1 Comp300a: Introduction to Computer Vision L. QUAN.

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Comp300a: Introduction to Computer Vision

L. QUAN

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Course organisation

• Lectures on Tuesday and Thursday

• 4 labs (or mini-projects)

• Mid-term and final

• 30% labs+30% midterm+40%final

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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)

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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• …

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What am I doing?

Some examples

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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

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http://www.dai.ed.ac.uk/CVonline/

On-line computer vision courses

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1. Basic Digital photography and image manipulations

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Digital Images

World Camera Digitizer DigitalImage

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

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x = 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72

414243444546474849505152535455

What is a digital image?

y =

Pixel: picture elementTypically: 0 = black 255 = white

Black/white=grayscale image

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Color Image

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Three types of images:

– Gray-scale images I(x,y) [0..255]

– Binary images I(x,y) {0 , 1}

– Color images IR(x,y) IG(x,y) IB(x,y)

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Image qualtiy:

• resolution (size, #pixels, aspect ratio)• color depth• compression

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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:

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Image Width x height Aspect Ratio

35 mm film 36 x 24 mm 1.50

Display monitor 1024 x 768 1.33

Nikon Coolpix 990 2048 x 1536 1.33

Photo paper 4 x 6 inches 1.50

Photo paper 8 x 10 inches 1.25

Cannon EOS D60 3072 x 2048 1.5

HDTV 16 x 9 1.80

Aspect ratio:

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Effects of down-sampling (reducing number of pixels):

4 x 432 x 32128 x 128

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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

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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:

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A heavily compressed image A less compressed one

Compression:

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Image processing

1) Basic (global and nonlinear) operators

2) Spatial Domain

3) Frequency Domain

- Histogram equalization

- Gamma correction

etc...

later

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

Image histograme:

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Occurrence(# of pixels)

Gray Level

H(k) = #pixels with gray-level k

Normalized histogram: Hnorm(k)=H(k)/N (N = # pixels in the image)

Histogram = The gray-level distribution:

Continuous probability density function: 1)( dxxp

k

norm kH 1)(

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PI(k)

k

PI(k)

k

1

1

0.5

PI(k)

k

0.1

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PI(k)

k0.5

0.1PI(k)

k

0.1

Histogram Stretching

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k k

)(khideal)(kh

Histogram Equalization

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0 50 100 150 200 2500

500

1000

1500

2000

2500

3000

3500

0 50 100 150 200 2500

500

1000

1500

2000

2500

3000

3500

Original Equalized

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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.

29Correction L' = L ^ (1/2.5)

Graph of Output L = V ^ 2.5

Sample Input to Monitor

Graph of Input

Output from Monitor