Transcript Chap2 Image enhancement

Chap2 Image enhancement
(Spatial domain)
Preprocessing
 Why we need image enhancement?
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Un-necessary noises
Defects caused by image acquisition
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Uneven illumination: non-uniform
Lens: blurring object or background
Motion : blurring
Distortion: geometric distortion caused by
lens
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registration
Chapter 2
Image Enhancement in the
Spatial Domain
2.1 Background
 Specific application—problem 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
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 of
an 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 power
s  cr 
function
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Produce images that are darker than intended
Is important if displaying an image accurately on a computer screen
Chapter 3
Image Enhancement in the
Spatial Domain
Chapter 3
Image Enhancement in the
Spatial Domain
Chapter 2
Image Enhancement in the
Spatial Domain
Chapter 2
Image Enhancement in the
Spatial Domain
Chapter 2
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Chapter 2
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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 areas
are 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
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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 interest
and a low value for all other gray levels : produce a binary
image
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Continue
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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
Chapter 2
Image Enhancement in the
Spatial Domain
Chapter 2
Image Enhancement in the
Spatial Domain
Chapter 2
Image Enhancement in the
Spatial Domain
Chapter 2
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Spatial Domain
2.3 Histogram processing
Histogram 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 and
the distribution of pixels is not too far uniform, with very few
vertical lines being much higher than the others
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A great deal of details and high dynamic range
2.3.1 Histogram equalization
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Histogram of S=T (r) 0 r1
 produce a level s for every pixel value in the original image,
the transformation satisfies the following conditions:
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(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
Chapter 2
Image Enhancement in the
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Chapter 2
Image Enhancement in the
Spatial Domain
3.4 Enhancement using arithmetic/logic operations
 Image subtraction —g(x,y)=f(x,y)-h(x,y)
 Masking
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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
Chapter 3
Image Enhancement in the
Spatial Domain
2.4.1 Image subtraction
 The difference between two images f(x,y) and h(x,y) is expressed
as g(x,y)=f(x,y)-h(x,y)
 Enhance the difference part of two images
 Contrast stretching transformation—useful 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 its
negative added to all the pixels in the difference image
 All the pixels in the image are scaled to [0,255] by
multiplying 255/Max
2.4.2 Image averaging
 g(x,y)=f(x,y)+(x,y) (assume every pair of coordinates (x,y) the
noise is uncorrelated and has zero average value)
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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 the
introduction of blurring
 Use integrating capabilities of CCD or similar sensors for noise
reduction by observing the same scene over long periods of
time
3.5 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 filter
coefficients R=
 In general, linear filtering of an image with a filter mask of size
MxN is given by g(x,y)
 Convolving a mask with an image by pixel-by-pixel basis
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2.6 Smoothing spatial filters
 Used for blurring and for noise reduction
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Blurring is used for removal of detail and bridging of small
gaps in lines or curves
2.6.1 Smoothing linear filters
 Averaging filter (low pass filter)
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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
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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 predefined interval
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 filter
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Arithmetic mean
 Harmonic mean
 Geometric mean
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Spatial Domain
3.7 Sharpening spatial filter
 Highlight fine detail or enhance detail
 Enhance detail that has been blurred
 Application ranging from electronic printing and
medical imaging to industrial inspection
 Can be accomplished by digital differentiation
3.7.1 Foundation
 Sharpening filter based on first- and second-order
derivatives
 Definition for first derivatives
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Must be zero in flat segment
Muse be nonzero at the onset of a gray level step or
ramp
Must be nonzero along ramps
Def. of first derivate:
f
 f ( x  1)  f ( x)
Produce “thick” edges
x
Has a strong response to gray-level step
 Definition for second derivatives: is better suited than the first-
derivative for image enhancement
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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:  f  f ( x  1)  f ( x  1)  2 f ( x)
 x
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
2
2
 Highlight the fundamental similarities and differences between
first- and second- order derivatives (Fig. 3.38)
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Image Enhancement in the
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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