computer vision for robotic navigation and augmented reality applications
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8/9/2019 Computer vision for robotic navigation and augmented reality applications
1/44
Introduction
Computer vision by phase encoding methods
Developed phase-based measurement system
Conclusions
References
Computer vision for robotic navigation and augmentedreality applications
Dr. Rigoberto Juarez Salazar
1Instituto Tecnológico Superior de ZacapoaxtlaDivisión de Ingenierı́a Informática
Congreso Multidisciplinario Ciencia y Tecnologı́a para elDesarrollo Sustentable
October 15, 2014
1 / 4 0 Dr. Rigoberto Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
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Introduction
Computer vision by phase encoding methods
Developed phase-based measurement system
Conclusions
References
Content
1 Introduction
2 Computer vision by phase encoding methods
3 Developed phase-based measurement systemNormalización de patrones de franjasFourier fringe-normalized analysisInhomogeneous phase-shiftingDesenvolvimiento de fase
4 Conclusions
5 References
2 / 4 0 Dr. Rigoberto Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
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Introduction
Computer vision by phase encoding methods
Developed phase-based measurement system
Conclusions
References
Introduction
Figura : Metrology is a very important task in most of human task. It increases our senses,particularly, vision sense. Vision is about discovering from images what is present in the scene and
where it is. It is our most powerful sense.
3 / 4 0 Dr. Rigoberto Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
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Introduction
Computer vision by phase encoding methods
Developed phase-based measurement system
Conclusions
References
What is computer vision?
In computer vision a camera (or several cameras) is linked to a computer. Thecomputer automatically interprets images of a real scene to obtain useful information(e.g., 3D reconstruction) and then acts on that information (e.g. for navigation or
manipulation).
4 / 4 0 Dr. Rigoberto Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
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Introduction
Computer vision by phase encoding methods
Developed phase-based measurement system
Conclusions
References
What is computer vision?
In computer vision a camera (or several cameras) is linked to a computer. Thecomputer automatically interprets images of a real scene to obtain useful information(e.g., 3D reconstruction) and then acts on that information (e.g. for navigation or
manipulation).
It is not:
Image processing. Image enhancement, image restoration, image compression. Takean image and process it to produce a new image which is, in someway, more desirable.
Pattern recognition. Classifies patterns into one of a finite set of prototypes.
4 / 4 0 Dr. Rigoberto Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
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Introduction
Computer vision by phase encoding methods
Developed phase-based measurement system
Conclusions
References
Applications of computer vision
Automation of industrial processes: object recognition, visual inspection, robothand-eye coordination, robot navigation.
Space and military: remote sensing, surveillance, target detection and tracking(traffic, aircraft, etc.), UAV localization.
Human-computer interaction: Face detection and recognition. Mobile-phoneapplications, augmented reality.
3D modeling.
5 / 4 0 Dr. Rigoberto Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
I t d ti
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Introduction
Computer vision by phase encoding methods
Developed phase-based measurement system
Conclusions
References
A proposed computer vision-based robotic navigation
6 / 4 0 Dr. Rigoberto Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
Introduction
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Introduction
Computer vision by phase encoding methods
Developed phase-based measurement system
Conclusions
References
Computer vision-based robotic navigation
7 / 4 0 Dr. Rigoberto Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
Introduction
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Introduction
Computer vision by phase encoding methods
Developed phase-based measurement system
Conclusions
References
Approaches in computer vision
There are two main approaches to obtain three-dimensional information of a scene.
Amplitude or intensity modulation
The information is obtained from variations of intensity of the object, for example,
shadows, illumination conditions, surface color, etc. It is simple to implement and easythe experimental setup. However, it is very sensitive to noise sources.
Phase modulation
The information of interest is encoded into a phase distribution, for example, by phaseshifting, or frequency carrier. The experimental setup is lightly more complex than
amplitude modulation approach. The data processing is more complex. The mainadvantages is that phase modulation have a very high robustness to noise sources. Itallows to reach a high resolution.
