Chap2 Image Enhancement

7/29/2019 Chap2 Image Enhancement

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Chap2 Image enhancement

(Spatial domain)


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Preprocessing

Why we need image enhancement?

Un-necessary noises

Defects caused by image acquisition

Uneven illumination: non-uniform

Lens: blurring object or background

Motion : blurring

Distortion: geometric distortion caused by

lens

registration


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Chapter 2Image Enhancement in the

Spatial Domain2.1 Background Specific applicationproblem oriented

Trial and error is necessary

Spatial domain will be denoted by the expression g(x,y)=T[f(x,y)]

The simplest form of T: s=T(r)

Contrast stretching: (Fig. 3.2 (a))

Thresholding function: binary image (Fig. 3.2)

Masks (filters, kernels, templates, windows)

Enhancement : mask processing or filtering

2.2 Some gray level transformations

Three basic types of functions used for image enhancement

Linear logarithmic

Power-law


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2.2.1 Image negatives

Is obtained by using the negative transformation s=L-1-r

Produces the equivalent of a photographic negative

Suited for enhancing white or gray detail embedded in dark regions ofan image

2.2.2 Log transformations

The general form of the log transformation : s=clog(1+r)

Expand the values of dark pixels while compressing the high-level

values Compress the dynamic range of images with large variations

2.2.3 Power-law transformation

The basic form:

Gamma correction

CRT device have an intensity-to-voltage response that is a powerfunction

Produce images that are darker than intended

Is important if displaying an image accurately on a computer screen

crs


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Spatial Domain


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Spatial Domain


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Spatial Domain


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Spatial Domain


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Spatial Domain


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Spatial Domain


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Low r: wash-out in the background (Fig. 3.8 r=0.3)

High r: enhance a wash-out appearance (Fig. 3.9 r=0.5 areasare too dark)

2.2.4 Piecewise-linear transformation functions Advantage: the form of piecewise functions can be arbitrary

complex over the previous functions

Disadvantage: require considerably more user input

Contrast stretching One of the simplest piecewise function

Increase the dynamic range of the gray levels in the image A typical transformation: control the shape of the

transformation

r1=r2 s1=0 and s2=L-1 Gray level slicing

Highlight a specific range of gray levels

Display a high value for all gray levels in the range of interestand a low value for all other gray levels : produce a binaryimage


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Continue

Brighten the desired range of gray levels, but

preserves the background and gray level

tonalities (Fig. 3.11)

The higher order bits (especially the top four)contain the majority of the visually significant

data


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Spatial Domain


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Spatial Domain


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Spatial Domain


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Spatial Domain


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2.3 Histogram processingHistogram of a digital image with the gray levels in the range[0, L-1]

Low contrast: a narrow histogram, a dull, wash-out gray look

High contrast : cover a broader range of the gray scale andthe distribution of pixels is not too far uniform, with very fewvertical lines being much higher than the others

A great deal of details and high dynamic range

2.3.1 Histogram equalization Histogram of S=T (r) 0 r1

produce a level s for every pixel value in the original image,the transformation satisfies the following conditions:(1) T(r) is single-valued and monotonically increasing in the interval

0 r 1; and

(2) 0 T ( r ) 1 for 0 r 1 r=T-1(s) 0 s 1


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Spatial Domain


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Spatial Domain


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3.4 Enhancement using arithmetic/logic operations

Image subtractiong(x,y)=f(x,y)-h(x,y) Masking

is referred to as ROI (region of interest) processing

Isolate an area for processing

Arithmetic operations

Addition:

Subtraction:

Multiplication: used to implement gray-level rather than binary

Division:

Logic operations And: used for masking (Fig. 3.27)

Or:used for masking

Not operation: negative transformation

Also are used in conjunction with morphological operations


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Spatial Domain


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2.4.1 Image subtraction

The difference between two images f(x,y) and h(x,y) is expressedas g(x,y)=f(x,y)-h(x,y)

Enhance the difference part of two images Contrast stretching transformationuseful for evaluating the

effect of setting to zero the lower-order planes (Fig. 3.28(d))

