Digital Image Processing - Örebro University Image Processing ... Course Book Chapter 3 Part 2: Image Enhancement in the Spatial Domain. ... Image Subtraction tracking with a stationary

2011-04-06

DDigital Image Processing

Achim J. Lilienthal

AASS Learning Systems Lab, Dep. Teknik

Room T1209 (Fr, 11-12 o'clock)

[email protected]

Course Book Chapter 3

Part 2: Image Enhancement

in the Spatial Domain

Achim J. Lilienthal

1. Image Enhancement in the Spatial Domain

2. Grey Level Transformations

3. Histogram Processing

4. Operations Involving Multiple Images

5. Spatial Filtering

Contents��1. Image Enhancement in the Spatial Domain

2. Grey Level Transformations

3. Histogram Processing

4. Operations Involving Multiple Images

5. Spatial Filtering

Achim J. Lilienthal

Image Enhancement in the Spatial Domain

� Contents� Contents

Achim J. Lilienthal

Image Enhancement in the Spatial Domain1

� Image Enhancement� image processing

� the result is supposed to be "more suitable"

� "more suitable" according to a certain application

more suitable for visual interpretation

Achim J. Lilienthal


We want to create an image which is "better" in some sense.

� helps visual interpretation (brightening, sharpening…)� subjective

� pre-processing for a subsequent image analysis algorithm� performance metric (performance of a task)

� make the image more "specific" � application dependent

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

original image(or set of images)

new image

T

Achim J. Lilienthal


� Spatial Domain versus Frequency Domain� spatial domain

� direct manipulation of the pixels

� discussed in this lecture

� two types of transformations in the spatial domain:

� pixel brightness transformations, point processing(depend only on the pixel value itself)

� spatial filters, local transformations or local processing(depend on a small neighbourhood around the pixel)

� frequency domain: modifications of the Fourier transform� discussed in the next lectures

Achim J. Lilienthal


� Transformations in the Spatial Domain

� standard approach:T is applied to a sub-image centred at (x,y)

� sub-image is called mask(kernel, filter, template, window)

� mask processing or filtering

� T can operate on a set of images

)],([),( yxfTyxg �

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� Transformations in the Spatial Domain

� fill new array with weighted sum of pixel values from the locations surrounding the corresponding location in the image using the same set of weights each time

)],([),( yxfTyxg �

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Gray Level Transformations


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Grey Level Transformations2

� Grey Level Transformations� simplest case: each pixel in the output image

depends only on the corresponding pixel in the input image

� 1x1 neighbourhood (point processing)

� example:contraststretching

)(rTs �)(rTs �

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� Grey Level Transformations

contrast stretching

thresholding


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� imadjust� parameters always specified in [0,1]

� values below 0.1 clipped to 1.0

� values above 0.9 clipped to 0.0

� image intensity reversed since 0.0 < 1.0


f = imread('bubbles.tif');fp = imadjust(f, [0.1 0.9], [1.0 0.0], 0.5);imshow(fp);

.5);

Achim J. Lilienthal


� imadjust� parameters always specified in [0,1]

� values below 0.1 clipped to 1.0

� values above 0.9 clipped to 0.0

� image intensity reversed since 0.0 < 1.0

� gamma function parameter < 1



.5);

g f ��

Achim J. Lilienthal




.5);

fp = imadjust(f, [0.55 0.9], [1.0 0.0], 3);3);

Achim J. Lilienthal


� imadjust� gamma function parameter > 1



.5);

fp = imadjust(f, [0.55 0.9], [1.0 0.0], 3);

g f ��

3);

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� Contrast Stretching� piecewise linear function

� power law transformation(gamma transformation)

�crs �


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� Common Grey Level Transformations (Single Image)� linear

� identity� inverse (negative)

� power law� n. power� n. root

� logarithmic


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� Common Grey Level Transformations (Single Image)� inverse transform


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� Contrast Stretching� piecewise linear function


Achim J. Lilienthal

� Common Grey Level Transformations (Single Image)� linear

� identity� inverse

� power law (gamma)� n. power� n. root

� logarithmic

� ... with more than one input image� sum, mean� statistical operations (variance, t-test …)


Achim J. Lilienthal

Histogram Processing


Achim J. Lilienthal

Histogram Processing3

� Grey Scale Histogram� shows the number of pixels per grey level

f = imread('bubbles.tif');imhist(f); % displays the histogram

% histogram display default splay default

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f = imread('bubbles.tif');h1 = imhist(f); % default number of bins = 256imhist(f,8); % number of bins = 8f bins 8

Achim J. Lilienthal



f = imread('bubbles.tif');h1 = imhist(f); % default number of bins = 256h = imhist(f,16); % number of bins = 16hN = h/numel(f); % normalized histogram

% numel �� num. of elements (pixels)bar(hN) % normalized histogram

. of elements (pixels)

Achim J. Lilienthal



f = imread('bubbles.tif');h1 = imhist(f); % default number of bins = 256h = imhist(f,16); % number of bins = 16hN = h/numel(f); % normalized histogram

% numel � num. of elements (pixels)bar(hN) % normalized histogram

of elements (pixels)

al

% numel � num.