8 / 4 0 Dr. Rigoberto Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
Introduction
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Introduction
Computer vision by phase encoding methods
Developed phase-based measurement system
Conclusions
References
Phase-based measurement systems
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Figura : General scheme of a phase-based measurement system.
The experimental setup generates fringe-patterns where the encoded phase isassociated with the physical parameter of interest.
The fringe analysis block extracts the physical information from the givenfringe-patterns.
9 / 4 0 Dr. Rigoberto Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
Introduction
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Introduction
Computer vision by phase encoding methods
Developed phase-based measurement system
Conclusions
References
Computer vision by phase encoding methods
By the good properties of using phase modulation, we are focused on reconstruction of3D objects by phase-shifting as well as Fourier fringe analysis to robotic navigation andaugmented reality applications.
The phase encoding approach consist on the following two procedures.
1. Wrapped phase extraction
One or more fringe-patterns are processed to obtain the encoded phase in a wrappedformat. For this, the two main methods are
Phase-shifting method.
Advantages. Full resolution is reached, algorithms are simple and very robust.Disadvantages. More than one image is required. This make it no much available
for real-time applications.Fourier fringe analysis.
Advantages Only one image is sufficient to work, it is appropriate for real-timeapplications.
Disadvantages. Reduced resolution, algorithms are complex. Filtering is difficult.
10 / 40 Dr. Rigober to Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
Introduction
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8/9/2019 Computer vision for robotic navigation and augmented reality applications
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Computer vision by phase encoding methods
Developed phase-based measurement system
Conclusions
References
Computer vision by phase encoding methods
By the good properties of using phase modulation, we are focused on reconstruction of3D objects by phase-shifting as well as Fourier fringe analysis to robotic navigation andaugmented reality applications.
The phase encoding approach consist on the following two procedures.
2. Phase unwrapping
The synthetic phase jumps induced by the phase extraction must be removed beforethat any useful information can be reached. For this, a phase unwrapping process isapplied in the pipeline.
.
11 / 40 Dr. Rigober to Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
Introduction
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Computer vision by phase encoding methods
Developed phase-based measurement system
Conclusions
References
Phase demodulation process
(a) (b) (c)
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Figura : General scheme of a phase-based measurement system.
12 / 40 Dr. Rigober to Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
IntroductionNormalización de patrones de franjas
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Computer vision by phase encoding methods
Developed phase-based measurement system
Conclusions
References
Normalizacion de patrones de franjas
Fourier fringe-normalized analysis
Inhomogeneous phase-shifting
Desenvolvimiento de fase
Fringe-pattern normalization. . .
An efficient and automatic processing algorithm.
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13 / 40 Dr. Rigober to Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
IntroductionNormalización de patrones de franjas
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Computer vision by phase encoding methods
Developed phase-based measurement system
Conclusions
References
Normalizacion de patrones de franjas
Fourier fringe-normalized analysis
Inhomogeneous phase-shifting
Desenvolvimiento de fase
Fringe-pattern normalization
Let be a set of K fringe-patterns of the form
I k (p ) = a k (p ) + b k (p ) cos Φk (p ), k = 0,K − 1. (1)
Then, the background and modulation lights can be recovered by1
a k = Aa A†a I k ,
b 2k = 2Ab A†b
(I k − a k )2.
(2)
Finally, the normalization is carried out by the function sat(·) as
Ī k = sat
I k − a k
b k
= cos Φk (p ) ∀b k (p ) = 0. (3)
I k
u
2 sat âk
LS +!
+
LS
b̂2
k 2 b̂
k u v
2 u
! I k
I k
Figura : Block diagram of the proposed fringe-pattern normalization method.
1Juarez-Salazar, R., Robledo-Sanchez, C., Meneses-Fabian, C., Guerrero-Sanchez, F., and Aguilar, L. A.Generalized phase-shifting interferometry by parameter estimation with the least squares method. Optics and
Lasers in Engineering , 51(5):626 – 632 (2013).
