1 Comp300a: Introduction to Computer Vision L. QUAN

2 Course organisation Lectures on Tuesday and Thursday 4 labs (or mini-projects) Mid-term and final 30% labs+30% midterm+40%final

3 What is Computer Vision about? These fields are all closely related to 2d images, but different: Image processing: 2D images  2D images, well-defined pb. Computer vision: 2D images  3D reconstruction, hard ill-posed inverse pb. Computer graphics: 3D  2D, well-posed forward pb (+analysis & Interpretation)

4 What are applications? modeling for graphics visualization photo/video manipulation and editing robot navigation autonomous vehicules guiding tools for blind security and monitoring object/face recognition, OCR medical applications visual communication digital libraries …

5 What am I doing? Some examples

6 Overview Introduction –intersection of vision, graphics and image-based modeling and rendring –some basic mathematical tools (linear algebra, homogeneous coordinates, and optimisation) Modeling –Digital photography –Basic radiometry –Geometric modeling of camera –Camera calibration and pose estimation Image features –Filtering –Edge detection, polygonal approximation –Points of interest detection 3D reconstruction by multiple views: stereovision –Epipolar geometry –Computing correspondences –3D reconstruction

7 On-line computer vision courses

8 1. Basic Digital photography and image manipulations

9

10 Digital Images WorldCameraDigitizer Digital Image Image Formation: (i) What determines where the image of a 3D point appears on the 2D image? (ii) What determines how bright that image point is? (iii) How is a digital image represented? (iv) Some simple operations on 2D images? today Reflectance, radiometry geometry

x = What is a digital image? y = Pixel: picture element Typically: 0 = black 255 = white Black/white = grayscale image

12 Color Image

13 Three types of images: –Gray-scale images I(x,y)  [0..255] –Binary images I(x,y)  {0, 1} –Color images I R (x,y) I G (x,y) I B (x,y)

14 Image qualtiy: resolution (size, #pixels, aspect ratio) color depth compression

15 This graphic shows the relative sizes of a frame of 35mm film (red), the D60 image sensor (yellow), and a 1/1.8 CCD used in another digital camera (blue). Resolution:

16 ImageWidth x heightAspect Ratio 35 mm film36 x 24 mm1.50 Display monitor1024 x Nikon Coolpix x Photo paper4 x 6 inches1.50 Photo paper8 x 10 inches1.25 Cannon EOS D x HDTV16 x Aspect ratio:

17 Effects of down-sampling (reducing number of pixels): 4 x 4 32 x x 128

18 Resolution isn't the only factor, equally important is color depth, pixel-depth, or bit-depth. Color depth: #bit for each pixel in each channel

19 2 gray levels (1 bit/pixel) BINARY IMAGE 8 gray levels (3 bits/pixel) 256 gray levels (8 bits/pixel) Effects of reducing number of bits for each pixel:

20 A heavily compressed image A less compressed one Compression:

21 Image processing 1) Basic (global and nonlinear) operators 2) Spatial Domain 3) Frequency Domain - Histogram equalization - Gamma correction etc... later

22 A histogram is a graph that shows how the 256 possible levels of brightness are distributed in the image. Image histograme:

23 Occurrence (# of pixels) Gray Level H(k) = #pixels with gray-level k Normalized histogram: H norm (k)=H(k)/N (N = # pixels in the image) Histogram = The gray-level distribution: Continuous probability density function:

24 P I (k) k k P I (k) k 0.1

25 P I (k) k P I (k) k 0.1 Histogram Stretching

26 kk Histogram Equalization

27 OriginalEqualized

28 Gamma correction: Gamma correction controls the overall brightness of an image. Images which are not properly corrected can look either bleached out, or too dark. Trying to reproduce colors accurately also requires some knowledge of gamma. Varying the amount of gamma correction changes not only the brightness, but also the ratios of red to green to blue.

29 Correction L' = L ^ (1/2.5) Graph of Output L = V ^ 2.5 Sample Input to Monitor Graph of Input Output from Monitor