. % nnnnnooooorrrrrmmmmmmaaaaallllliiiiizzzzeeeeeddddddddd hhhhhhiiiiissssstttttooooogggggrrrrraaaaammmmmmm

Achim J. Lilienthal

� Grey Scale Histogram� neutral transform


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� inverse transform


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� inverse transform

� logarithmic transform


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� Histogram Equalization� contrast / brightness adjustments sometimes

need to be automatised

� "optimal" contrast for an image?� flat histogram

� histogram matching� to get a given shape for the histogram (see GW 3.3.2)


Achim J. Lilienthal

� Histogram Equalization� consider the continuous case:

� probability density functions (PDFs) of s and r are related by

� transformation function = cumulative density function (CDF)

� �

]1,0[, �rs

)(1)()()(rT

rpdsdrrpsp rrs �

��

)()()(0

rpdpdrdrT

drds

r

r

r ��

��

�� 1)( �sps


gray levels as random variables!

�� )(rTs

��r

r dprT0

)()( ��

Achim J. Lilienthal

� Histogram Equalization� discrete case

� does not generally produce a uniform PDF

� tends to spread the histogram

� enables automatic contrast stretching

nnrp k

kr �)( ��

��k

j

jk

jjrkk n

nrprTs

00)()(


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� Histogram Equalization

CDF


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Achim J. Lilienthal



f = imread('bubbles.tif');g = histeq(f, 256);imshow(g);

f = imread('bubbles.tif');g = histeq(f, 4); % 4 output levelsimshow(g);

Achim J. Lilienthal

� Adaptive / Localized Histogram Equalization� transform a single pixel by histogram equalization

calculated over a square or rectangular neighbourhood

original image

global histogram equalization


http://www.cromwell-intl.com/3d/histogram/index.html

Achim J. Lilienthal



original image

local histogram equalization (radius = 100)


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original image



Achim J. Lilienthal



original image



Achim J. Lilienthal



original image



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Operations Involving Multiple Images


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� Operations Between Two or More Images� image subtraction

� Arteriography

� tracking

Operations Involving Multiple Images4

Achim J. Lilienthal

� Image Subtraction� DSA (Digital Subtraction Arteriography)


mask image live image DSA image

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� Arteriography

� tracking

� image averaging (GW 3.4.2)� noise reduction

� background modeling

� image subtraction


�

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� Image Subtraction� tracking with a stationary camera


background image live image difference image

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� Arteriography

� tracking

� image averaging (GW 3.4.2)� noise reduction

� background modeling

� image subtraction

� time constant of averaging ? (stability – plasticity dilemma)� recency weighted averaging

� sample-based background modelling


Achim J. Lilienthal

� Sample-Based Background Modelling� stationary camera

� no assumptions about the distribution required

� not sensitive to outliers (robust statistics)

� Dynamic Sample Set Representation� representation as a set of measurements (samples)� sample set S(ti ) evolves by replacing samples randomly

� u � n samples replaced between two time steps

� probability to have been added nt timesteps before:


(update rate u)� � � �� tnueutp �� 1ln � ��

� ��2ln

1ln2ln

2/1 ��

�u

t

Achim J. Lilienthal

� Interpretation of a Dynamic Sample Set! dynamic sample sets correspond to a time scale

� Deriving Foreground Probability Images� estimate background distribution

� calculate kernel estimator (Parzen window)

� background probability according to intensity density estimate

� foreground probability = 1 - background probability


� � Tcnt �� 2ln2/1

T

tu c

p �� pu : sample set update probability

�t : time interval since the last frame

ct : time constant

Achim J. Lilienthal

� Foreground Probability Images


t1/2 = 1.5 s, � = 20

t1/2 = 115 s, � = 20

Achim J. Lilienthal

IntroductionApplications – People Tracking


Achim J. Lilienthal

Introduction – Applications1

� Imaging in the Visible and Infrared Bands� person tracking in mobile robotics

Achim J. Lilienthal

Achim J. Lilienthal

Example: Person Tracking in Mobile Robotics1

� PeopleBoy (ActiveMedia PeopleBot)

� colour camera320 � 240 pixels15 Hz

� thermal cam:320 � 240 pixels15 Hz

Achim J. Lilienthal

� Thermal Camera� humans have a distinctive thermal profile

� not influenced by changing lighting conditions

� works in darkness

Thermo Tracer TH7302, NEC visible range: 24°C to 36°C

Person Tracking in Mobile Robotics1

Achim J. Lilienthal

� Thermal Camera� humans have a distinctive

thermal profile

� not influenced by changing lighting conditions

� works in darkness

� Colour Camera� improves accuracy

� helps to resolve occlusions� dynamical colour model


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� Person Tracking� no occlusions


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� Person Tracking� distinguish persons using an elliptic contour model


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� Person Tracking – Measurement Model

� elliptic contour model


! applicable if the person is far away

! applicable if side-view is visible

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� Person Tracking� no occlusions


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� Person Tracking� thermal and

colour information

� occlusions


Achim J. Lilienthal

� Person Tracking� stationary

webcam

� sample-basedbackground subtraction(motion heat)

� occlusions


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Digital Image Processing - Örebro University Image Processing ... Course Book Chapter 3 Part 2: Image Enhancement in the Spatial Domain. ... Image Subtraction tracking with a stationary