14 / 40 Dr. Rigober to Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
Introduction
C i i b h di h dNormalización de patrones de franjas
http://goforward/http://find/http://goback/
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Computer vision by phase encoding methods
Developed phase-based measurement system
Conclusions
References
Normalizacion de patrones de franjas
Fourier fringe-normalized analysis
Inhomogeneous phase-shifting
Desenvolvimiento de fase
Example for the two-dimensional caseFringe-pattern normalization
Video...
15 / 40 Dr. Rigober to Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
Introduction
C t i i b h di th dNormalización de patrones de franjas
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Computer vision by phase encoding methods
Developed phase-based measurement system
Conclusions
References
p j
Fourier fringe-normalized analysis
Inhomogeneous phase-shifting
Desenvolvimiento de fase
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Wrapped phase extraction. . .
Advanced algorithms for the extraction of wrapped phase byusing spatial and temporal carriers.
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16 / 40 Dr. Rigober to Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
Introduction
Computer vision by phase encoding methodsNormalización de patrones de franjas
http://find/http://goback/
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8/9/2019 Computer vision for robotic navigation and augmented reality applications
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Computer vision by phase encoding methods
Developed phase-based measurement system
Conclusions
References
Fourier fringe-normalized analysis
Inhomogeneous phase-shifting
Desenvolvimiento de fase
Fourier fringe-normalized analysis
17 / 40 Dr. Rigober to Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
Introduction
Computer vision by phase encoding methodsNormalización de patrones de franjas
http://find/
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Computer vision by phase encoding methods
Developed phase-based measurement system
Conclusions
References
Fourier fringe-normalized analysis
Inhomogeneous phase-shifting
Desenvolvimiento de fase
Fourier fringe-normalized analysis
The classical approach considers fringe-patterns of the form
I (p ) = a (p ) + b (p ) cos[φ(p ) + 2πf · p ]. (4)
The respective spectrum is
I (µ) = A(µ) + C (µ − f ) + C ∗(µ + f ). (5)
If a fringe-pattern normalization is previously applied, both background and modulation
lights are removed and the respective spectrum is suppressed. Thus, the filteringprocedure is less critical
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Figura : (Top) Analysis scheme with the Fourier method. (Down) Proposed scheme.2
2Casco-Vasquez, J. F., Juarez-Salazar, R., Robledo-Sanchez, C., Rodriguez-Zurita, G., Sanchez, F. G.,Arévalo Aguilar, L. M., and Meneses-Fabian, C. Fourier normalized-fringe analysis by zero-order spectrum
suppression using a parameter estimation approach. Optical Engineering , 52(7):074109 –074109 (2013).18 / 40 Dr. Rigober to Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
Introduction
Computer vision by phase encoding methodsNormalización de patrones de franjas
http://find/
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8/9/2019 Computer vision for robotic navigation and augmented reality applications
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Computer vision by phase encoding methods
Developed phase-based measurement system
Conclusions
References
Fourier fringe-normalized analysis
Inhomogeneous phase-shifting
Desenvolvimiento de fase
Numerical example
Casco-Vasquez, J. F., Juarez-Salazar, et. al., Fourier normalized-fringe analys is by ze ro -ord er s p ec tru m suppression using a parameter estimation approach. Optical Engineering , 52(7):074109–074109 (2013).19 / 40 Dr. Rigober to Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
Introduction
Computer vision by phase encoding methodsNormalización de patrones de franjas
F i f i li d l i
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Computer vision by phase encoding methods
Developed phase-based measurement system
Conclusions
References
Fourier fringe-normalized analysis
Inhomogeneous phase-shifting
Desenvolvimiento de fase
Numerical and experimental examplesWrapped phase extraction by using the proposed Fourier fringe-normalized analysis.
