Gonzalez, rafael,c.digitalimageprocessingusing matlab

Gonzalez, Rafael,C.
digital image processing
using MATLAB
chapter 3 :

Intensity transformations & spatial ﬁltering
1

By: H.Mostafavi
Urmia university of technology

Introduction
• Spatial domain : all the methods
are directly operate on the pixels
of an image.
• In this season we’ll going to focus on a
important category of spatial domain
process.
• *most of the examples are about image
enhancement.
Intensity transforms
3

A. Background
• The total form of processes that they are related to the
spatial domain is : g(x,y)=T[f(x,y)]
4

B.Intensity Transformation Functions
• The simplest form of the transformation T is when the
Neighborhood is of size 1x1 (a single pixel).
• In this case :
• Because the T function depends only on the intensity value at a
point, it’s frequently are written in simpliﬁed form as :
g at (x,y) intensity of f at that point
* And T, becomes an intensity or gray-level transformation function.
s = T( r ) The intensity of f
The intensety of g
5

B.1.imadjust Function
• Function imadjust is the basic IPT toolbox function for intensity transformations of
gray-scale images. It has the general syntax :
• As the Fig illustrates,
this function maps
the intensity values
in image f to new
value in g.
• The input image can be of class :
g = imadjust(f, [low_in high_in], [low_out high_out], gamma)
Uint8
Uint16
Int16
Single
Double
6

• All inputs to function imadjust, other than f and gamma, are
speciﬁed as values between 0 and 1, independently of the class of f.
Class
of
image
Uint8:
values x 255
Uint16:
values x 65535
Using
empty
matrix [ ]
[low_in high_in]
[low_out high_out]
Result in
Default range
[0 1]
7

• Parameter gamma shape of the curve.
Gamma < 1
Gamma = 1
Gamma >1
Brighter
Darker
Omitted from function
8

clc,clear
f = imread('Fig0304(a)(breast_digital_Xray).tif');
g1 = imadjust(f,[0 1],[1 0]);
g2 = imadjust(f,[0.5 0.75],[0 1]);
g3 = imadjust(f,[],[],2);
g4 = imadjust(f, stretchlim(f), [ ]);
g5 = imadjust(f, stretchlim(f), [1 0]);
subplot(2,3,1);imshow(f)
subplot(2,3,2);imshow(g1)
Negative image
Note:
The negative of an image can be
obtained also with
toolbox function imcomplement :
g = imcomplement(f)
Note:
Sometimes, it is of interest to be able to use function imadjust
“automatically,” without having to be concerned about the low and
high parameters discussed above. Function stretchlim is
useful in that regard, its basic syntax is :
low_high = stretchlim(f)
9

B.2. Logarithmic and Contrast-Stretching Transformation
• Logarithmic and contrast-stretching transformations are basic tools for dynamic range
manipulation.
• log transformation Compress dynamic range.
• To bring the resulting compressed values back to the full range:
g = c*log(1 + double(f))
The shape is similar to the gamma curve
For example:
Fourier spectrom:[0,106]
Loge(106) = 13.8
1 of the Principal uses:
For 8 bits: gs = im2uint8(mat2gray(g)); mat2gray:
Back to [0 1]
im2uint8:
Back to [0 255]
10

• The function in ﬁg 3.4(a) is called
a contrast-stretching
transformation function
because it expands
a narrow range of input
level into a wide range
of output levels
• The the function in 3.4(b) is called
a thresholding function
Is a simple tools used for image segmentation.
• The function in ﬁg 3.4(a) has the form:
• r : input image intensity
• s : output image intensity
• E : control the slope of the
function
• less than m = narrow &
dark
• more than m = narrow &
bright
11

• In MATLAB :
g = 1./(1 + (m./(double(f)+eps)).^E)
eps : avoid overﬂow
This transformation :
Maps output into [0 1]
Fig 3.4(a) E = 20
Figure 3.5(a) is a Fourier spectrum with values in the range
0 to 106, displayed on a linearly scaled, 8-bit display system.
Figure 3.5(b) shows the result obtained using the commands
g = im2uint8(mat2gray(log(1 + double(f))));
12

B.3.Some Utility M-Functions for Intensity Transformations
• Handling a Variable Number of Inputs and/or Outputs:
• To check the number of input arguments
n = nargin
• To check the number of output arguments
n = nargout
Ex : T = testhv(4,5)
{
nargin = 2
nargout = 1
Function : msg = nargchk(low, high, number)
Number < low : not
enough input parameter
Number > high : too many input
parameter
low < Number < high :
Empty matrix
13

• function G = testhv2(x, y, z)
error(nargchk(2, 3, nargin));
Typing
>> testhv2(6);
Not enough input arguments
• function [m, n] = testhv3(varargin)
• function [varargout] = testhv4(m, n, p)
• function [m, n] = testhv3(x, varargin)
14
Cell array
[m n] = testhv3(f,[0 0.5 1.5],A,’label’);

