Chap2 Image enhancement (Spatial domain)

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

Chapter 2Image Enhancement in the

Spatial Domain

Chapter 2Image Enhancement in the

Spatial Domain2.1 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 image2.2.2 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

function Produce images that are darker than intended Is important if displaying an image accurately on a computer screen

crs

Chapter 3Image Enhancement in the

Spatial Domain

Chapter 3Image Enhancement in the

Spatial Domain

Chapter 3Image Enhancement in the

Spatial Domain

Chapter 3Image Enhancement in the

Spatial Domain

Chapter 2Image Enhancement in the

Spatial Domain

Chapter 2Image Enhancement in the

Spatial Domain

Chapter 2Image Enhancement in the

Spatial Domain

Chapter 2Image Enhancement in the

Spatial Domain

Chapter 2Image Enhancement in the

Spatial Domain

Chapter 2Image Enhancement in the

Spatial Domain

Chapter 2Image Enhancement in the

Spatial Domain

Chapter 2Image Enhancement in the

Spatial Domain

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

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

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

Chapter 2Image Enhancement in the

Spatial Domain

Chapter 2Image Enhancement in the

Spatial Domain

Chapter 2Image Enhancement in the

Spatial Domain

Chapter 2Image Enhancement in the

Spatial Domain

Chapter 2Image Enhancement in the

Spatial Domain

Chapter 2Image Enhancement in the

Spatial Domain

Chapter 2Image Enhancement in the

Spatial Domain

Chapter 2Image Enhancement in the

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

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

Chapter 2Image Enhancement in the

Spatial Domain

Chapter 2Image Enhancement in the

Spatial Domain

Chapter 2Image Enhancement in the

Spatial Domain

Chapter 2Image Enhancement in the

Spatial Domain

3.4 Enhancement using arithmetic/logic operations

Image subtraction —g(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

Chapter 3Image Enhancement in the

Spatial Domain

Chapter 3Image 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 25

5 (-255 to 255) (1) Add 255 to every pixel and divide by 2: fast and simple to im

plement, 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 noi

se is uncorrelated and has zero average value)

Chapter 3Image Enhancement in the

Spatial Domain

Chapter 3Image Enhancement in the

Spatial Domain

Chapter 3Image Enhancement in the

Spatial Domain

Chapter 3Image Enhancement in the

Spatial Domain

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

Chapter 3Image Enhancement in the

Spatial Domain

Chapter 3Image Enhancement in the

Spatial Domain

Chapter 3Image Enhancement in the

Spatial Domain

Chapter 3Image Enhancement in the

Spatial Domain

Chapter 3Image Enhancement in the

Spatial Domain

Chapter 3Image Enhancement in the

Spatial Domain

Chapter 3Image Enhancement in the

Spatial Domain

Chapter 3Image Enhancement in the

Spatial Domain

Used for blurring and for noise reduction 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)

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 spatial filters

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

Arithmetic mean Harmonic mean Geometric mean

Chapter 3Image Enhancement in the

Spatial Domain

Chapter 3Image Enhancement in the

Spatial Domain

Chapter 3Image Enhancement in the

Spatial Domain

Chapter 3Image Enhancement in the

Spatial Domain

Chapter 3Image Enhancement in the

Spatial Domain

Chapter 3Image Enhancement in the

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 differentiation3.7.1 Foundation Sharpening filter based on first- and second-order

derivatives Definition for first derivatives

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: Produce “thick” edges Has a strong response to gray-level step

( 1) ( )f

f x f xx

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 ( )

ff x f x f x

x

Chapter 3Image Enhancement in the

Spatial Domain

Chapter 3Image Enhancement in the

Spatial Domain

Chapter 3Image Enhancement in the

Spatial Domain

Chapter 3Image Enhancement in the

Spatial Domain

Chapter 3Image Enhancement in the

Spatial Domain

Chapter 3Image Enhancement in the

Spatial Domain

Chapter 3Image Enhancement in the

Spatial Domain

Chapter 3Image Enhancement in the

Spatial Domain

Chapter 3Image Enhancement in the

Spatial Domain

Chapter 3Image Enhancement in the

Spatial Domain

Approximate the magnitude of the gradient by using absolute values

Lost isotropic feature property Vertical and horizontal edges preserve the isotropic properti

es 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