3Casco-Vasquez, J. F., Juarez-Salazar, R., Robledo-Sanchez, C., Rodriguez-Zurita, G., Sanchez, F. G.,Arévalo Aguilar, L. M., and Meneses-Fabian, C. Fourier normalized-fringe analysis by zero-order spectrum
suppression using a parameter estimation approach. Optical Engineering , 52(7):074109 –074109 (2013).20 / 40 Dr. Rigober to Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
Introduction
Computer vision by phase encoding methodsNormalización de patrones de franjas
Fourier fringe normalized analysis
http://find/http://goback/
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p y p g
Developed phase-based measurement system
Conclusions
References
Fourier fringe-normalized analysis
Inhomogeneous phase-shifting
Desenvolvimiento de fase
Improved efficiency and robustnessFourier fringe-normalized analysis
Video...
21 / 40 Dr. Rigober to Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
Introduction
Computer vision by phase encoding methodsNormalización de patrones de franjas
Fourier fringe normalized analysis
http://find/
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Developed phase-based measurement system
Conclusions
References
Fourier fringe-normalized analysis
Inhomogeneous phase-shifting
Desenvolvimiento de fase
Inhomogeneous generalized
phase-shifting algorithm
22 / 40 Dr. Rigober to Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
IntroductionComputer vision by phase encoding methods
Normalización de patrones de franjas
Fourier fringe-normalized analysis
http://find/
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8/9/2019 Computer vision for robotic navigation and augmented reality applications
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Developed phase-based measurement system
Conclusions
References
Fourier fringe normalized analysis
Inhomogeneous phase-shifting
Desenvolvimiento de fase
Inhomogeneous generalized phase-shifting algorithm
For phase-shifting, it are considered fringe-patterns of the form
I k (p ) = a k (p ) + b k (p ) cos[φ(p ) + δk (p )], (6)
where the phase shift δk (p ) is, in general, inhomogeneous and unknown .Video...
xy
P h a s e
s h i f t δ
(a)
xy
P h a s e
s h i f t δ
(b)
xy
(c)
P h a s e
s h i f t δ
xy
(d)
P h a s e
s h i f t δ
Figura : Generalized phase shift. Homogeneous: (a) linear, and (b) nonlinear in k . Inhomogeneous:(c) nonlinear in k but linear in p , and (d) nonlinear in both k and p .
23 / 40 Dr. Rigober to Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
IntroductionComputer vision by phase encoding methods
D l d h b d
Normalización de patrones de franjas
Fourier fringe-normalized analysis
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Developed phase-based measurement system
Conclusions
References
Fourier fringe normalized analysis
Inhomogeneous phase-shifting
Desenvolvimiento de fase
Algoritmo de corrimiento de fase generalizado inhomogéneoDescripción del algoritmo
1 Normalización de los patrones de franjas.2 De las cantidades Ak = Ī k −1 + Ī k y S k = Ī k −1 − Ī k de dos patrones adyacentes,
el coseno del paso de fase entre esos patrones se obtiene mediante
c Ak = Ac A†c (A
2k − 1), (7a)
c Sk = Ac A†c (1 − S
2k ). (7b)
3 La función Γ(·) [ver Fig. 8(b)] se usa para seleccionar entre c Ak y c Sk comocosαk = c Sk Γ(ωc k ) + c Ak Γ(−ωc k ), (8)
donde el paso de fase αk se obtiene calculando el coseno inverso de (8).
−3
−2
−1
0
1
2
3
(a)
0 π /4 π /2
Phase step αk
3π /4 π −1 −0.5 0 0.5 1
0
0.2
0.4
0.6
0.8
1
ck
(b)
−3
−2
−1
0
1
2
3
(c)
0 π /4 π /2
Phase step αk
3π /4 π
A2 − 1
1 − S2
cos(α
k ) Γ(−ω c k )
Γ(ω ck )
Equivalent data
cos(αk )
k
k
Figura : (a) Los datos A2k − 1 y 1 − S 2k para estimación de cos αk . Para αk ∈ [0, π/2] es
conveniente elegir 1 − S 2k porque la amplitud del ruido es baja, y viceversa para αk ∈ [π/2, π].24 / 40 Dr. Rigober to Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
IntroductionComputer vision by phase encoding methods
D l d h b d t t
Normalización de patrones de franjas
Fourier fringe-normalized analysis
http://find/http://goback/
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Developed phase-based measurement system
Conclusions
References
g y
Inhomogeneous phase-shifting
Desenvolvimiento de fase
Algoritmo de corrimiento de fase generalizado inhomogéneo
4 El corrimiento de fase es recuperado mediante la sumatoria:
δk = δ0 +k
=1
α, k = 1, 2, · · · ,K − 1. (9)
5 finalmente, la fase envuelta es obtenida mediante
φw = arctan(ζ/ξ), (10)
donde ζ = sin φ y ξ = cosφ son obtenidos mediante:ξζ
= A†
φ
I 0 I 1 · · · I K −1
T , Aφ =
cos δk − sin δk
. (11)
!
