S. Mandayam/ DIP/ECE Dept./Rowan University

Digital Image ProcessingDigital Image Processing

ECE.09.452/ECE.09.552ECE.09.452/ECE.09.552 Fall 2007Fall 2007

Shreekanth MandayamECE Department

Rowan University

http://engineering.rowan.edu/~shreek/fall07/dip/

Lecture 5Lecture 5October 15, 2007October 15, 2007

S. Mandayam/ DIP/ECE Dept./Rowan University

PlanPlan• Image Spectrum

• (Recall) 2-D Fourier Transform (DFT & FFT)• Spectral Filtering

• Digital Image Restoration• Enhancement vs. Restoration

• Environmental Models• Image Degradation Model• Image Restoration Model• Point Spread Function (PSF) Models

• Linear Algebraic Restoration• Unconstrained (Inverse Filter, Pseudoinverse Filter)• Constrained (Wiener Filter, Kalman Filter)

• Lab 2: Spatial and Spectral Filtering

S. Mandayam/ DIP/ECE Dept./Rowan University

Image PreprocessingImage Preprocessing

Enhancement Restoration

SpatialDomain

SpectralDomain

Point Processing• >>imadjust• >>histeq

Spatial filtering• >>filter2

Filtering• >>fft2/ifft2• >>fftshift

• Inverse filtering• Wiener filtering

S. Mandayam/ DIP/ECE Dept./Rowan University

Noise ModelsNoise Models

• SNRg = 10log10(Pf/Pn)

• Power Variance (how?)

• SNRg = 10log10(f2/ n

2)

f(x,y) g(x,y)

n(x,y)

Degradation Model: g = f + n

S. Mandayam/ DIP/ECE Dept./Rowan University

2-D Discrete Fourier Transform2-D Discrete Fourier Transform

1

0

1

0

)(2exp),(v)u,(F

N

x

N

y Nvyux

jyxf

>>fft2>>ifft2

u=0 u=N/2 u=N

v=N

v=

N/2

v

=0

S. Mandayam/ DIP/ECE Dept./Rowan University

2-D DFT Properties2-D DFT Properties

• Conjugate symmetrydemos/demo3dft_properties/con_symm_and_trans.m

• Rotationdemos/demo3dft_properties/rotation.m

• Separabilitydemos/demo3dft_properties/separability.m

>>fftshift

S. Mandayam/ DIP/ECE Dept./Rowan University

Spectral Filtering: Spectral Filtering: Radially Symmetric FilterRadially Symmetric Filter

• Low-pass Filterdemos/demo4freq_filtering/lowpass.m

u=-N/2 u=0 u=N/2v=

N/2

v=

0

v=

-N/2

D0

D(u,v)

S. Mandayam/ DIP/ECE Dept./Rowan University

DIP: DetailsDIP: Details

Gray-level Histogram

Spatial

DFT DC T

Spectral

Digital Image Characteristics

Point Processing M asking Filtering

Enhancem ent

Degradation M odels Inverse Filtering W iener Filtering

Restoration

Pre-Processing

Inform ation Theory

LZW (gif)

Lossless

Transform -based (jpeg)

Lossy

Com pression

Edge Detection

Segm entation

Shape Descriptors Texture M orphology

Description

Digital Im age Processing

S. Mandayam/ DIP/ECE Dept./Rowan University

Image PreprocessingImage Preprocessing

Enhancement Restoration

SpatialDomain

SpectralDomain

Point Processing• >>imadjust• >>histeq

Spatial filtering• >>filter2

Filtering• >>fft2/ifft2• >>fftshift

• Inverse filtering• Wiener filtering

S. Mandayam/ DIP/ECE Dept./Rowan University

Enhancement vs. RestorationEnhancement vs. Restoration

• “Better” visual representation

• Subjective

• No quantitative measures

• Remove effects of sensing environment

• Objective

• Mathematical, model dependent quantitative measures

S. Mandayam/ DIP/ECE Dept./Rowan University

Degradation ModelDegradation Model

f(x,y) h(x,y) g(x,y)

n(x,y)

Degradation Model: g = h*f + n

demos/demo5blur_invfilter/

demos/demo5blur_invfilter/degrade.m

S. Mandayam/ DIP/ECE Dept./Rowan University

Restoration ModelRestoration Model

f(x,y) DegradationModel

f(x,y)RestorationFilter

Unconstrained Constrained• Inverse Filter• Pseudo-inverse Filter

• Wiener Filter

demos/demo5blur_invfilter/

S. Mandayam/ DIP/ECE Dept./Rowan University

ApproachApproach

demos/demo5blur_invfilter/

f(x,y)

Builddegradation model

Formulate restoration algorithms

f(x,y)

Analyze usingalgebraic techniques

Implement usingFourier transforms

g = h*f + n

g = Hf + nW -1 g = DW -1 f + W -1 n

f = H -1 g

F(u,v) = G(u,v)/H(u,v)

S. Mandayam/ DIP/ECE Dept./Rowan University

Lab 2: Spatial & Spectral Lab 2: Spatial & Spectral FilteringFiltering

http://engineering.rowan.edu/~shreek/fall07/dip/lab2.html

S. Mandayam/ DIP/ECE Dept./Rowan University

SummarySummary