Mask mode radiography (Fig 3.29)

Sort of scaling : solve image values outside form the range 0 to

255 (-255 to 255) (1) Add 255 to every pixel and divide by 2: fast and simple to

implement, but the full rang of the display may not be used

(2) more accuracy and full coverage of the 8-it range

The values of the minimum difference is obtained and itsnegative added to all the pixels in the difference image

All the pixels in the image are scaled to [0,255] bymultiplying 255/Max

2.4.2 Image averaging

g(x,y)=f(x,y)+(x,y) (assume every pair of coordinates (x,y) thenoise is uncorrelated and has zero average value)


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Spatial Domain


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Reduce the noise content by adding a set of noise images {gi(x,y)}

An image is formed by averaging K different noisy images

As k increases, the variability of the pixel values at each

location (x,y) decreases

The image gi(x,y) must be registered in order to avoid theintroduction of blurring

Use integrating capabilities of CCD or similar sensors for noisereduction by observing the same scene over long periods of

time3.5 Basics of spatial filtering

Sub-image: (filter, mask, kernel, template or window)

Frequency domain:

Spatial domain

Linear spatial filtering: is give by a sum of products of the filtercoefficients R=

In general, linear filtering of an image with a filter mask of sizeMxN is given by g(x,y)

Convolving a mask with an image by pixel-by-pixel basis


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Spatial Domain


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Spatial Domain


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Spatial Domain


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Spatial Domain


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Used for blurring and for noise reduction

Blurring is used for removal of detail and bridging of smallgaps in lines or curves

2.6.1 Smoothing linear filters

Averaging filter (low pass filter)

Replace the value of every pixel by the average of the gray

levels in the neighborhood by the filter mask

Reduce sharp transition (such as random noise)

Blur edges

The average of the gray levels in the 3x3 neighborhoods

Averaging with limited data validity only to pixels in the original image in a pre-defined interval of

invalid data

Only if the computed brightness change of a pixel is in some pre-

defined interval

2.6 Smoothing spatialfilters


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Averaging according to inverse gradient

=Averaging using a rotation mask

2.6.2 Order Statistics filters (rank filters) Nonlinear spatial filter based on ordering (ranking)

Median filter

Remove impulse noises (salt and pepper noises)

Represent 50 percent of a ranked set Large clusters are affected considerably less

Min filter

Max filter--useful in finding the brightest points

Non-linear mean filterArithmetic mean

Harmonic mean

Geometric mean


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Spatial Domain


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3.7 Sharpening spatial filter

Highlight fine detail or enhance detail

Enhance detail that has been blurred

Application ranging from electronic printing andmedical imaging to industrial inspection

Can be accomplished by digital differentiation

3.7.1 Foundation

Sharpening filter based on first- and second-orderderivatives

Definition for first derivatives Must be zero in flat segment

Muse be nonzero at the onset of a gray level step orramp

Must be nonzero along ramps

Def. of first derivate:

Produce thick edges

Has a strong response to gray-level step

( 1) ( )f

f x f xx


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Definition for second derivatives: is better suited than the first-

derivative for image enhancement

Must be zero in flat areas Muse be nonzero at the onset and end of a gray level

step or ramp

Must be zero along ramps of constant slope

Def. Of a second order derivate: Produces finer edges

Enhance fine detail much more than a first order

derivate for example: a thin line

The stronger response at an isolated point

Has a transition form positive back to negative

Produces a double response to a gray-level step

Highlight the fundamental similarities and differences between

first- and second- order derivatives (Fig. 3.38)

2

2 ( 1) ( 1) 2 ( )

f

f x f x f xx


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Approximate the magnitude of the gradient by using

absolute values

Lost isotropic feature property

Vertical and horizontal edges preserve the isotropic

properties only for multiples of 90

Mask of odd sizes

Robert operator

Robert Ross-gradient operators

An approximation using absolute values (3.7-18)

Sobel operator

Use a weight value of 2 to achieve some smoothing by

giving more importance to the center point Constant or slowly varying shades are eliminated

Prewitt operator

Chap2 Image Enhancement

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