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I I sw cos
!1
LS
LS
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cos! !
I
! ! w
#$% #$$%
LS
Figura : Diagrama de bloques del algoritmo de corrimiento de fase generalizado inhomogéneo
propuesto.4
4R. Juarez-Salazar, et. al., Generalized phase-shifting algorithm for inhom og ene ou s pha se s hi ft an d
spatio-temporal fringe visibility variation. Opt. Express , 22(4):4738–4750 (2014).25 / 40 Dr. Rigober to Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
IntroductionComputer vision by phase encoding methods
Developed phase based measurement system
Normalización de patrones de franjas
Fourier fringe-normalized analysis
http://find/
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Developed phase-based measurement system
Conclusions
References
g y
Inhomogeneous phase-shifting
Desenvolvimiento de fase
Extracción rápida, automática y robusta de fase envueltaAlgoritmo de corrimiento de fase generalizado inhomogéneo
Video...
•Corrimiento de fase generalizado •Visibilidad espacio-temporal •Solo dos patrones
26 / 40 Dr. Rigober to Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
IntroductionComputer vision by phase encoding methods
Developed phase based measurement system
Normalización de patrones de franjas
Fourier fringe-normalized analysis
http://find/http://goback/
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8/9/2019 Computer vision for robotic navigation and augmented reality applications
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Developed phase-based measurement system
Conclusions
References
Inhomogeneous phase-shifting
Desenvolvimiento de fase
Extracción rápida, automática y robusta de fase envueltaAlgoritmo de corrimiento de fase generalizado inhomogéneo
Video...
•Corrimiento de fase no-lineal inhomogéneo •Visibilidad espacio-temporal •Solo dos
patrones
27 / 40 Dr. Rigober to Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
IntroductionComputer vision by phase encoding methods
Developed phase-based measurement system
Normalización de patrones de franjas
Fourier fringe-normalized analysis
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Developed phase based measurement system
Conclusions
References
Inhomogeneous phase-shifting
Desenvolvimiento de fase
Desenvolvimiento de fase. . .
Desenvolvimiento de fase rápido y exacto
! !!! 1
2! round
!k LS
!k 2!
2! k
!
! +round
k
28 / 40 Dr. Rigober to Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
IntroductionComputer vision by phase encoding methods
Developed phase-based measurement system
Normalización de patrones de franjas
Fourier fringe-normalized analysis
I h h hifti
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Developed phase based measurement system
Conclusions
References
Inhomogeneous phase-shifting
Desenvolvimiento de fase
Desenvolvimiento de fase
Un mapa de fase envuelto ψ(p ) puede ser descrito como
ψ(p ) = φ(p ) − 2πk (p ), k (·) ∈ Z , (12)
donde φ(p ) es el mapa de fase continuo y 2πk (p ) (con k una función de valor entero)son los saltos de fase.
