Mathematical Optimization in Graphics and Vision - Luiz Velho - Impa

List of Figures
1.1 Computer graphics: transforming data into images. . . . . . . . . 1
1.2 Computer graphics: related areas. . . . . . . . . . . . . . . . . . 3
1.3 Animation and related areas. . . . . . . . . . . . . . . . . . . . . 4
1.4 The four-universe paradigm. . . . . . . . . . . . . . . . . . . . . 6
1.5 Aboboral mountain, scale 1:50000 (Yamamoto, 1998). . . . . . . 8
1.6 A grid on the function domain. . . . . . . . . . . . . . . . . . . . 9
1.7 Grayscale image and the graph of the image function. . . . . . . . 10
1.8 Circle with normal and tangent vector fields. . . . . . . . . . . . . 12
1.9 Representation and reconstruction. . . . . . . . . . . . . . . . . . 15
1.10 Uniform sampling the circle with reconstruction. . . . . . . . . . 16
1.11 Different reconstructions from the same terrain data. . . . . . . . 17
1.12 Ambiguous representation. . . . . . . . . . . . . . . . . . . . . . 19
2.1 Three examples of solution set. . . . . . . . . . . . . . . . . . . . 24
2.2 Discrete solution sets. . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3 Polygonal representation of a circle. . . . . . . . . . . . . . . . . 31
2.4 Well-posed formulation of a problem. . . . . . . . . . . . . . . . 33
3.1 Ambiguous reconstructions. . . . . . . . . . . . . . . . . . . . . 42
3.2 Inverse specification to frame a point in the image (Gomes &
Velho, 1998). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.3 Image deformation. . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.4 Image metamorphosis. . . . . . . . . . . . . . . . . . . . . . . . 47
3.5 Correcting distortions. . . . . . . . . . . . . . . . . . . . . . . . 48
3.6 Punctual specification. . . . . . . . . . . . . . . . . . . . . . . . 49
3.7 Edges of an image. . . . . . . . . . . . . . . . . . . . . . . . . . 50
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