IMAGE 1
An image is a two
dimensional
Function f(x,y) where
x and y are spatial
coordinates
And f at any x,y is
related to the
brightness at that point
A digital image is a
2D representation of a
continuous image by a
2D array of discrete
samples
Each element of the
2D array is a pixel.
Definition
Histograms count the number of
occurrences of each possible value
HD
Count
Grey level
Properties
• Sum of all values in the histogram equals
the total number of pixels

 HDdD  image
0
area
Properties
• Sum of all values between a and b equals the
area of all objects in that range
b
 HDdD  area of all
a
parts a  I  b
Properties
• Integrated optical density

IOD   D HDdD
0
• Mean greylevel
MGL  IOD area
Application: Adjusting Camera
Parameters
• Too bright - lots of pixels at 255 (or max)
• Too dark - lots of pixels at 0
• Gain too low - not enough of the range used
Application: Segmentation
• Can be used to separate bright objects from
dark background (or vice versa)
Normalizing Histograms
• Probability density function =
histogram normalized by area
1
p D   H  D 
A
Cumulative Histograms
• Counts pixels with values up to and
including the specified value
a
Ca   HDdD
0
Cumulative Density Functions
• Normalized cumulative histograms
a
1
Pa    pDdD  Ca
A
0
IMAGE 1
Image 1: Bright
Image 1: Dark
Image 1: Low contrast
Image 1: High contrast
RESOLUTION
INTERPOLATION
HISTOGRAM EQUALIZATION
THRESHOLDING
104
199
34
137
Inverted
SMOOTH
3
SMOOTH
7
MEDIAN
3
MEDIAN
5