Digital Image Processing

Digital Image Processing

Digital Image 

For every point in a 2D region, 

the image has a pixel value. 

Pixel value is an integer 

between 0 and 255 

Pixel value is a triplet of 

integers, each of which is 

between 0 and 255


• Image 

– An image is a two-dimensional signal 

Digital images 

f 

:{0,1, 

,3007} 

{0,1, 

,2047} 

{0,1, 

,255} 

f 

:{0,1, 

,3007} 

{0,1, 

,2047} 

{0,1, 

,255} 

3


f 

:{0,1, 

,3007} 

{0,1, 

,2047} 

{0,1, 

,255} 

Domain of the image; 

also called the support 

Range of the 

image 

For every point in the domain, the image f assigns a 

value from the range 

When both the domain and the range are integer 

values, f is a digital image


The set of all possible pixel 

values is the range of the 

image 

Range = 

{ 0,1, ,255} 

Range = 

{ 0,1, ,255} 

3




image 

{ 0,1, ,255} 

Can be represented by an 8-bit number; the 

image is therefore referred to as an 8-bit 

image; the bit-depth of the image is 8.




image 

{ 0,1, ,255} 

3 

Can be represented by three 8-bit numbers; the 

image is therefore referred to as a 24-bit color 

image; the bit-depth of the image is 24.

Digital Images: 90 years ago 

Range has 5 values! 

15-tone

Digital Images 

Not all images are recorded in the visible range

X-ray Imaging

Visible Range

Visible Range 

In the visible 

range does 

not mean 

visible to the 

naked eye

Visible Range

Lafayette, Louisiana; August 1992

Imaging Process

Digital Camera 

• Sensor size 

15.6mm by 23.6mm 

• resolution 

49283264 pixels 

• each pixel can see only one 

color 

Bayer 

matrix

Imaging Process 

Digital Image

Imaging Process: Color Image 

A block of pixels; each 

has 1 (of 3) colors 

Demosaicking 

A block of 

color pixels 

Bayer filter 

The red and blue 

components of this 

pixel are estimated 

from the neighbors

Imaging Process


Sampling and Quantization

Pixel Size 

Also called “pixel pitch” 

Pixel width and height are not always 

the same; ie the pixel is not always 

square 

EXAMPLE 

sensor size 

15.6mm by 23.6mm 

resolution 

49283264 pixels 

Pixel width = 23.6/4928mm = 4.79μm 

Pixel height = 15.6/3264mm = 4.78μm


Sampling and Quantization 

Sampling is rounding 

off in the spatial 

domain of the image 

Quantization is 

rounding off in the 

range of the image 

Is a sensor with higher spatial resolution always better?


A digital image is a two-dimensional signal with a countable 

domain and a countable range 

f 

:{0,1,...,59} 

{0,1,...,59} 

{0,1,...,255}


A digital image is a two-dimensional signal with a countable 

domain and a countable range 

In other words, we work with integers (with no 

units), not with volts, microns, etc. 

Example 

f :{0,1,...,59} 

{0,1,...,59} 

{0,1,...,255} 

f (5,8) = 151 

By convention, (row, column)

Image Representation


“m” indexes row; 

“n” indexes column 

Origin; 

row=0, column=0

Digital Image Processing 

• Digital Image 

f 

0,1, 

,639 

0,1, 

,479 

012 

, , , 255 

: , 

Which of these pictures does the above expression 

refer to?

Image Size 

• How big is an image? 

• Number of pixels = 

M N 

• Number of gray levels = 

2 

L 

Is a higher spatial 

resolution sensor always 

better? 

• Total number of bits = 

M 

 

N 

 

L 

Color image 

Number of color channels = 3 

Total number of bits = 

3M 

 

N 

 

L

Digital Image Processing 

• Digital Image 

f 

:{0,1,...,639} 

{0,1,...,479} 

{0, 

1 

255 

, 

2 

...,1} 

255 

How many bits does it 

take to represent the 

range of this image? 

Sometimes the domain and the range values are not 

always integers; as long as they are countable, we 

consider it a digital image.

Spatial Resolution

Spatial Resolution

Spatial Resolution

Changing the Domain 

• When the scale or resolution of an image is changed, 

we are forming a new image with a different domain 

set 

• Related problems 

– Interpolation 

– Scale change 

– Rotation

Pixel Depth Resolution

Pixel Depth Resolution

Changing the Range 

• When we change the number of gray levels or the 

number of colors, we are forming a new image with 

a new range set 

• Related problems 

– Image quantization 

– Halftoning 

– Tone-mapping 

Mapping the number of 

} 

levels of intensities to the 

capability of the image 

display device

Pixel Depth Resolution 

• How many levels of 

gray level can we 

see? 

256 gray levels


• Clearing (or setting) the least significant bit of each 

pixel amounts to halving the number of levels


65


33


17


9


5


2

Image Processing Programming

Image Processing Programming 

• Image data stored as an array of bytes 

Range = 

{ 0,1, ,255} 

unsigned char gbuffer[HEIGHT][WIDTH];


• Image data stored as arrays of bytes 

Range = 

{ 0,1, ,255} 

3 

unsigned char cbuffer[3][HEIGHT][WIDTH]; 

unsigned char cbuffer[HEIGHT][WIDTH][3];

Image Storage 

unsigned char cbuffer[3][HEIGHT][WIDTH]; 

Conceptually: 

3 consecutive 

planes

Image Storage 

unsigned char cbuffer[HEIGHT][WIDTH][3]; 

Conceptually: 3 values 

for each pixel location; 

also known as 

interlaced 

Values for one pixel


• Simple code fragments 

(++‏i for (i=0; i


• Unless the method is very simple, avoid working in 

“unsigned char” since it is easy to overflow or 

underflow 

• Convert to integer or float first, then do the 

computation, then convert back to unsigned 

char for display 

– Scale 

– Clip


• Input/Output 

• Image data stored in binary format, usually one row 

at a time 

– Top to bottom: most formats 

– Bottom to top: Microsoft’s BMP format 

• The program needs to know the dimensions of an 

image, among other information

ead/fread 

• read(0, buffer, 640*480); 

• fread(buffer, 640*480, 1, fp);

Image File Formats 

• Many file formats 

– Jpg, gif, tiff, bmp 

– Jbig, png, rast, rle 

• Many formats compress the image data

Image File Formats 

• Have an environment that opens file for the 

programmer 

– Matlab 

– Photoshop 

– libnetpbm

Digital Image Processing

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