Enfoque espacial de desenvolvimiento de fase
En general, los algoritmos de desenvolvimiento de fase se basan en la ecuación deItoh:
∇φ(p ) = W [∇ψ(p )]. (13)
La ecuación (13) se puede resolver para φ mediante los métodos de seguimiento de
trayectoria o de norma mı́nima:
φ(p ) = φ0(p ) +
Ω
W{ψ(p )} dp , o mı́nφ
W [∇ψ(p )] − ∇φ(p ). (14)
29 / 40 Dr. Rigober to Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
IntroductionComputer vision by phase encoding methods
Developed phase-based measurement system
Normalización de patrones de franjas
Fourier fringe-normalized analysis
Inhomogeneo s phase shifting
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p p y
Conclusions
References
Inhomogeneous phase-shifting
Desenvolvimiento de fase
Desenvolvimiento de fase
Usualmente, el desenvolvimiento de fase se realiza removiendo los saltos de fase yreconstruyendo el mapa de fase continuo.
φ(p ) = ψ(p ) + 2πk (p ), (15)
Alternativamente, es posible reconstruir los saltos de fase y entonces agregar lainformación de fase envuelta para obtener un mapa de fase continuo.
φ(p ) = ψ(p ) + 2πk (p ). (16)
Algunas ventajas del método alternativo
∇ψ(·) ∈ , ∇k (·) ∈ D ={−1,0, 1} Caso discreto,
{−∞, 0,∞} Caso continuo. (17)
Esto sugiere algoritmos más simples y robustos debido a que es directo y estableaproximar a un elemento de tres posibles.
30 / 40 Dr. Rigober to Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
IntroductionComputer vision by phase encoding methods
Developed phase-based measurement system
Normalización de patrones de franjas
Fourier fringe-normalized analysis
Inhomogeneous phase shifting
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Conclusions
References
Inhomogeneous phase-shifting
Desenvolvimiento de fase
Desenvolvimiento de fase por mı́nimos cuadrados y redondeo
Se puede mostrar que el gradiente ∇k (p ) satisface la ecuación
∇k (p ) = round
1
2π∇ψ
, (18)
donde round(·) indica la operación de redondeo. Entonces, la función k se puedeestimar desde ∇k mediante el problema de optimización:
m ı́nk̃ k x − k̃LT x 2
F
+ k y − Ly k̃ 2F , (19)
donde k̃ es la función que aproxima a los datos k .
El problema de optimización (19) es equivalente a resolver la ecuación de Lyapunov[?] Ak̃ + k̃ B = C , con A = LT y Ly , B = L
T x Lx , y C = L
T y k y + k x Lx .
! !!!
1
2! round !k LS
!
k 2! 2! k
!
! +round k
Figura : Desenvolvimiento de fase por mı́nimos cuadrados y redondeo.5
5R. Juarez-Salazar, et. al., Phase-unwrapping algorithm by a rounding-lea st- squ ar es ap pro a ch . Op t.
Engineering , 53(2):074109 (2013).31 / 40 Dr. Rigober to Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
IntroductionComputer vision by phase encoding methods
Developed phase-based measurement system
Normalización de patrones de franjas
Fourier fringe-normalized analysis
Inhomogeneous phase-shifting
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Conclusions
References
Inhomogeneous phase-shifting
Desenvolvimiento de fase
Desenvolvimiento de fase rápido, automático y exactoDesenvolvimiento de fase por mı́nimos cuadrados y redondeo
Video... •Funcionamiento del algoritmo de desenvolvimiento de fase propuesto
32 / 40 Dr. Rigober to Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
IntroductionComputer vision by phase encoding methods
Developed phase-based measurement system
C
Normalización de patrones de franjas
Fourier fringe-normalized analysis
Inhomogeneous phase-shifting
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Conclusions
References
Inhomogeneous phase shifting
Desenvolvimiento de fase
Desenvolvimiento de fase rápido, automático y exactoDesenvolvimiento de fase por mı́nimos cuadrados y redondeo
Video... •Factibilidad del algoritmo propuesto
33 / 40 Dr. Rigober to Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
IntroductionComputer vision by phase encoding methods
Developed phase-based measurement system
C l i
Normalización de patrones de franjas
Fourier fringe-normalized analysis
Inhomogeneous phase-shifting
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Conclusions
References
o oge eous p ase s t g
Desenvolvimiento de fase
Desenvolvimiento de fase rápido, automático y exactoDesenvolvimiento de fase por mı́nimos cuadrados y redondeo
Figura : Ejemplos de desenvolvimiento de fase. (1ra columna) Datos sintéticos, (2da y 3racolumna) Datos experimentales obtenidos por interferencia, (4ta columna) Datos experimentales
obtenidos por proyección de franjas.
