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EE465: Introduction to Digital Image Processing 2

Introduction

Apa itu perbaikan citra? Proses peningkatan kualitas visual dari citra

karena proses pengambilan gambar yang tidak ideal. (Tidak fokus, gerakan blurring, illumminasi yang jelek, dll)

Menilai kualitas visual citra


A Plague in Image Processing: Blur Dari mana blur itu berasal?

Optical blur: kamera out-of-focus Motion blur: Kamera bergerak

Mengapa perlu deblurring? Mengganggu secara visual Target yang salah untuk kompressi Jelek untuk dianalisa

Numerous applications in astronomical imaging, biomedical imaging, biometrics ...


Restoration Images


Another Example


The Real (Optical) Solution

Before the repair After the repair


Application (II): Medical Image Deblurring (Deconvolution)


Application (III): Law Enforcement

Motion-blurred license plate image


Restoration Example


A Grand Challenge in Iris Recognition

out-of-focus iris image


h(m,n) +x(m,n) y(m,n)

),( nmw

• Linear degradation model

),( nmh blurring filter

),0(~),( 2wNnmw additive white Gaussian noise

Modeling Blurring Process


2

2

10log10w

zBSNR

Blurring SNR

The Curse of Noise

h(m,n) +x(m,n) y(m,n)

),0(~),( 2wNnmw

z(m,n)


h(m,n): 1D horizontal motion blurring [1 1 1 1 1 1 1]/7

BSNR=40dB

Image Example

BSNR=10dBx(m,n)


Mengapa butuh metode non linier ? Proses pemodelan degradasi citra dengan

linear system muncul terutama karena dapat dinyatakan secara matematis

Tetapi ada fenomena dalam visualisasi dan pencitraan secara fisik sulit dijelaskan degna persamaan sederhana secara linier Examples: relationship between illumination and

luminance on a complex surface, quantization of intensity values, Gamma-correction in display devices


Point Operations Overview

Point operations are zero-memory operations wherea given gray level x[0,L] is mapped to anothergray level y[0,L] according to a transformation

)(xfy

L

L

x

y

L=255: for grayscale images


Lazy Man Operation

L

L

x

y

xy

No influence on visual quality at all


Digital Negative

xLy

L x0

L


Contrast Stretching

Lxbybx

bxayax

axx

y

b

a

)(

)(

0

L x0 a b

ya

yb

200,30,1,2,2.0,150,50 ba yyba


Clipping

Lxbab

bxaax

ax

y

)(

)(

00

L x0 a b

2,150,50 ba


Range Compression

)1(log10 xcy

L x0

c=100


Kesimpulan operasi titik

Pemetaan f(x) mengahasilkan hasil perbaikan yang berbeda beda

Bagaimana memilih fungsi f(x) yang sesuai untuk sembarang citra?

One systematic solution is based on the histogram information of an image Histogram equalization and specification


Histogram based Enhancement

Histogram of an image represents the relative frequency of occurrence of various gray levels in the image

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MATLAB function >imhist(x)


Why Histogram?

Histogram information reveals that image is under-exposed

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0

0.5

1

1.5

2

2.5

3

3.5

4

x 104

It is a baby in the cradle!


Another Example

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Over-exposed image


How to Adjust the Image?

Histogram equalization Basic idea: find a map f(x) such that the histogram

of the modified (equalized) image is flat (uniform). Key motivation: cumulative probability function

(cdf) of a random variable approximates a uniform distribution

x

t

thxs0

)()(Suppose h(t) is the histogram (pdf)


Histogram Equalization

x

t

thLy0

)(Uniform

Quantization

L

t

th0

1)(Note:

L

1

x

t

ths0

)(

x

L

y

0

cumulative probability function


MATLAB Implementation

function y=hist_eq(x)

