Pa is the PDF of the image

1
Histogram Flattening
P(a) is the PDF of the image A Area of the
image H(a) Histogram of the image
2
Histogram Flattening
The Cumulative Distribution Function (CDF)
will Flatten the Histogram of the Image
Processed by this Function
3
ALGEBRAIC OPERATIONS
C(x,y) A(x,y) - B(x,y)
C(x,y) A(x,y) x B(x,y)
C(x,y) A(x,y) ? B(x,y)
4
SUMMED IMAGES
Uncorrelated Images
5
Geometric Operations Spatial Transformations
Identity
a(x,y) x b(x,y) y
Translation
Reflection about the y Axis
Magnification
Rotation
6
Continuous Fourier Transform
One Dimensional
7
Continuous Fourier Transform
Two Dimensional
8
Discrete Fourier Transform
One Dimensional
9
Discrete Fourier Transform
Two Dimensional
10
General Transforms and Separability
Kernel is Separable IF
IF Separable, THEN
11
OTHER TRANSFORMS
Hadamard ( Walsh )
Hough Transform
Haar Transform
Wavelet Transforms
12
Transform Processing and Encoding
Objective
(a) Redistribute Variance to Decorrelate
Transform Coefficients
(b) Transform Variance of each Pixel into
Low Order Coefficients of Transform
13
Transform Processing and Encoding
14
Waves and wavelets
The Haar transform is the earliest example of
what we now call a wavelet transform 2. It
differs from the other transforms in Chapter 13
in that its basis vectors are all generated by
translations and scalings of a single function.
The Haar function, which is an odd rectangular
pulse pair, is the oldest and simplest wavelet.