## Spatio-Temporal Image Processing: Theory and Scientific ApplicationsImage sequence processing is becoming a tremendous tool to analyze spatio-temporal data in all areas of natural science. It is the key to studythe dynamics of of complex scientific phenomena. Methods from computer science and the field of application are merged establishing new interdisciplinary research areas. This monograph emerged from scientific applications and thus is an example for such an interdisciplinaryapproach. It is addressed both to computer scientists and to researchers from other fields who are applying methods of computer vision. The results presented are mostly from environmental physics (oceanography) but they will be illuminating and helpful for researchers applying similar methods in other areas. |

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### Contents

Introduction and Overview | 1 |

Image Sequence Acquisition | 14 |

21 Geometrical Optics | 15 |

211 World and Camera Coordinates | 16 |

212 Perspective Projection | 18 |

213 Geometric Distortion | 20 |

214 Depth of Focus and 3D OTF | 21 |

215 Imaging of Volumetric Objects | 26 |

48 General Approach | 108 |

Fourier Transform Methods | 110 |

51 Cross Spectral Method | 111 |

52 Wave Number Frequency Spectra | 116 |

Differential Methods | 119 |

61 Least Squares Approach | 120 |

62 Differential Geometric Modelling | 124 |

63 Formulation as Filter Method | 127 |

22 Radiometry | 28 |

223 Reflection from Surfaces | 29 |

224 Emitting Surfaces | 30 |

23 Stereo Imaging of the Water Surface | 31 |

231 Stereo Setup with Parallel Camera Axes | 32 |

233 Geometry of Stereo Imaging of Ocean Surface Waves | 33 |

234 Geometry of A ShortBase Tele Lens Stereo System | 36 |

Principles | 39 |

242 Surface Reconstruction | 41 |

25 Shape from Reflection | 43 |

Stilwell Photography | 46 |

253 The Stereo Correspondence Problem at Specular Surfaces | 48 |

254 Measurements of the Wave Slope Statistics | 50 |

26 Shape from Refraction | 52 |

261 Principle | 53 |

263 IrradianceWave Slope Relation | 56 |

27 Mass Boundary Layer Visualization | 60 |

Kinematics and Dynamics of Motion | 63 |

32 Motion Kinematics | 64 |

322 Deformable Objects | 66 |

323 Kinematics of Projected Motion | 69 |

324 Motion of Planar Surfaces | 71 |

33 Motion Dynamics | 74 |

Motion in SpaceTime Images | 76 |

42 Pro and Contra Regularization | 78 |

43 Motion as Orientation in xt Space | 81 |

44 Optical Flow | 84 |

442 Fluid Flow versus Optical Flow | 86 |

443 Lambertian Objects in Isotropic Illumination | 87 |

444 Lambertian Objects in Parallel Light | 88 |

445 Light Emitting Surfaces and Volumes | 89 |

446 Light Absorbing or Scattering Objects | 90 |

447 Light Refracting Objects | 91 |

45 Motion in Fourier Domain | 92 |

46 Sampling in xt Space | 93 |

462 Sampling and the Correspondence Problem | 96 |

463 Sampling and Subpixel Accuracy | 97 |

47 Classification of Local Structure in SpaceTime Images | 99 |

472 Classification of Local Structures | 101 |

473 Examples of Complex Motion | 103 |

64 Analytic results | 129 |

Quadrature Filter Set Methods | 133 |

722 Vectorial Filter Response Addition | 135 |

73 SpatioTemporal Energy Models | 136 |

74 Directional Filter Sets in 3D and 4D | 138 |

742 Symmetric Distribution of Filter Directions in 3D and 4D | 139 |

75 Analytic Results | 140 |

Tensor Methods | 143 |

812 Analogy to the Inertia Tensor | 145 |

813 Computation in the Spatial Domain | 146 |

82 Structure Tensor Method | 147 |

823 Further Equivalent Approaches | 148 |

83 Formulation as a Filter Method | 149 |

84 Eigenvalue Analysis | 150 |

842 3D Tensor | 152 |

85 Analytic Results | 153 |

852 Three Dimensions | 156 |

Correlation Methods | 158 |

92 Formulation as Filter Method | 159 |

94 Evaluation and Comparison | 160 |

Phase Methods | 161 |

102 Computation of Phase Gradients | 162 |

103 Formulation as a Filter Method | 163 |

104 Analytic Results | 164 |

Implementation | 166 |

112 Binomial Smoothing Filters | 167 |

1123 Cascaded Multistep Binomial Filters | 170 |

1124 Cascaded Multigrid Binomial Filters | 174 |

113 FirstOrder Derivative Filters | 178 |

1132 Bspline Based Derivative Operators | 180 |

114 Hilbert Filter | 182 |

Experimental Results | 185 |

121 Synthetic Test Images | 186 |

122 Results with Synthetic Images | 188 |

1222 Noise Sensitivity | 191 |

123 Conclusion | 192 |

193 | |

206 | |

### Common terms and phrases

algorithms angle applied approach axes axis B-spline BCCE brightness coefficient coherency complex components computer vision consecutive images convolution coordinate system corresponding denote derivative operator differential method displacement distance edge eigenvalue equation feature filter mask filter set first-order Fourier transform frequency Gabor filters geometry gradient space gray value structure grid Hilbert filter illumination changes image plane image processing image sequence processing inertia tensor irradiance isotropic Jdhne Lambertian lens light source linear mask matrix mean square gradient measure motion analysis motion determination motion discontinuities motion estimation motion field nonlinear objects obtain ocean surface optical flow orientation partial derivatives pattern perspective projection phase speed pixel problem quadrature filters radiance radiometry refraction resolution rotation sampling scene setup shape from reflection shape from shading smoothing space-time images spatial stereo images structure tensor surface element surface normal techniques transfer function vector velocity field wave number wave slope wavelength wind speed xt space zero