[M,N]=size(x);for i=1:256 h(i)=sum(sum(x= =i-1));End

y=x;s=sum(h);for i=1:256 I=find(x= =i-1); y(I)=sum(h(1:i))/s*255;end

Calculate the histogramof the input image

Perform histogramequalization

21/04/23 PERTEMUAN KE-6 28

Ic. Histogram Equalization

Histogram: diagram yang menunjukkan jumlah kemunculan grey level (0-255) pada suatu citra

Histogram processing: Gambar gelap: histogram cenderung ke sebelah kiri Gambar terang: histogram cenderung ke sebelah

kanan Gambar low contrast: histogram mengumpul di suatu

tempat Gambar high contrast: histogram merata di semua

tempat Histogram processing: mengubah bentuk histogram agar pemetaan gray level pada citra juga berubah


Ic. Histogram Equalization in all grey level and all area (1)

Ide: mengubah pemetaan greylevel agar sebarannya (kontrasnya) lebih menyebar pada kisaran 0-255

Sifat: Grey level yang sering

muncul lebih dijarangkan jaraknya dengan grey level sebelumnya

Grey level yang jarang muncul bisa lebih dirapatkan jaraknya dengan grey level sebelumnya

Histogram baru pasti mencapai nilai maksimal keabuan (contoh: 255)



- mengubah pemetaan grey level pada citra, dengan rumus:

citra pada ada yang maksimal levelgrey adalah L

1,.....,1,010

)()(0 0

Lkdanr

rpn

nrTs

k

k

j

k

jj

jkk



Contoh : citra dengan derajat keabuan hanya berkisar 0-10

Citra awal: 3 5 5 5 45 4 5 4 45 3 4 4 44 5 6 6 3

Derajat Keabuan

Kemunculan

Probabilitas Kemunculan

Sk

SK * 10

Derajat keabuan baru

0 1 2 3 4 5 6 7 8 9 10

0 0 0 3 8 7 2 0 0 0 0

0 0 0 0.15 0.40 0.35 0.1 0 0 0 0

0 0 0 0.15 0.55 0.90 1 1 1 1 1

0 0 0 1.5 5.5 9 10 10 10 10 10

0 0 0 1 5 9 10 10 10 10 10

Citra Akhir: 1 9 9 9 59 5 9 5 59 1 5 5 55 9 10 10 1


Ic. Histogram Equalization specific grey level (hist. specification)

Histogram equalization tidak dilakukan pada seluruh bagian dari histrogram tapi hanya pada bagian tertentu saja


Image Example

before after


Histogram Comparison

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before equalization after equalization


Application (I): Digital Photography


Application (II): Iris Recognition

before after


Application (III): Microarray Techniques

before after


Frequency-Domain Techniques (I): Unsharp Masking

0),,(),(),( nmgnmxnmy

g(m,n) is a high-pass filtered version of x(m,n)

• Example (Laplacian operator)

)]1,()1,(

),1(),1([4

1),(),(

nmxnmx

nmxnmxnmxnmg


MATLAB Implementation

% Implementation of Unsharp masking

function y=unsharp_masking(x,lambda)

% Laplacian operationh=[0 -1 0;-1 4 -1;0 -1 0]/4;dx=filter2(h,x);y=x+lambda*dx;


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1D Example

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-6

-4

-2

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2

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8

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x(n) xlp(n)

g(n)=x(n)-xlp(n) )()()( ngnxny


2D Example

>roidemoMATLAB command


Frequency-Domain Techniques (II): Homomorphic filtering

),(),(),( yxryxiyxf

Illumination(low freq.)

reflectance(high freq.)

Basic idea:

),(ln),(ln),(ln yxryxiyxf

freq. domain enhancement


Image Example

before after


Summary of Nonlinear Image Enhancement Understand how image degradation occurs first

Play detective: look at histogram distribution, noise statistics, frequency-domain coefficients…

Model image degradation mathematically and try inverse-engineering

Visual quality is often the simplest way of evaluating the effectiveness, but it will be more desirable to measure the performance at a system level Iris recognition: ROC curve of overall system Microarray: ground-truth of microarray image segmentation

result provided by biologists

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