Computer Vision and Measurements in Aerospace Applications
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1 Computer Vision and Measurements in Aerospace Applications ianshu Liu Department of Mechanical and Aeronautical Engineering Western Michigan University Kalamazoo, M 49008
2 Objective o build a unified theoretical framework for quantitative image-based measurements of morphology and motion fields of deformable bodies like fluids Geometric Structures: Points, Curves, Surfaces Motion Fields: Points, Curves, Surfaces (Geometric Flow Comple Continuous Patterns
3 Background Photogrammetry Computer Vision Human Vision Analogy Computer Vision
4 Optical nfo Processing
5 Geometric and Physical-Based Processing Emission Radiance in mages Geometric Features n mages Perspective ransformation Geometrical, Kinematical and Physical Representations in 3D object Space Mapping of Geometry and Motion Mapping of Physical Quantities Emission Radiance in mages Principles of Physics Mathematical Models
6 mportant Quantities in Aerodynamics ( Pressure ( emperature (3 Skin Friction (4 Velocity Field (5 Attitude and Kinematics (6 Shape Molecular Sensors!
7 Needs for New Methods Quantitative, Dynamic, Universal, Applicable to Comple Patterns & Motions of Deformable Bodies Combination of Approaches Perspective Geometry Differential Geometry Continuum Kinematics & Dynamics Radiometry
8 Relevant opics ( Perspective Projection ransformation ( Projective Developable Conical Surface (3 Perspective Projection under Surface Constraint (4 Perspective Projection of Motion Field Constrained on Surface (5 he Correspondence Problem (6 Composite mage Space and Object Space (7 Perspective nvariants of 3D Curve (8 Reflection and Shape Recovery (9 Motion Equations of mage ntensity
9 Perspective Projection ransformation Camera parameters 3 Π (,,, c, c, c,c, p, p,k, K, P, P eterior interior distortion
10 Formulations of Perspective ransformation ( ( c ( ( c p p c 3 c c 3 c m m m m h h h P ( Collinearity Equations ( Homogenous Coordinate Form (3 W-Vector Form 0 ( 0 ( c c W W
11 Geometric mage Measurements 3D Projection D Recover the Lost Dimension
12 Perspective Developable Conical Surface Plane parallel to image 3D curve Ray Equation s c ( P h 3 P t ds 0 C P 0 Conical Surface Equations ( c N ( s 0 D ( c dn ( s / ds 0 D
13 Reconstruction of 3D Curves and Surfaces Using Projective Conical Surfaces 3D Space Curve Surface
14 Reconstruction of 3D Displacement Vectors Providing a rational and general method for Stereoscopic Particle mage Velocimetry (SPV and Scalar mage Velocimetry (SV
15 Motion Field of 3D Space Curve time time St Variational Problem: St U( t min Physical and Geometric Constraints: G i [ U( ] 0 i,,
16 Perspective Projection under Surface Constraint 3 F(, One-to-One Differential Relation d d m3 ( c f S Q d d Geometric Structures ds d g d d Quantities: tangents, normal, length, angle, area topology
![Motion Field ] ( [ U ] ( [ U ( Q dt d f f f m u S S S c 3 Optical](/docs-images/74/70325118/images/17-0.jpg "Flow Surface-Constrained Motion Field Motion Field on Surface")
17 Motion Field ] ( [ U ] ( [ U ( Q dt d f f f m u S S S c 3 Optical Flow Surface-Constrained Motion Field Motion Field on Surface mage
18 he Point Correspondence Problem Epipolar Line Epipolar Line h( h( mage mage Generalized Longuet-Higgins Relation: ( h( h( Q ( h( h( 0
19 Determining Point Correspondence Four mages or Cameras 3 Si Longuet-Higgins Equations for Si Unknowns 4
20 Composite mage Space and Object Space m ( m 3( m ( Provide additional dimensions One-to-One Relation Reconstruct 3D Displacement Vectors from Composite mage Coordinates
21 Perspective nvariants of 3D Curve Rectifying plane orsion im, im, d d obj, obj, D D new Curvatures Osculating plane Geometrical Flow Problem im, im, d d i i (,',,3 (,,',3 d d 4 obj, obj, Distances d d 43 3 D D 4 D D 43 3 D D (,',,3 (,,',3 (Brill, et al. 99 new
22 Shape and Reflection ( c sys E a a c sys E ls [ d N L s s p( a N N V a L L s V ]
23 Motion Equations of mage ntensity mage ntensity and Radiance (, t c L(,a, g, t Physical parameters: Geometric parameters: p (p, p,, pn q (q,q,,qm Radiance: L(, p, q
24 Generic Motion Equations of mage ntensity t u c sys L t U L dp dt p L dq dt q L Optical Flow Velocity Field Physical parameters: Geometric parameters: p (p, p,, pn q (q,q,,qm Radiance: L(, p, q
25 Emitting Passive Scalar ransport Luminescence Governing Equation Radiance d dt U t D L(,t c (,t Perspective Projection onto mage Plane
26 Motion Equation of mage ntensity for Emitting Passive Scalar ransport h h D u t ] ( [ U ] ( [ U ( dt d f f f m G u S S S c 3 Optical Flow and Velocity Field on Surface
27 Light ransmitting Scalar ransport Governing Equation d dt U t D L L0 ep( 0 s et ds Perspective Projection onto mage Plane
28 D u t u U Optical Flow and Path-Averaged Velocity Motion Equation of mage ntensity for Light ransmitting Scalar ransport 3 3 d d U U where
29 Schlieren mage of Density-Varying Flows mage ntensity and Density Gradient K Cschl K d Motion Equations of mage ntensity 3 t ( d [ K U 0 0 ( K d ] 0 where U U d d 3 3 ( /, /
30 Shadowgraph mage of Density-Varying Flows mage ntensity and Second-Order Density Derivative Cshad d 3 Motion Equations of mage ntensity t ( [ U ( ] 0 where solution (
31 ransmittance mage of Density-Varying Flows mage ntensity and Density C trans d 3 Motion Equations of mage ntensity t ( [ U ( ] 0
32 ypical Applications Aerodynamic measurements: pressure and temperature sensitive paints, videogrammetric attitude measurement, stereoscopic PV, lasertagging technique, schlieren, shadow and transmittance imaging, oil-film/liquid-crystal skin friction measurements. Metrology and kinematics of large inflatable space structure.
33 Unification of Measurement Systems Conventional echniques mage-based echniques Force Balances Accelerometers PSP & SP Videogrammetry Hot-Wires & Films Pressure aps & Probes Global Velocimetries (PV, DGV Schlieren/Shadowgraph emperature & Heat ransfer Gauges Oil & LC -Film Skin Friction Meters
34 Data Fusion and Understanding Measurements Data Base & Models ntegrated data & data at discrete locations Aerodynamics data base Distributions on surfaces heoretical models CFD Fields in 3D space SuperAerodynamicist : ntelligent Epert System!?
35 Conclusions We will see unified image-based instrumentation providing non-contact, global measurements of important physical, geometric and dynamical quantities in wind tunnel testing. deal Aerodynamics Lab Unified Measurement echniques Wind unnel esting CFD heories Aerospace System Design
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