Index

. evolution equation, 35 3D interpretation implicit, 15 dense, 175 normal, 14, 15 direct, 175, 183, 189 parametric, 13 ego-motion, 181 regular, 13 indirect, 175, 193 tangent, 13, 15 joint 3D-motion segmentation, 189, 193 non-stationary environment, 184 point-wise, 185 D region-based, 188 Density tracking sparse, 175 Bhattacharyya flow, 153 stationary environment, 181 Kullback-Leibler flow, 155 3D motion segmentation, 189 Depth, 189, 191, 196, 199 3D rigid motion constraint, 180 Deriche-Aubert-Kornprobst algorithm, 43, 54 Descent optimization A integral functional, 32 Aperture problem, 46 real function, 31 vectorial function, 32 Differentiation under the integral sign, 31 B Disparity, 84 Background, 95 Displaced frame difference, 130 Background template, 95, 107 Background template subtraction boundary based, 109 E region based, 107 Ego-motion, 4, 181 direct, 183 indirect, 182 C Essential parameters, 180, 194 Connected component analysis, 133 Euler-Lagrange equations Continuation method, 65 definite integral, 18 Cremers method, 75 length integral, 23 Curvature path integral, 24 definition, 14 region integral, 22 of implicit curve, 15 several dependent variables, 20 of parametric curve, 14 several independent variables, 20 Curve surface integral, 26 active, 35 variable domain, 22 arc length, 13 volume integral, 29 curvature, 13 Extension velocity, 38

A. Mitiche and J. K. Aggarwal, Computer Vision Analysis of Image Motion by Variational 205 Methods, Springer Topics in Signal Processing 10, DOI: 10.1007/978-3-319-00711-3, Ó Springer International Publishing Switzerland 2014 206 Index

F contrast, 119 Foreground, 95 visible, 114 Functional derivative, 22 normal component, 114 Motion detection, 8, 95 a contrario, 130 G background template subtraction, 109 Gauss theorem, 29 feature integration, 134 Geodesic active contour geodesic, 130 balloon velocity, 111 image differencing, 113 functional, 109 moving camera, 125 velocity interpretation, 111 optical flow based, 121 Gibson’s optical flow, 2 selective, 132 Gradient equation, 118 geometric cue, 134 Green’s theorem, 23 normal component residuals, 125 optical flow residuals, 128 photometric cue, 95, 138 H Motion segmentation, 8, 87, 95, 132, 138 Half quadratic algorithm, 57, 58 Motion tracking, 9 Helmhotz, 2 Multigrid processing, 70 Horn and Schunck algorithm, 42, 48 Multiregion segmentation, 80 Horn and Schunck equation, 3 Multiresolution processing, 70 Human activity analysis, 6

N I Narrow banding, 38 image differencing motion detection Normal vector, 14, 15 boundary based, 117 MAP, 116 region based, 114 O Image registration, 41 Optical flow, 2, 41, 48, 178 Image segmentation, 5 3D interpretation, 175 Isophote, 114 constraint, 3, 45, 118 Deriche-Aubert-Kornprobst algorithm,, 43, 54 K estimation, 7, 41 Kineopsis, 2 Gauss-Seidel iterations, 50 Kinetic depth effect, 2 Horn and Schunck algorithm, 42 image driven smoothing, 42 Jacobi iterations, 50 L joint estimation and segmentation (Cre- Laplacian approximation, 52 mers method), 75 Level sets joint optical flow and disparity estimation,, evolution equation, 35 83 fans, 36 length penalty term, 43 narrow banding, 36 Lucas-Kanade algorithm, 42 shocks, 36 outliers, 43 velocity, 37 residual, 128 Longuet-Higgins and Prazdny model, 4, 179 minimum description length (MDL), 63 Lucas-Kanade algorithm, 42, 47 motion boundary preservation, 42, 84 multigrid processing, 70 multiresolution processing, 70 M oriented smoothness constraint, 61 Mean shift procedure, 148 parametric estimation, 67 Motion selective image diffusion, 61 Index 207

P kinematic, 143 Pattern vision, 5 photometric, 143 Projection equations, 178 Three-dimensional interpretation, 11 Projection models, 177 Tracking, 5, 143 Prolongation, 72, 73 density tracking, 152 dynamic systems, 144 energy minimization, 146 R kernel based, 148 Refinement term, 111 mean shift, 151 Region-based matching occlusion, 163 basic method, 157 particle filtering, 145 local statistics, 160 region-based matching, 157 motion, 162 spatiotemporal, 165 shape, 161 target description, 150 Restriction, 73 Rigid body motion, 179 Robotics, 5 U Robust statistics, 42 Ullman’s rotating cylinder, 2

S V Scene flow, 4, 198 Video compression, 6 Signed distance function, 161 Video description, 6 Spatiotemporal derivatives, 51 Stereokinematic constraint, 83 Stopping function, 111 W Structure-from-motion, 2 Warped image, 47 Warping, 72 Window function T Epanechnikov, 149 Tangent vector, 13, 15 Gaussian, 149 Target characterization Parzen, 149 geometric, 143