma mesa rotativa;
Relativamente baratos (DAVID laser scanner ~$550 USD);
No fazem tudo automaticamente;
Falta normalmente o modulo de calibrao.
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3D Triangulation: plane-ray intersection
ray
plane
intersection point
projector /
coordinate
systems
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Representation of lines and rays
line
q
v
vqp reference
point
vector
scaleparameter
point
q
v
ray=1/2 line vqp
parameteris positive
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Representation of planes
2211 vvqp
1v
2vq
p
P
parametric
n
q
p
0)( qpntP
implicit
2 scaleparameters
referencepoint
2 vectors
point
referencepoint
normalvector
1 implicit
equation
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Triangulation by line-plane intersection
object being
scanned
pqn
}0)(:{ pt qpnpP
projected light plane
p
illuminatedpoint on object
}{ vqpL L
camera ray
Lq
v
intersectionof light plane
with object
same
coordinate
system
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Triangulation by line-line intersection
object beingscanned
}{ 2222 vqpL
camera ray
2q
2v
projected light ray
1q 1v
}{ 1111 vqpL
p
lines may not intersect !
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Approximate line-line intersection
1q
1v
2q
2v
1111 vqp
2222 vqp
),( 2112 p
Midpoint of segment joiningarbitrary points in the two lines
1q1v
2q
2v
),( 2112 p
Least-squares approach
Find parameters which minimize
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Approximate line-line intersection
1111 vqp
2222 vqp
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Perspective projection under the pinhole model
center of projection
imagepoint
image plane
3D point
light directionfor a projector
light directionfor a camera
Calibration: mapping from image points to rays
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The ideal pinhole camera
camera coordinate system = world coordinate system
1v3v2v
1
2
1
u
u
u
0q
3
2
1
pp
p
p
1f
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The general pinhole model
world coordinate systemcamera coordinate system
W
C
1 2
3
1
2 3 u
p
TRXWC
Ideal assumptions Image lengths = world lengths Focal length = 1 Image origin = optical center Image plane spanned by two basis vectors
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The general pinhole model
world coordinate systemcamera coordinate system
W
C
1 2
31
2 3 up
TRXWC
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Plane defined by image line and center of projection
center of projection
q
n
image plane
}0)(:{ qpnpP t
}0:{ uluL t
Implicit equation of line in image coordinates
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Triangulao por Laser
A linha laser move-se manualmente ou atravs de um mecanismo;
Triangulao por profundidade de cada pixel;
Requer uma correcta calibrao;
Utilizado em DIY 3D scanners.
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Materiais Necessrios
Camera (QuickCam 9000);
Laser;
Painis de Calibrao;
Montagem.
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Processo de Digitalizao
C
1
2
3
)(tVl
),( yxVC
)(),( tVyxVP lC
P
p
)(tVl
),( yxVC
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Processo de Digitalizao
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I max (x;y) = maxt I (x; y; t)I min (x; y) = mint I (x; y; t)I shadow (x; y) = I m ax (x ;y)+ I m i n (x;y)
2
Converter o video de RGB para tons de cinzento;
Determinar per-pixel minima e maxima intensidade;
Calcular o intervalo de variao.
Anlise do Processo
I min (x; y) = mint I (x; y; t)
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Anlise do Processo
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Exemplos
J.-Y. Bouguet and P. Perona. 3D photography
on your desk. Intl. Conf. Comp. Vision, 1998
J. Kim and J. Wu. Scanning with Shadows. CSE
558 Project Report (U. Washington), 2001
P. Blaer, N. Hasan, C. Tripp, and L. Volchok. 3D DesktopPhotography by Eclipse. Project Report (Columbia), 2001 J. Kubicky. Home-Brew 3-DPhotography. EE 149 Project Report
Caltech 1998
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As digitalizaes tm ento de ser
fundidas
U M O B J E C T O N OP O D E S E R
D I G I T A L I Z A D O D EU M A S V E Z
Cada digitalizao feita num referencial
diferente;
Por forma a juntar e fundir as vrias
digitalizaes, todos os referncias devem ser
determinados em relao a um referencial
global.
