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Converting from an analog to a digital image.

1. Sampling image into pixels----> "picture element"

2. Quantize the pixel value to make discrete or finite

Digital imaging is the process of sampling and quantizing the analog image (can store in computer)

SAMPLING in more detail

1. fit a grid over the image, create pixels

pixel location = (r,c)=(row,column)

2.Get value of each pixel

Pixel(r,c) =(R,G,B) = (red,green,blue)

RED = red(x,y) dxdy

(over pixel area)

red(x,y) = function of red spectral energy at each contigous point in your sensor

Image size = (rows)*(colomns)

Resolution = size of image = #pixels

low resolution ---> # of pixels is small

high resolution ----> # of pixels is big

HOW DO YOU SELECT A RESOLUTION?

if grid is too large you will get jagged edges

QUANTIZATION in more detail

continuous value ---> discrete value

Z = decision level (Z1, Z2, Z3)

Qk = quantization level (Q0, Q1, Q2)

the above are all discrete values

The rule to convert

If Z k-1 <= pixel (r,c) <= Zk: then new pixel (r,c) = Qk

How do we choose the Q's and Z's

The goal is to choose Q's & Z's to minimize error produced from quantization, E

where

E = Expected value{(pixel- newpixel)*(pixel-newpixel )}

= mean squared error

Note:

square error= (pixel value - new value)

expected value = a type of average or mean

If we try to minimize this error this leads to the following equation

Qk= (Zk+1+Zk) / 2

So, Steps to follow are:

choose Zk
calculate Q's via above equation

How Do We Choose Z's?

Basically, it is function of image content
You want more levels (Z values) in greyvalue or color ranges in which much of the image pixels fall.

What do you loose in making a Digital Image?

1. Loss from sampling?

Over-Sampling = when you have more samples than you need

Under-Sampling = not enough samples are used

How many samples do you need?

You need 2 times the Nyquest rate.
Nyquest rate= function of highest frequency in the image
highest frequency in image = function of fastest varying spatial patter in the image = f(how fast things change)

2. Loss from Quantization?

There is always loss from process of quantization