CS535 Fall Department of Computer Science Purdue University

Transcription

1 Camera Models CS535 Fall 21 Daniel G Aliaga Daniel G. Aliaga Department of Computer Science Purdue University

2 Biology 11 Some animals are capable of panoramic vision e.g., certain insects, crustaceans (e.g., lobster) Diurnal Insect Vision Nocturnal Insect Vision Crustacean Vision

3 Optics: Terminology Dioptric All elements are refractive (lenses) Catoptric All elements are reflective (mirrors) Catadioptric Elements are refractive and reflective (mirrors + lenses)

4 Thin Lens Equation d i d o focal point object plane image plane f 1 d + 1 d i = 1 f

5 Pinhole Camera Model f d image plane pinhole object

6 Pinhole Camera Image

7 Digression: Non Pinhole Camera Models dl Why restrict the camera to a pinhole camera model? Aperture is large: lightfields/lumigraphs Multi perspective imaging Sample based camera Tailored camera designs Occlusion resistant cameras (kinda ) Graph cameras and more!

8 Large Aperture Cameras f d image plane pinhole object

9 Large Aperture Cameras f d image plane pinhole object Is this bad? Is this terrible? Is this bug a feature? More later

10 Multiperspective Imaging Hand-crafted semi-automated to produce this [Roman-Vis4]

11 Multiperspective Imaging [Seitz-CGA3]

12 Multiple COP Images [Rademacher-SIG98]

13 Multiple COP Images [Rademacher-SIG98]

14 Multiperspective Imaging for Cel Animation

15 Multiperspective Imaging for Cel Animation [Wood-SIG97]

16 Multiperspective Imaging for Cel Animation [Wood-SIG97]

17 Multiperspective Imaging for Cel Animation [Wood-SIG97]

18 General Linear Camera [Yu-ECCV4]

19 General Linear Camera [Yu-ECCV4]

20 General Linear Camera [Yu-ECCV4]

21 Occlusion Resistant Cameras Input images Output images [Aliaga-CGA7]

22 Occlusion Resistant Cameras [Aliaga-CGA7]

23 Occlusion Resistant Cameras [Aliaga-CGA7]

24 Occlusion Cameras [Popescu-I3D6]

25 Occlusion Cameras [Popescu-JDT6]

26 Graph Cameras [Popescu-SIGA9]

27 Graph Cameras [Popescu-SIGA9]

28 Let s get back on track: Pinhole Camera Model dl f d image plane pinhole object

29 What is perspective projection? Z image plane f (X, Y, Z) (x, y) object x=fx Z y=fy Z

30 Computer Graphics Pinhole Camera Model f d eye image plane object

31 What is perspective projection? eye/viewpoint /i it f Z z (x, y) y? image plane (X, Y, Z) Y optical axis y = Y f Z y = f Y Z & x = f X Z

32 Perspective Camera Parameters Intrinsic/Internal Focal length Principal point (center) Pixel size (Distortion coefficients) Extrinsic/External Rotation f p x, p y s x, s y k 1,... φ, ϕ, ψ t, t, t Translation x y z 32

33 Perspective Camera Parameters Intrinsic/Internal Focal length Principal point (center) (=middle of image) Pixel size (Distortion coefficients) Extrinsic/External Rotation Translation f (=1, irrelevant) (=, assuming no bugs ) φ, ϕ, ψ t, t, t x y z 33

34 Focal Length Focal Length Focal Length Focal Length X f fx = 1 1 Z Y f f Z fy fx Z fy Z fx / / = y x 1

35 Principal Point Principal Point Principal Point Principal Point + Y X p f Zp fx x x = Z Y p f Z Zp fy y y y x

36 CCD Camera: Pixel Size sx f px P = sy f py 1 1 In graphics, often s x s = y p x = p α x px P = α y py Projection matrix 1 = y =1 =

37 Translation & Rotation ~ x c ~ x c ~ X = R( X C) R=Rx RyR z ~ R t t Y = RX ~ RC x c = 1 Z t t = t t 1 x y World-to-camera matrix M 3x3 rotation matrices [ t ] T z translation vector

38 Perspective Projection Process Perspective Projection Process Perspective Projection Process Perspective Projection Process X Given = ~ Z Y X X 1 the perspective projection is X = ~ Z Y PM x p = p z p y p z p x x x x x y x ~ / ~ ~ / ~ 1

39 OpenGL Equivalent glmatrixmode(gl_projection); gluperspective(6, 1.,.1, 1.); glmatrixmode(gl_modelview); gltranslatef(tx,ty,tz); glrotatef(rx,1,,); glrotatef(ry,,1,); glrotatef(rz,,,1); /* or glloadmatrixf(mat); */

40 OpenGL Note OpenGL is row major and left multiplies This means from the previous (more intuitive explanation) theactual matrix is thetranspose transpose T of what I wrote; e.g. M = M OpenGL Also, the order of multiplication li li i is from most recent matrix command to least recent matrix command; e.g. glrotate(rx,1,,); glrotate(ry,,1,) rotates a vertex about the y axis and then the x axis

41 Next: Linear Algebra Homogeneous Coordinates Point, Vector, Matrix Operations Projections: Orthographic, Weak Perspective, Perspective

42 Transformations Translation Rotation Shear Scale