EVC Computer Vision R h Rehersal 1 l 1 http:// - PowerPoint PPT Presentation

EVC ‐ Computer Vision R h Rehersal 1 l 1 http:// www.caa.tuwien.ac.at/cvl/teaching/sommersemester/evc  Content:  Image Acquisition  Image Acquisition  Image Encoding and Compression  Point Operations  Local Operations  Image Sensors  Edge Filtering Edge Filtering 1 Robert Sablatnig, Computer Vision Lab, EVC ‐ W1: Rehersal 1

Human Eye y 2 Robert Sablatnig, Computer Vision Lab, EVC ‐ W1: Rehersal 1

Human Eye ‐ Components y p  Cornea + Lens:  Light fraction  Light fraction  Iris:  variable aperture i bl t  Retina: Image Detector  (ca. 100 Mio. Photoreceptors) 3 Robert Sablatnig, Computer Vision Lab, EVC ‐ W1: Rehersal 1

Retina  Rods: Monochrome  Cones:  Cones: Color (RGB) Color (RGB)  Fovea: Cones only  Number: N b 6 Mi 6 Mio. Cones C 120 Mio. Rods  But only 1 1 Mio. nerve fibers Mio. nerve fibers in optic nerve => intelligent intelligent sensor sensor ! ! 4 Robert Sablatnig, Computer Vision Lab, EVC ‐ W1: Rehersal 1

The Plenoptic Function p Adelson & Bergen, 91 Image coordinates The intensity P can be parameterized as: The intensity P can be parameterized as: (sperical) (sperical) Color P (   t, Vx, Vy, Vz) Time 3D space “Th “The complete set of all convergence points constitutes the permanent possibilities of vision.” l t t f ll i t tit t th t ibiliti f i i ” Gibson 5 Robert Sablatnig, Computer Vision Lab, EVC ‐ W1: Rehersal 1

Measuring the Plenoptic Function g p Why is there no picture appearing on the paper? Why is there no picture appearing on the paper? 6 Robert Sablatnig, Computer Vision Lab, EVC ‐ W1: Rehersal 1

Measuring the Plenoptic Function g p The camera obscura The pinhole camera 7 Robert Sablatnig, Computer Vision Lab, EVC ‐ W1: Rehersal 1

Image Geometry g y  Simplest Model: Pinhole camera p  Has a very small hole (Aperture = ∞ ), Light is led (Aperture ), Light is led through the hole and forms an image at the back of the g box (upside down and side ‐ inverted) 8 Robert Sablatnig, Computer Vision Lab, EVC ‐ W1: Rehersal 1

Image Geometry g y  Perspective Projection (Central projection)  Is the projection of the 3d world onto a 2d plane by rays passing  Is the projection of the 3d world onto a 2d plane by rays passing through a common point the center of projection.  => models image formation by a pinhole camera  => models image formation by a pinhole camera 9 Robert Sablatnig, Computer Vision Lab, EVC ‐ W1: Rehersal 1

Equations of the perspective projection q p p p j x  x f f f f x  X Z X Z y  f f y  y Y Y Z Y Z  Perspective projection is non ‐ linear ! 10 Robert Sablatnig, Computer Vision Lab, EVC ‐ W1: Rehersal 1

Recap: Limits of Pinhole Cameras p  A picture of a filament taken with a pinhole camera. In the image on the left, the hole was too big (blurring), and in the image on , g ( g), g the right, the hole was too small (diffraction). Ruechardt, 1958 11 Robert Sablatnig, Computer Vision Lab, EVC ‐ W1: Rehersal 1

Simple Lens Parameters p u u v v 12 Robert Sablatnig, Computer Vision Lab, EVC ‐ W1: Rehersal 1

Lenses  Pin has no lens => small Aperture => few light Pi h l ll A t f li ht  „thin" lenses: small Aperture but much light  Thin lens law: y  u  0 y i v y  f  0  y i v f 13 Robert Sablatnig, Computer Vision Lab, EVC ‐ W1: Rehersal 1

Lenses  f: focal length = distance of the point on the optical axis where all rays emerging p y g g from infinity meet to the lens plane ( = all rays are parallel to the optical axis) y p p )  if u = ∞ then v = f  Rays going through the optical center of  Rays going through the optical center of the lens are not diffracted 1 1 1 1 1 1    Field of view: area that is recorded by a  Field of view: area that is recorded by a camera: u v f f  The bigger f the smaller the area that is Th bi f th ll th th t i imaged  Wide ‐ angle ‐ small f; Zoom ‐ large f d l ll f l f 14 Robert Sablatnig, Computer Vision Lab, EVC ‐ W1: Rehersal 1

Depth of Field p  Only objects in a certain distance are imaged sharply at the image plane, all other distances are blurred because of blur circles. p ,  The bigger the aperture, the bigger the blur circles  The smaller the aperture the sharper is the image  The smaller the aperture, the sharper is the image  The bigger the depth of field the darker the image  Large Aperture = small depth of field p 15 Robert Sablatnig, Computer Vision Lab, EVC ‐ W1: Rehersal 1

