Image Enhancement The objective is to process an image to improve - - PDF document

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IIP 1

Image Enhancement

• The objective is to process an image to

improve its suitability for a specific application; thus, application-oriented

• Two basic methods:

spatial-domain (manipulating image pixels) frequency-domain (modifying the Fourier transform) combination of the two

• No general theory of image enhancement

(subjective/visual judgment)

IIP 2

Image Enhancement – Agenda

• Gray level histogram – definition,

properties & use

• Point operations (contrast enhancement)
• Image enhancement in the spatial domain

gray level transformations histogram equalization

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IIP 3

The Gray-Level Histogram

• Distribution of the gray levels in the image
• Thus, a function summarizing an image content
• Simple to compute
• For specific image types may specify precisely the image

(e.g., bi-modal, narrow uni-modal)enhancement

• Provides global description, i.e., spatial information is

discarded (for good and for bad) (consider: info. about edges, translation etc., “random image(s)” having similar histogram to any given image)

IIP 4

Gray-Level Histogram (1)

Castleman, 1996

• histogram shape

appearance of image (location/width/shape

• f peak(s) )
• bimodal; unimodal
• evaluation of

enhancement: equalization sliding (brightness) stretching (contrast)

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IIP 5

Gray-Level Histogram (2)

• Too dark image

Gonzalez & Woods, 2002

IIP 6

Gray-Level Histogram (3)

• Too bright image

Gonzalez & Woods, 2002

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IIP 7

Gray-Level Histogram (4)

• Low-contrast image

Gonzalez & Woods, 2002

IIP 8

Gray-Level Histogram (5)

• High-contrast image

Gonzalez & Woods, 2002

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IIP 9

Image Histogram & Area (1)

• D(x,y) is a continuous image with intensity (gray

level) increasing smoothly towards the center

• Equal gray-level contours define regions of gray

level greater than or equal to Di

• The area function, A(D), is the area enclosed by

contour lines of gray level D

• Define the histogram as (the negative of the area function),
• For images (discrete functions) we fix so

) ( ) ( ) ( ) (

lim

D A dD d D D D A D A D H

D

− = ∆ ∆ + − =

→ ∆ A(D) decreases with increasing D minus sign

( ) ( ) ( 1) H D A D A D = − +

1 D ∆ =

IIP 10

Image Histogram & Area (2)

Castleman, 1996

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IIP 11

Image Histogram & Area (3)

• By integration, we get the area function
• The area function of a digital image is the

number of pixels having gray level greater than or equal to D for any gray level D

' ) ' ( ) (

∫

∞

=

D

dD D H D A

IIP 12

Image Histogram & Area (4)

• Assuming non-negative gray levels,
• r in the discrete case
• Assuming an object (on a contrasting

background) having a boundary defined by contour line with gray level Do

( ') ' area of image H D dD

∞

=

∫

255

( ) ,

• # of rows,
• # of columns

D

H D NR NC NR NC

=

= ×

∑

( ') ' area of object

O

D

H D dD

∞

=

∫

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IIP 13

Image Histogram & Area (5)

• Normalizing the gray level histogram by the

image area produces the probability density function (pdf) of the image

• Normalizing the area function by the image

area produces the cumulative distribution function (cdf) of the image

IIP 14

Histogram Uses

• 1. Monitoring the digitization process as an image should

utilize all or most of the gray levels. Digitization is irreversible process that may end up in a too narrow band

• r clipping to 0/255
• 2. Boundary threshold selection ( image segmentation)
• 3. Integrated optical density (IOD) ( “mass” of an image)

where k is a gray level and H(k) the histogram evaluated at gray level k. Thus, the IOD is a gray level weighted summation of the histogram

∑ ∑∑ ∫∫

= = =

= = =

255 1 1 0 0

) ( ) , ( ) , (

k NR i NC j a b

k kH j i D dxdy y x D IOD

for a digital image

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IIP 15

Histogram Uses – Boundary Threshold Selection

• A bimodal histogram
• bject

boundaries background

• bject

different T’s

• different

segmentations (object area,

• verlapping,…)

IIP 16

Image Enhancement in the Spatial Domain – Background

• Procedures (operators) operating on pixels
• Three basic groups:
• 1. Histogram processing (single pixel-based)
• 2. Enhancement using arithmetic/logic operations

(pixel-by-pixel) (e.g., subtraction, AND,…)

• 3. Spatial filtering (neighborhood-based) (e.g.,

smoothing, sharpening, combinations)

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IIP 17

Histogram Processing (Point Operations/Contrast Stretching/Gray- Scale Transformations)

• Modify the way in which the image data fills the available

range of gray levels display (may be part of a digitizer)

• Goal: produce histogram of a desired form
• Transforms input image to output image so each output

pixel’s gray level depends only upon the gray level of the corresponding input pixel (compared to local operations)

• May be expressed as or
• Overcome digitizer limitations & improve image display
• Divided into linear and nonlinear operators

[ ]

) , ( ) , ( y x A f y x B = ( )

B A

D f D =

IIP 18

Linear Point Operations (1)

• The gray scale transformation is

where DB & DA are gray levels of the output & input images, respectively

• a=1, b=0 identity operation

a>1 or a<1 contrast is increased or decreased a=1, b nonzero shift gray level up or down a<0 complementation (light dark & dark light)

b aD D f D

A A B

+ = = ) (

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IIP 19

Linear Point Operations (2)

IIP 20

Nonlinear Point Operations

• Emphasize midrange gray levels

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IIP 21

Image Enhancement in the Spatial Domain – Masks & Transformations

contrast stretching (darkening the darks (below m) & brightening the brights (above m)) in the limit, contrast stretching is thresholding producing a binary image neighborhood (mask) about a point (1X1 for now) (a) (b) (c) Note: change of notation

IIP 22

Basic Gray Level Transformations (1)

1 s L r = − − log(1 ), is cont. & s c r c r = + ≥ , & 0 (usually 1) s cr c c

γ

γ = > =

• negative: emphasizing white on black
• log: expansion/compression
• f dynamic range; too

dark/bright image

• power-low:

family of functions for each c “gamma correction”