Exploring Three-dimensional Objects by Controlling the Point of Observation

Front Cover
University of Wisconsin--Madison, 1994 - Computer vision - 558 pages
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Contents

Dependence of the visible rims connectivity changes on the initial
15
A Framework for Visual Exploration of Surface Geometry
22
Tangential Viewpoint Control
44
viewpoint
56
A configuration of three rotational axes for object reorientation
59
Geometry of object reorientation
60
Reorienting a pipeshaped object
61
Objects used in the experiments
64
selected points on the occluding contour of the two tori
145
The point being tracked for surface curvature estimation
146
Curvature variation with viewpoint for the rotating toy experiment
147
Viewpoints corresponding to the global minima and maxima of the curvature measurements
148
Viewpoints corresponding to the global curvature minima and maxima for a different run of the tracking process
149
Global Surface Reconstruction
150
Difficulties in reconstructing the surface of a pipeshaped object
156
The epipolar parameterization
159

Tracking a visible rim point while moving on its tangent plane
66
The window used for point tracking
67
Application of the point tracking system to a different object
68
Detecting point disocclusion
69
Occluding Contour Detection
71
Point correspondences induced by the epipolar geometry
78
Distinguishing stationary from nonstationary points
84
Bounding the distance between qt and qt
87
Changing viewing directions on the selected motion plane
88
Polyhedral model of a bottle and its visible rim
98
Detecting the occluding contour of a bottle
99
Two images of a rotating toy
100
Detecting the occluding contour of a toy
101
Detecting the stationarity of the m curve
104
Detecting the nonstationarity of the right arm curve
106
Recovering Local Surface Shape
109
Aligning the viewing direction with a principal direction on TP S
120
Finding the principal directions
121
Determining the complete visibility of rim points
124
Selecting points for surface recovery
125
Recovering the shape of surfaces of revolution
127
Removing p from the rim
131
Models of a candlestick and two tori used for the simulations
134
A sequence of 120 frames used in our experiments
135
Snapshots of the occluding contour of a candlestick model as the view ing direction changes
142
Snapshots of the occluding contour of two tori as the viewing direction changes
143
Variation of the absolute curvature with respect to viewpoint at the selected points on the occluding contour of the candlestick model
144
The visual events
160
Reconstructing a region around an ordinary visible rim point on a torus
168
Forcing a visible rim point to become ordinary
170
Reconstructing a region around a degenerate point on the torus
171
The visibility arcs
175
The reconstructible regions on some surfaces studied by Petitjean et al and Koenderink
176
The reconstructible regions for a pipeshaped surface
177
Difficulties involved in globally reconstructing a dimpleshaped surface
180
Geometry of the reconstruction of a curve segment drawn on an objects surface
184
Moving to the middle of the visibility arc for a point on a pipeshaped object by tangential viewpoint control
186
Changing viewpoint on the normal plane of a point on a pipeshaped object
187
Finding the middle of the visibility arc of a point on a different pipe shaped object
188
Strategies used to accomplish global surface reconstruction
193
Three views of the region reconstructed on the pipes interior surface
196
Reconstructing the surface of a pipeshaped object
201
Two views of the path traced by the moving viewpoint during global reconstruction
218
Conclusions and Future Work
222
A Proofs of Chapter 4 Theorems
229
B Proofs of Chapter 5 Theorems
233
The effects of global occlusion
236
Extent of Viewing Direction Adjustments for Local Shape Recovery
237
The Darboux Frame
239
Changing directions on the TN plane
244
Visual Events and their Associated Visual Event Curves
245
The visual events
249
Inducing the visibility of points in a neighborhood of an ordinary hy perbolic point
251
Representing the configurations of the asymptotes and bitangent lines through a visible rim point
255

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