34 / 40 Dr. Rigober to Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
IntroductionComputer vision by phase encoding methods
Developed phase-based measurement system
Conclusions
Normalización de patrones de franjas
Fourier fringe-normalized analysis
Inhomogeneous phase-shifting
http://find/http://goback/
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Conclusions
References
g p g
Desenvolvimiento de fase
Desenvolvimiento de fase rápido, automático y exactoDesenvolvimiento de fase por mı́nimos cuadrados y redondeo
Reconstrucción de objetos 3D mediante proyección de franjas usando el algoritmo dedesenvolvimiento de fase propuesto.
35 / 40 Dr. Rigober to Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
IntroductionComputer vision by phase encoding methods
Developed phase-based measurement system
Conclusions
Normalización de patrones de franjas
Fourier fringe-normalized analysis
Inhomogeneous phase-shifting
http://find/http://goback/
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Conclusions
ReferencesDesenvolvimiento de fase
Desenvolvimiento de fase rápido, automático y exactoDesenvolvimiento de fase por mı́nimos cuadrados y redondeo
Reconstrucción de objetos 3D mediante proyección de franjas usando el algoritmo dedesenvolvimiento de fase propuesto.
35 / 40 Dr. Rigober to Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
IntroductionComputer vision by phase encoding methods
Developed phase-based measurement system
Conclusions
Normalización de patrones de franjas
Fourier fringe-normalized analysis
Inhomogeneous phase-shifting
http://find/http://goback/
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Conclusions
ReferencesDesenvolvimiento de fase
Desenvolvimiento de fase rápido, automático y exactoDesenvolvimiento de fase por mı́nimos cuadrados y redondeo
Reconstrucci´on de objetos 3D mediante proyecci
´on de franjas usando el algoritmo dedesenvolvimiento de fase propuesto.
35 / 40 Dr. Rigober to Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
IntroductionComputer vision by phase encoding methods
Developed phase-based measurement system
Conclusions
Normalización de patrones de franjas
Fourier fringe-normalized analysis
Inhomogeneous phase-shifting
D l i i d f
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Conclusions
ReferencesDesenvolvimiento de fase
Desenvolvimiento de fase rápido, automático y exactoDesenvolvimiento de fase por mı́nimos cuadrados y redondeo
Reconstrucción de objetos 3D mediante proyección de franjas usando el algoritmo dedesenvolvimiento de fase propuesto.
35 / 40 Dr. Rigober to Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
IntroductionComputer vision by phase encoding methods
Developed phase-based measurement system
Conclusions
Normalización de patrones de franjas
Fourier fringe-normalized analysis
Inhomogeneous phase-shifting
D l i i t d f
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ReferencesDesenvolvimiento de fase
Desenvolvimiento de fase rápido, automático y exactoDesenvolvimiento de fase por mı́nimos cuadrados y redondeo
Reconstrucción de objetos 3D mediante proyección de franjas usando el algoritmo dedesenvolvimiento de fase propuesto.
(a) (b) (c)
36 / 40 Dr. Rigober to Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
IntroductionComputer vision by phase encoding methods
Developed phase-based measurement system
Conclusions
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References
Conclusions
General conclusions
1 A fringe analysis scheme to phase demodulation for fast and automaticapplications was presented.
2 The simplicity of the developed algorithms, makes possible the implementation ofthe fringe analysis toolbox in dedicated hardware to address real-time
applications.
3 By the flexibility of the proposed scheme, it may be implemented in many othermeasurement areas such as machine vision and adaptive optics.
Particular conclusions
1 Like the Fourier fringe analysis method, the proposed fringe-pattern and thegeneralized phase-shifting algorithms may be extended to more than two spatialdimensions.
