Field of View (Zoom)
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1 Image Projection
2 Field of View (Zoom)
3
4 Large Focal Length compresses depth 400 mm 200 mm 100 mm 50 mm 28 mm 17 mm Michael Reichmann
5 FOV depends of Focal Length f f Smaller FOV = larger Focal Length
6 Field of View (Zoom)
7 Field of View (Zoom)
8
9
10 Fisheye lens distortion
11
12 Camera Model
13 Lens Pixel CCD sensor 3D object
14 3D Point Projection (Metric Space) 3D point ( X, Y, Z) ( u, v ) f m : Focal length in meter ( u, v ) ( X, YZ, ) X Y ( u, v ) ( fm, fm ) Z Z 2D projection onto CCD plane
15 3D Point Projection (Metric Space) Projection plane 3D point ( X, Y, Z) ( u, v ) ( u, v ) f m ( u, v ) Focal length in meter ( u, v ) ( X, YZ, ) X Y ( u, v ) ( fm, fm ) Z Z 2D projection onto CCD plane
16 3D Point Projection (Metric Space) Projection plane 3D point ( X, Y, Z) ( u, v ) ( u, v ) f m Focal length in meter ( X, YZ, ) X Y ( u, v ) ( fm, fm ) Z Z 2D projection onto CCD plane
17 3D Point Projection (Pixel Space) ( u, v ) (0,0) w h ( u, v ) w (0,0) h ( px, p ) y : Image principal point CCD sensor (mm) Image (pixel) u w u p x w v h v p y h w u u p w x h v v p h y
18 3D Point Projection (Pixel Space) O ( u, v ) w f m Projection plane h (0,0) ( u, v ) Z CCD sensor (mm) h (0,0) ( X, YZ, ) ( u, v ) w ( p, p ) x Image (pixel) y X Y ( XY,, Z) ( u, v ) ( fm, fm ) Z Z w w X u u px fm p w w Z Focal length in pixel h h Y v v py fm p h h Z Focal length in pixel y x
19 3D Point Projection (Pixel Space) O ( u, v ) w f m Projection plane h (0,0) ( u, v ) Z CCD sensor (mm) h (0,0) ( X, YZ, ) ( u, v ) w ( p, p ) x Image (pixel) y X Y ( XY,, Z) ( u, v ) ( fm, fm ) Z Z w w X u u px f f m x p w w Z Focal length in pixel h h Y v v py f f m y p h h Z Focal length in pixel y x
20 3D Point Projection (Pixel Space) Projection plane 3D point ( X, Y, Z) ( u, v ) ( u, v ) f m Focal length in meter ( X, YZ, ) w X h Y ( u, v ) ( fm, fm ) w Z h Z
21 Homogeneous Coordinate Projection plane ( X, YZ, ) 2D point =: 3D ray λ( xy,,1) O ( fx, fy, f ) f 2 ( xy, ) ( xy,,1) : A point in Euclidean space ( ) can be represented by fxy (,,1) ( xy,,1) 2 a homogeneous representation in Projective space ( P ) (3 numbers).
22 Homogeneous Coordinate 2D point =: 3D ray Projection plane ( X, YZ, ) λ( xy,,1) O ( fx, fy, f ) f λ( xy,,1) ( XYZ,, ) Homogeneous coordinate : 3D point lies in the 3D ray passing 2D image point.
23 3D Point Projection (Metric Space) 2D point =: 3D ray Projection plane ( X, YZ, ) λ( xy,,1) O f m ( fx, fy, f ) Z X Y ( xy,,1) ( fxfyf m, m, m) ( fm, fm, fm) Z Z
24 3D Point Projection (Pixel Space) O ( u, v ) w f m Projection plane h (0,0) ( u, v ) Z CCD sensor (mm) h (0,0) ( X, YZ, ) ( u, v ) w ( p, p ) x Image (pixel) y X Y ( XY,, Z) ( u, v ) ( fm, fm ) Z Z X Y u fx px v fy p Z Z u fx px X v fy py Y 1 1 Z Homogeneous representation y
25 Camera Intrinsic Parameter Pixel space Metric space O f m ( u, v ) Z ( X, YZ, ) u fx px X v fk y py Y 1 1 Z + Projection plane Camera intrinsic parameter : metric space to pixel space
26 2D Inverse Projection O f m ( u, v ) Z Projection plane ( X, YZ, ) 2D point == 3D ray K -1 u v 1 Note: arrow direction Pixel space Metric space u fx px X v fk y py Y 1 1 Z K -1 u X v Y 1 Z 3D ray The 3D point must lie in the 3D ray passing through the origin and 2D image point.
27 3D Point Projection (Pixel Space) Projection plane 3D point ( X, Y, Z) ( u, v ) ( u, v ) f m Focal length in meter ( X, YZ, ) w X h Y ( u, v ) ( fm, fm ) w Z h Z
28 Exercise What f to make the height of Eifel tower appear 960 pixel distance? 960 pix 21.8 mm 1280 pix 324 m size fm? Y h Y y f f m Z h Z 1500 m fm fm m
29 Exercise What f to make the height of Eifel tower appear 960 pixel distance? 960 pix 21.8 mm 1280 pix 324 m size fm = 50 mm Y h Y y f f m Z h Z Z? Z m Z
30 Exercise What Zp to make the height of Eifel tower appear twice of the person? h e h p 324 m fm = 50 mm Z p m Y f h e Y Z p f Y Z f p 2 Y Z h p f Z p p s.t. h p h e Z p m 234
31 Where Was I? 324 m 670 pix fm = 50 mm 0.9 m Z pix Circa 1984 Z 2 Y h Y h 1 Y y1 f fm Z1 fm m Z h Z h y Y h h 2 Y2 Y y2 f fm Z2 fm m Z h Z h y
32 Where Was I? Y h h 2 Y2 Y y2 f fm Z2 fm m Z h Z h y pix 250 pix Circa m 400m 600m 800m 1000m
33 Where Was I? 800 m
34 f Focal Length
35 f Focal Length
36 f Focal Length
37 Focal Length
38 Dolly Zoom (Vertigo Effect) (Jaws 1975)
39 Dolly Zoom Given focal length (fm=100mm), what Z100 to make the height of the person remain the same as fm=50mm? h p H p f100 = 100 mm Z 100? Z 50 =157.41m
40 Dolly Zoom Given focal length (fm=100mm), what Z100 to make the height of the person remain the same as fm=50mm? h p H p f100 = 100 mm h f Y Z 50 h f Y Z 100 Z 100? s.t. h h Z 50 =157.41m
41 Dolly Zoom Given focal length (fm=100mm), what Z100 to make the height of the person remain the same as fm=50mm? h p H p f100 = 100 mm h f Y Z 50 h f Y Z 100 Z 100? s.t. h h Z 50 =157.41m Z f f Z Z m 50
42 Dolly Zoom (Jaws 1975) Dolly Zoom (Vertigo Effect)
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