Digital Image ProcessingSpring 2007

Sankalp Kallakuri

elsanky@gmail.comBooks refererenced –

Digital Image Processing by Gonzalez and Woods

Fundamentals of Digital Image Processing by A K Jain

Digital Picture Processing By Rosenfeld and Kak

Syllabus

• Fundamentals

• Image Enhancement [spatial]

• Image Enhancement [frequency]

• Sampling and Quantization

• Image Restoration

• Color Image Processing

• Image Compression

• Image Reconstruction

Syllabus

• Grading:

Assignments - 40%

Homework - 10%

Mid Term - 20%

Final - 30%

• Assignments:

Matlab and C/C++

IP 101

• Colour images

• Grey level images

• File formats JPG BMP TIFF

• 2D representations

• Examples of Fields that use IP

X-Rays, UV Imaging, IR Imaging, Satellite Images, Astronomy, License plates, Water Marking, Microwaves, MRI, sonograms, TEMs

Image Processing System

Image Displays Processors Mass storage

Hard CopySpecialized IP

Hardware

IP software

Image Sensors

network

Problem domain

From Gonzalez and Woods

Human Eye

Vision Details

• Lens Iris Pupil Cornea Retina

• Rods / Cones [distribution number use]

• Blind spot

• Photopic[bright]/ Scotopic[dim]

• Brightness adaptation

• Weber Ratio

Ic

I

Examples of Brightness perception

Figures from Gonzalez and Woods

Light and EM Spectrum

• Wavelength = C/ frequency

• Energy = h * frequency

• Reflected light

• Radiance is total amount of energy that flows

from the light source

• Luminance is the perceived from light source

• Sensor design

Image Sensing and Acquisition

• Single , Line and Array

• Array Strips

• Linear , circular

Bayer and RGB Filter type CCDS

From wikipedia

Projection

• Perspective

• Orthographic

Image Model

• f(x,y)

• 0 < f(x,y) <

• f(x,y)=i(x,y)r(x,y)

• i - illuminance r- reflectance

• 0 < i(x,y) <

• 0 < r(x,y) < 1

Sampling and Quantization

• In 1 dimension

• In 2 dimension

• Effects of quantisation

• Colour levels and bit requirements

Signals

sampling

Quantization

levels

Sampled

&

Quantized

signal

Continuous phenomenon

Two orthogonal sine waves

added to each other Continuos Image

Sampled and Quantised in 1 Dimension

Quantized and sampled Effects are contour lines

Sampled and Quantised

Contour lines appear on both X and Y dimensions

Bit Requirements

• L = 2 K

• b= M x N x K

• Example:

100 distinct colors needed to capture a

phenomenon. How many bits would be

needed to store an image of dimensions

49x10?

3430

Resolution

• Easier to change number of Pixels rather than

number of grey levels.

• Optimal number to use is until there is no

discernible difference by increasing the number.

• Isopreference Curves : curves on the N k plane

• More detail fewer grey levels.

• The higher grey levels will mean better contrast

perception.

Aliasing

0 frfl

0 Fs-Fs

Zooming and Interpolation

• Simple zoom would leave blank spaces in the grid.

• Nearest neighbor interpolation.

• Repetition of pixels [integer zoom]

• Bilinear Interpolation

v(x,y)=ax+by+cxy+d

• Shrinking done by removal of columns and rows.

• In case of non integer shrink factor the grid Is zoomed out. Interpolation is performed and then rows and columns are stripped out.

• Smoothing is useful before shrinking.

Relationships between Pixels

• Neighborhood N4(p) N8(p) ND(p)

• 4 adjacency ,8 adjacency and m adjacency

• Digital path

• Connected Components

• Connected Set [region]

• Border

• Edge [may be local ]

Distance Measures

• For Pixels p,q and z with coordinates (x,y) (s,t) and (v,w)

• D(p,q) > 0 (D(p,q)=0 iff p=q)

• D(p,q) = D(q,p)

• D(p,z) < D(p,q) + D(q,z)

• City block distance

D4(p,q) = |x-s| + |y-t|

• Chessboard Distance

D8(p,q)=max(|x-s| + |y-t|)

Home Work & Assignment

• Label all images

• Scripts should be commented.

• A read me file should be attached.

• Assignments shall be incremental.

• So try and complete them by the deadlines.

Homework -1

• Learn how to read and write an image in matlab.

• Learn basic syntax in Matlab.

• Create a 256x256 2D array. Populate every row with a sine wave which rides on a DC level of 128 with Peak-Peak amplitude 220 , which has exactly two cycles fit in a row.

• display this array as an image.

• Create a 256x256 2D array. Populate every column with a sine wave which rides on a DC level of 10, with Peak-Peak amplitude 20, which has exactly 4 cycles fit in a column.

• Add the two arrays

• Display the sum array as an image