2 For the proposed generalized phase-shifting algorithm, if the optical setup is staticand the object is dynamic, the computed phase shift will correspond to the object.It may be useful to extract the phase object without a phase shift. An application of
this may be optical coherent tomography.37 / 40 Dr. Rigober to Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
IntroductionComputer vision by phase encoding methods
Developed phase-based measurement system
Conclusions
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References
References I
R. Juarez-Salazar, C. Robledo-Sanchez, C. Meneses-Fabian, F. Guerrero-Sanchez, and L. A. Aguilar,
“Generalized phase-shifting interferometry by parameter estimation with the least squares method,” Optics and Lasers in Engineering 51, 626–632 (2013).
Robledo-Sanchez, C., Juarez-Salazar, R., Meneses-Fabian, C., Guerrero-Sánchez, F., Aguilar, L. M. A.,
Rodriguez-Zurita, G., and Ixba-Santos, V. “Phase-shifting interferometry based on the lateral displacement ofthe light source” Opt. Express , 21(14):17228–17233 (2013).
Casco-Vasquez, J. F., Juarez-Salazar, R., Robledo-Sanchez, C., Rodriguez-Zurita, G., Sanchez, F. G.,Arévalo Aguilar, L. M., and Meneses-Fabian, C. “Fourier normalized-fringe analysis by zero-order spectrumsuppression using a parameter estimation approach” Optical Engineering , 52(7):074109–074109 (2013).
Gannavarpu Rajshekhar and Pramod Rastogi “Fringe analysis: Premise and perspectives” Optics and Lasers
in Engineering , 50(8):iii–x (2012).
J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, ”Digital
wavefront measuring interferometer for testing optical surfaces and lenses,.Appl. Opt. 13, 2693-2703 (1974).
K. Creath, ”Phase measurement interferometry techniques,ı̈n ”Progress in optics,”vol. 26, E. Wolf, ed.
(Elsevier Science Publishers, 1988), pp. 349-393.
L. L. Deck, ”Suppressing phase errors from vibration in phase-shifting interferometry,.Appl. Opt. 48,
3948-3960 (2009).
38 / 40 Dr. Rigober to Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
IntroductionComputer vision by phase encoding methods
Developed phase-based measurement system
Conclusions
http://find/http://goback/
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References
References II
C. J. Morgan, ”Least-squares estimation in phase-measurement interferometry,.Opt. Lett. 7, 368-370 (1982).
J. E. Greivenkamp, ”Generalized data reduction for heterodyne interferometry,.Optical Engineering 23,
350-352 (1984).
G. Lai and T. Yatagai, ”Generalized phase-shifting interferometry,”J. Opt. Soc. Am. A 8, 822-827 (1991).
L. Z. Cai, Q. Liu, and X. L. Yang, ”Generalized phase-shifting interferometry with arbitrary unknown phase
steps for difraction objects,.Opt. Lett. 29, 183-185 (2004).
X. Xu, L. Cai, H. Yuan, Q. Zhang, G. Lu, and C. Wang, ”Phase shift selection for two-step generalized
phase-shifting interferometry,.Appl. Opt. 50, H171-H176 (2011).
A. Patil and P. Rastogi, .Approaches in generalized phase shifting interferometry,.Optics and Lasers in
Engineering 43, 475-490 (2005).
C. T. Farrell and M. A. Player, ”Phase-step insensitive algorithms for phase-shifting
interferometry,”Measurement Science and Technology 5, 648 (1994).
Pramod K. Rastogi. Digital speckle pattern interferometry and related techniques. John Wiley and Sons, LTD ,2001.
D. Malacara, ed., Optical shop testing (John Wiley & Sons, Inc., 2007), 3rd ed.
39 / 40 Dr. Rigober to Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
IntroductionComputer vision by phase encoding methods
Developed phase-based measurement system
Conclusions
R f
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References
Thank you very much for your attention
Any question?
40 / 40 Dr. Rigober to Juárez Salazar rjuarezsalazar@gmail.com Computer vision in robotic navigation and augmented reality applications
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