Introduction: Image Acquisition and Representation CS 4640: Image - - PowerPoint PPT Presentation

Introduction: Image Acquisition and Representation

CS 4640: Image Processing Basics January 12, 2012

The Electromagnetic Spectrum and Images

We are familiar with visual light images (photographs), but images can be made from almost any form of EM radiation.

Buildings Humans Butterflies Needle Point Protozoans Molecules Atoms Atomic Nuclei 104 108 1012 1015 1016 1018 1020 1 K 100 K 10,000 K 10,000,000 K Penetrates Earth's Atmosphere? Radio Microwave Infrared Visible Ultraviolet X-ray Gamma ray 103 10−2 10−5 0.5×10−6 10−8 10−10 10−12 Radiation Type Wavelength (m) Approximate Scale

• f Wavelength

Frequency (Hz) Temperature of

• bjects at which

this radiation is the most intense wavelength emitted −272 °C −173 °C 9,727 °C ~10,000,000 °C From Wikipedia

Types of Images

◮ Radar imaging (radio waves) ◮ Magnetic Resonance Imaging (uses radio waves) ◮ Microwave imaging ◮ Infrared imaging ◮ Photographs ◮ Ultraviolet imaging telescopes ◮ X-rays and Computed Tomography ◮ Positron emission tomography (gamma rays) ◮ Ultrasound (not EM waves)

The Pinhole Camera

Projective Geometry of the Pinhole Camera

Gives a relationship between coordinates in the 3D world, X, Y, Z, and the corresponding coordinates to which they are projected onto the imaging plane, x, y. Depends on the focal length, f .

x = − f Z X, y = − f Z Y

Camera Obscura

◮ Uses a pinhole camera to project image into a dark

box or room

◮ In Latin “Camera” = room, “Obscura” = dark ◮ Pinhole camera first described by the ancient

Chinese and Greeks (roughly 400-300 BC)

◮ First working camera obscura built by Ibn

al-Haytham (around 1000 AD)

The Thin Lens

Images as Functions

We can think of the intensity of light falling on the imaging plane as a function of position on that plane. Let Ω ⊂ R2 be the image domain. Then an image is a function

I : Ω → R

This is an idealistic mathematical model of an image.

Images as Functions: Example

A simple image

20 40 60 80 20 40 60 80 0.2 0.4 0.6 0.8 1

Image function as a height field

Spatial Sampling

We cannot record (or store) a continuum of values on the imaging plane. So, a finite number of sensors are arranged in a grid.

Spatial Sampling

1 2 3 4 5 6 −1.0 −0.5 0.0 0.5 1.0 x sin(x)

×

x III(x)

• −5

−4 −3 −2 −1 1 2 3 4 5 −0.5 0.5 1.0 1.5

=

1 2 3 4 5 6 −1.0 −0.5 0.0 0.5 1.0 x sin(x) * comb(x)

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• We can think of spatial sampling as multiplication of a

continuous signal with a comb function.

Quantization

We also have to discretize the output intensity I(u, v) to store digitally. This is an analog-to-digital conversion.

1 2 3 4 5 6 −1.0 −0.5 0.0 0.5 1.0 x quantize(sin(x) * comb(x))

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Images as Discrete Functions

After spatial sampling and quantization, an image is a discrete function. The image domain Ω is now discrete:

Ω ⊂ N2,

and so is the image range:

I : Ω → {1, . . . , K},

where K ∈ N.

Representing an Image

The data structure for an image is simply a 2D array of

• values. The values in the array can be any datatype (bit,

byte, int, float, double, etc.)