Overview. Pinhole camera model Projective geometry Vanishing points and lines Projection matrix Cameras with Lenses Color Digital image

Transcription

1 Camera & Color

2 Overview Pinhole camera model Projective geometry Vanishing points and lines Projection matrix Cameras with Lenses Color Digital image Book: Hartley 6.1, Szeliski 2.1.5, 2.2, 2.3

3 The trip of Light Light source properties Sensor characteristics Exposure Optics Surface shape Surface reflectance properties

4 Image formation Let's design a camera. Is this going to work? object film

5 Pinhole Camera object barrier film Add a barrier to block off most of the rays This reduces blurring The opening known as the aperture

6 Pinhole Camera f f c f = focal length c = camera center

7 Dimensionality Reduction 3D to 2D 3D world Pointofobservation 2D image

8 Projection Illusion

9 Projection Illusion

10 Projective Geometry Lost Properties Length (size) Angles Shape Invariant Properties Straight Lines

11 Projective Geometry Angles-Shape

12 Projective Geometry Length-Size

13 Projective Geometry Straight Lines

14 Projection Properties Many-to-one: any point along the same ray map to the same point in the image. Points Points Lines Lines Line through the camera center projects to a point. Planes Planes Plane through the camera center projects to a line.

15 Vanishing Points Parallel lines in the world intersect in the image at a vanishing point Vanishing Point

16 Vanishing Lines Planes in the world form the vanishing line in the image. Vanishing Line

17 Vanishing Lines camera center plane in the scene Horizon: vanishing line of the ground plane.

18 Homogeneous Coordinates Converting to homogeneous coordinates homogeneous image coordinates homogeneous scene coordinates Converting from homogeneous coordinates

19 Projection 3D World Coordinates to 2D Image Coordinates [] u p= v Y Y c Z o v f Z c: Camera center o: Optical center (0,0) i: Image plane X i Intrinsic Assumptions Unit aspect ratio Optical center at (0,0) Extrinsic Assumptions No rotation Camera at (0,0,0) ][ ] X Projection u f Y w v =0 f 0 0 Matrix: Z [][ [] X P= Y Z

20 Projection Matrix [] u p= v Y Y c Z o v f Z X i c: Camera center o: Optical center (u0,v0) i: Image plane [] X P= Y Z If the position of the optical center is at (u 0,v0): K:intrinsic matrix [][ f 0 u0 u w v = 0 f v ][ ] X 0 Y 0 Z 0 1 x=k [ I 0 ] X Rotation (R), Translation (t) x=k [ R t ] X

21 Field of View

22 Field of View Y c φ Z d o f X i 1 ϕ=tan (d /2f )

23 Lenses focal point f A lens focuses light onto the film.

24 Lens Focus circle of confusion There is a specific distance at which objects are in focus.

25 Lens Focus Depth of Field

26 Depth of Field and Aperture Changing the aperture size affects depth of field A smaller aperture increases the range in which the object is approximately in focus But small aperture reduces amount of light need to increase exposure

27 Lens flaws: Spherical aberration Rays farther from the optical axis focus closer.

28 Lens flaws: Vingetting

29 Radial Distortion Caused by imperfect lenses Deviations are most noticeable on the edges. No distortion Pin cushion Barrel

30 Real Lenses

31 Color

32 What is color? Color is the result of interaction between physical light in the environment and our visual system Color is a psychological property of our visual experiences when we look at objects and lights, not a physical property of those objects or lights (S. Palmer, Vision Science: Photons to Phenomenology) Wassily Kandinsky, Murnau Street with Women, 1908

33 Physics of Light A source of light can be described physically by its spectrum: the amount of energy emitted at each wavelength (~ nm).

34 Color Perception by Humans Photoreceptor cells: Rods and cones on the retina. Rods provide black and white vision. Cones provide color vision. 3 kind of cones.

35 Color Perception by Humans Rods and cones act as filters on the spectrum:to get the output of a filter, multiply its response curve by the spectrum, integrate over all wavelengths

36 RGB Color Space Additive color model. Each pixel is characterized by a value for each of the three components: (vr,vg,vb). Examples: Black: (0,0,0) Gray: (v,v,v) White: (vmax,vmax,vmax)

37 Uses of Color in Computer Vision Skin Detection

38 Uses of Color in Computer Vision Image Segmentation and Retrieval

39 Digital Camera

40 Digital Image - Binary

41 Digital Image - Grayscale

42 Digital Image - Color

43 Digitization Digital camera, scanner. Quality depends on: Spatial Sampling (image resolution, number of pixels). Depth (number of intensity values).

44 Digitization Spatial Sampling Initial image Sampling points Coarse sampling Dense sampling

45 Sampling Interval Look at the fence: Sampling interval White image! Grey image!

46 Sampling Interval Look at the fence: Sampling interval Now the fence is visible!

47 Sampling Theorem If the width of the thinest structure is d, then the sampling interval should be smaller than d/2.

48 Image Quantization Determines the value of each sample. Mapping between analog continuous values and K digital quantized values. K-1 Quantization Level Signal Value M

49 Selection of K Gray Scale Image Analog image K=2 K=4 K=16 K=32

50 Selection of K - Color Image Analog Image K=2 (for each color) K=4 (for each color)

51 Loss during Quantization

52 Loss during Spatial Sampling

53 Image Histogram H H(i) is the number of image pixels that have the value i. 8 Pixel Count For a MxN image: I max 4 3 H (i) MN Gray Value 6 7 i I min

54 Histogram Examples

55 ? Questions?