3D Photorealistic Modeling Process

Different Sensors Scanners Local coordinate system Cameras Local camera coordinate system GPS Global coordinate system

Coordinate Systems Individual local scanner coordinates (each scan) Object coordinate system (single coordinate system aligning all scans) Camera coordinate system (each photograph) Global coordinates

Scanner Coordinate Individual scanner local coordinate –Not necessary to level Y X Z

Y X Z Camera Coordinate System Each photograph has its own coordinates –Units: mm or pixel

Putting it together From individual scan coordinates to object coordinates From object (or global) coordinates to camera coordinates From object coordinates to global coordinates

Individual coordinates to object coordinates (1/2) Traditional survey approaches –Need to level the scanner –set up backsight –Knowing scanner location and backsight angle transform each point to the object coordinate system, usually global. –Advantage: easy to set up one-step from local to global coordinates. –Disadvantage: problem in generating mesh models.

From individual coordinates to object coordinates (2/2) Use mesh alignment techniques (Polyworks) –No need to level. –Requires overlap with common features to minimize the distance. Z X Y sc1sc2 T =

From Object to Camera (1/2) Two approaches –Polynomial fit (rubber sheeting) Low accuracy, No need to know camera intrinsic parameters –Projection transform (pinhole model) High accuracy

From Object to Camera (2/2) 1.From object to camera coordinate system (pin hole model) 2.Perspective projection to convert to image coordinates (uv, pixel, or mm) 6 unknowns assuming known f Nonlinear-needs initial value

Camera Calibration Correct lens distortion –Radial distortion –Tangential distortion –Calculate f, k1, k2, p2, p2 in the lab for each lens.

Example of the calibration (Canon 17mm) )Radial distortion 2)Tangential distortion 3)Complete model

Example Iteration = 8 Residuals pts51 = pts50 = pts2034 = pts 2010 = omage: phi: kappa: X: Y: Z:

Bundle Adjustment Adjust the bundle of light rays to fit each photo

Bundle Adjustment (2/2) Photo no : 7734 pt no U V Photo no omega phi kappa X Y Z Photo no : 7735 pt no U V

From Object to Global (1/2) 7-parameter conformal transformation s Where m11 = cos(phi) * cos(kappa); m12 = -cos(phi) * sin(kappa); m13 = sin(phi) m21 = cos(omega) * sin(kappa) + sin(omage) * sin(phi) * cos(kappa); m22 = cos(omage) * cos(kappa) – sin(omega) * sin(phi) * sin(kappa); m23 = -sin(omage) * cos(phi); m31 = sin(omage) * sin(kappa) – cos(omage) * sin(phi) * cos(kappa); m32 = siin(omage) * cos(kappa) + cos(omage) * sin(phi) * sin(kappa); m33 = cos(omage) * cos(phi); and s is scale factor

Transform to Global (2/2) Object GPS Iteration:5 scale : (*****) omega : phi : kappa : X trans: Y trans: Z trans: Pt: 1, X Y Z Pt: 2, X Y Z Pt: 3, X Y Z Pt: 4, X Y Z Pt: 5, X Y Z 0.006

REDUCTION TO THE ELLIPSOID h N H R Earth Radius 6,372,161 m 20,906,000 ft. Earth Center S D S = D x R R + h h = N + H S = D x R + N + H R

REDUCTION TO GRID S g = S (Geodetic Distance) x k (Grid Scale Factor) S g = x = meters

REDUCTION TO ELLIPSOID S = D x [R / (R + h)] D = meters (Measured Horizontal Distance) R = 6,372,162 meters (Mean Radius of the Earth) h = H + N (H = 158 m, N = - 24 m) = 134 meters (Ellipsoidal Height) S = [6,372,162 / 6,372, ] S = x S = meters

COMBINED FACTOR CF = Ellipsoidal Reduction x Grid Scale Factor (k) = x = CF x D = S g x = meters

Surface Generation Through merge process in Polyworks Through fitting through GoCad Through direct triangulation (Delauney triangulation, TIN)

Surface cleaning (in Polyworks) The single most time consuming part of entire process (90% of time). –Filling the holes (because of scan shadow) –Correct triangles

Summarize