Juntando e Trabalhando as Superfices
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A densely sampled point cloud covering the whole surface of the object
usually requires merging many scans
Juntando e Trabalhando as Superfices
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http://www.research.ibm.com/pieta
Shape
Appearance
Por vezes sero necessrios muitas Digitalizaes
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Juntando vrios Point Clouds
Um a um as nuvens de pontos devem ser juntas;
Por fim os erros introduzidos devem ser eliminados.
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Processo Manual
Escolher no mnimo 3 pontos comuns;
Resolver a matriz de transformao de coordenadas e aplicar nuvem de pontos;
Corrigir a posio de forma automtica.
Simples se o modelo for
pequeno
Moving
Fixed
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Iterative Closest Point Algorithm (ICP)
1.
Torna o processo automtico:
2.
Encontra os pontos correspondentes:
3.
Calcula a matriz de transformao de coordenadas:
4.
E repete o processo at obter convergncia.
p1; : : : ; pN
q1; : : : ; qN
E(R; T) = 1NN
j = 1 kR pj + T qjk2
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Formas de representar Superfcies
Superfcies:
Paramtrica
Implcita
Para alterar uma superfcie, temos de trabalhar sobre a sua representao:
A representao composta por um conjunto de parmetros;
O que til para efectuar operaes
Point clouds (superfcie representada por um conjunto
de pontos):
Posies, normais, cores, etc
Malhas:
Vrtices e faces, normais, cor, textura.
S = f p : f (p) = 0gS = f p = (s1; s2)g
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Slidos e Superfcies Fechadas
Muitas aplicaes requerem que a point cloud seja transformada numa superfcie fechada:
Point clouds no possuem informao suficiente:
Como tal esta deve ser calculada, normais e pontos
vizinhos.
Assim possvel ligar os pontos da malha por arestas.
Se a superfcie for totalmente fechada, torna-se
prova de gua
Desta forma ser possvel recriar um slido e como tal trabalh-lo em programas como o SolidWorks.
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Exemplos
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Reconstruo de Superfcies
Todas as superfcies implcitas so prova de gua
Uma Iso-superfcie uma aproximao poligonal a uma superfcie implcita;
Marching Cubes um dos algoritmos para obter uma iso-superfcie a partir de uma superfcie implcita ou de
um point cloud;
Estes algoritmos so normalmente baseados nas equaes de Poisson.
S = f p : f (p) = 0g
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Exemplos
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Exemplos
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Exemplos
1. Filters -> Normals, Curvatures and Orientation ->
Compute normals for point sets (50-100)
2. Filters -> Point Set -> Poisson Reconstruction (Octree
Depth (try 9-11))
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Processamento Elementar de Superfcies
ALG O R I T M O S S I M P L E S E I T E R AT I V O S P A R A M E L H O R A R O R E S U LTA D O ;
PO LY G O N M E S H S M O O T H I N G / D E N O I S I N G
PO LY G O N M E S H S I M P L I F I C AT I O N
J 3 D P G P ( JA V A 3 D PH O T O G R A P H Y A N D GE O M E T R Y PR O C E S S I N G )
ME S H L A B
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S /
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Polygon Mesh Smoothing / Denoising
Laplacian Smoothing
Low Pass Filter
N=10 N=40 N=240
Laplacian smoothing is the simplest smoothing/denoising algorithm
Fix to shrinkage problem: toggle parameter sign at each iteration
L l i S thi
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Laplacian Smoothing
viv
j
Intuition: remove noise by averaging neighboring positions
Compute displacement vector for each vertex
Move vertices in the displacement vector direction
Can use more general weights
v0i = vi + vi
j i vi = 1jvij j 2 i ? (vj vi ) vi = j 2 i ?wi j (vj vi )
wi j > 0 j 2 i ?wi j (vj vi )
P li M h Si lifi ti / D i ti
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Poligon Mesh Simplification / Decimation
A L G O R I TH M S T O R E D U C E T H E N U M B E R O F V E R T I C E S A N D F A C E SW H I L E P R E S E R V I N G G E O M E T R I C A P P R O X I M A T I O N T O O R I G I N A LS H A P E
Vertex clustering (Rossignac & Borrel, 1993)
Edge Collapse (Garand Heckbert 1997; many others)
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