Depth of Field p 16 Robert Sablatnig, Computer Vision Lab, EVC ‐ W1: Rehersal 1

Different numbers of Gray Levels y 17 Robert Sablatnig, Computer Vision Lab, EVC ‐ W1: Rehersal 1

Radiometric Resolution  Number of digital values (“gray levels”) that a sensor can use to express variability of signal (“brightness”) within the data p y g ( g )  Determines the information content of the image  The more digital values the more detail can be expressed  The more digital values, the more detail can be expressed  Determined by the number of bits of within which the digital information is encoded information is encoded 2 1 = 2 levels (0,1) 2² = 4 levels (0,1,2,3) 2 8 = 256 levels (0 ‐ 255) 2 12 = 4096 levels (0 ‐ 4095) 18 Robert Sablatnig, Computer Vision Lab, EVC ‐ W1: Rehersal 1

How many gray levels are required? y g y q  Contouring is most visible for a ramp  Digital images typically are quantized to 256 gray levels.

Transition to a Digital Image ‐ 1 g g 20 Robert Sablatnig, Computer Vision Lab, EVC ‐ W1: Rehersal 1

Transition to a Digital Image ‐ 2 g g 21 Robert Sablatnig, Computer Vision Lab, EVC ‐ W1: Rehersal 1

Image Size and Resolution g  These images were produced by simply picking every n ‐ th sample horizontally and vertically and replicating that value nxn times: y y p g 22 Robert Sablatnig, Computer Vision Lab, EVC ‐ W1: Rehersal 1

Sampling Theorem p g Shannon Theorem Shannon Theorem : Exact reconstruction of a continuous ‐ time h h h h i f i i baseband signal from its samples is possible if the signal is b bandlimited and the sampling frequency dli it d d th sampling frequency is greater than li li f f i greater than twice t t th th t i twice t i the signal bandwidth the signal bandwidth . y x y y Abtastsignal x x abzutastendes Signal abzutastendes Signal abgetastetes Signal 23 Robert Sablatnig, Computer Vision Lab, EVC ‐ W1: Rehersal 1

Image Sensors g  Convert light into electric charge  CCD (charge coupled device)  CCD (charge coupled device)  CMOS (complementary metal  CMOS (complementary metal Oxide semiconductor) Higher dynamic range Lower voltage g High uniformity High uniformity Higher speed Lower noise Lower system complexity y p y 24 Robert Sablatnig, Computer Vision Lab, EVC ‐ W1: Rehersal 1

Chromatic Aberration longitudinal chromatic aberration transverse chromatic aberration (axial) (lateral) 25 Robert Sablatnig, Computer Vision Lab, EVC ‐ W1: Rehersal 1

Spherical Aberration p  Effect: sharp image superimposed by a blurred one  Caused by spherical lens surfaces (manufacturing)  Parallel rays are focused in one point only if they are close to the optical axis h i l i  Can be avoided by using aspherical lenses with h i l l ith parabolic surfaces 26 Robert Sablatnig, Computer Vision Lab, EVC ‐ W1: Rehersal 1

Geometric Lens Distortions Radial distortion Tangential distortion Photo by Helmut Dersch Photo by Helmut Dersch Both due to lens imperfection 27 Robert Sablatnig, Computer Vision Lab, EVC ‐ W1: Rehersal 1

How CCDs Record Color 28 Robert Sablatnig, Computer Vision Lab, EVC ‐ W1: Rehersal 1

Bayer Filter y 29 Robert Sablatnig, Computer Vision Lab, EVC ‐ W1: Rehersal 1

Goal of Image Compression g p  Digital images require huge amounts of space for storage and large bandwidths for transmission. g  A 640 x 480 color image requires close to 1MB of space.  The goal of image compression is to reduce the amount of data  The goal of image compression is to reduce the amount of data required to represent a digital image.  Reduce storage requirements and increase transmission rates. Red ce storage req irements and increase transmission rates 30 Robert Sablatnig, Computer Vision Lab, EVC ‐ W1: Rehersal 1

Data Compression p  Data compression implies sending or storing a smaller number of l d ll b f bits.  lossless and  lossy methods.  Trade ‐ off: image quality vs compression ratio 31 Robert Sablatnig, Computer Vision Lab, EVC ‐ W1: Rehersal 1

Run Length Encoding (RLE) g g ( )  Simplest method of compression  Can be used to compress data made of any combination of  Can be used to compress data made of any combination of symbols, does not need to know the frequency of occurrence of symbols symbols  Replace consecutive repeating occurrences of a symbol by one occurrence of the symbol followed by the number of occurrences occurrence of the symbol followed by the number of occurrences Original Original 2 3 6 4 3 Coded  Lossless compression! p 32 Robert Sablatnig, Computer Vision Lab, EVC ‐ W1: Rehersal 1