B.4 another M-function for intensity transformations
• In this section we develop a function that computes the following transformation
functions: negative, log, gamma and contrast stretching.
• Intrans function:
g = changeclass(newclass, f) Class of f new class
• Logical
• Uin8
• Uint16
• Int16
g = intrans(f, 'stretch', mean2(im2double(f)), 0.9);
Note:
mean2 : mean of f directly.
im2double : f to [0 1]
15

B.5 an M-function for Intensity Scale
• When working with digital images, computations that result in pixel values that span a
wide negative to positive range are common.when we want to use an 8-bit or 16-
bit format for saving or viewing an image(uint8, uint16), in which case it usually is
desirable to scale the image to the full, maximum range, [0, 255] or [0, 65535] .

• The syntax of function gscale is :
g = gscale(f, method, low, high)
full8 [0,255]
full16 [0,65535]
minmax [low high]:[0 1]
For example:
If input : f of class uint8 ‘minmax’=[0,0.5]
Output : g of class uint8 : [0,128]
16

C.Histogram Processing and Function Plotting
• Intensity transformation functions based on

information extracted from image intensity
histograms play a central role in image

processing, in areas such as enhancement,
compression, segmentation,
and description. The focus of this section is

on obtaining, plotting, and using histograms

for image enhancement.
17

C.1.Generating and Plotting Image Histograms
• The histogram of a digital image with L total possible
intensity levels in the range [0,G] is deﬁned as the
discrete function :
h(rk ) = nk
Is the kth intensity level in [0,G] Is the number of pixels in the image whose intensity level is rk
G values for :
Uint8 = 255
Uint16 = 65535
Double = 1
Note :
For Images of
class uint8, uint16
G = L-1
*To work with
normalized
histogram:
p(rk ) = h(rk ) / n
= nk / n
18

• The core function in the toolbox for dealing with image histogram is
imhist, with the basic syntax :
h = imhist(f, b)
Is the number of bins used in forming the histogram
Is the input imageIs the input image’s histogram
For example:
For b = 2.
The intensity scale :
[0 127] & [128 255]
h(1) = [0 127]
h(2) = [128 255]
The normalized histogram:
p = imhist(f, b)/numel(f)
Histogram using bar graph:
bar(horz, z, width)
Is a row vector containing the points to be plotted
Is a vector of same dimension as z
Contains the increments of horizontal
Scale.if it’s omitted the horizontal axis is
divided in units from 0 to length(z).
A number between 0 and 1, when it’s 0
The bars are vertical lines & when it’s 1
The bars touch
19

clc,clear
f = imread('pout.tif');
h = imhist(f,25);
hi = h(1:10:256);
horz = 1:10:256;
bar(horz,h1)
axis([0 255 0 15000])
set(gca,'xtick',0:50:250)
set(gca,'ytick',0:2000:15000)
xlabel('text string', 'fontsize', size)
ylabel('text string', 'fontsize', size)
axis([horzmin horzmax vertmin vertmax])
20

• text(xloc, yloc,’text string’,’fontsize’, size)
• title(‘titlestring’)
• stem(horz, v, ‘color_linestyle_marker’,’fill’)
• plot(horz,v,’color_linestyle_marker’)
• Hold on
21

C.2.Histogram Equalization
• Assume for a moment that intensity levels are continuous quantities normalized to the range [0, 1],
and let pr (r) denote the probability density function (PDF) of the intensity levels in a given image.

• The probability density function(PDF) of output level :
***The net result of this intensity-level equalization process is an image with increased dynamic range,

which will tend to have higher contrast.
22
It’s just a CDF

• When dealing with discrete quantities we work with histograms and call the preceding
technique histogram equalization :
• Histogram equalization is implemented in the toolbox by function histeq, which has
the syntax:
g = histeq(f, nlev)
Is the number of intensity levels
nlev < L : histeq approximate
ﬂat
Default nlev = 64
23

• imshow(f); % Fig. 3.8(a).
• figure, imhist(f) % Fig. 3.8(b).
• ylim('auto')
• g = histeq(f, 256);
• figure, imshow(g) % Fig. 3.8(c).
• figure, imhist(g) % Fig. 3.8(d).
• ylim('auto')
24

• Plotting CDF:
clc,clear
f = imread('Fig0320(4)(bottom_left).tif');
hnorm = imhist(f)./numel(f); % Normalized
histogram.
cdf = cumsum(hnorm); % CDF.
x = linspace(0, 1, 256);
plot(x, cdf)
axis([0 1 0 1]);
set(gca, 'xtick', 0:.2:1)
set(gca, 'ytick', 0:.2:1)
xlabel('Input intensity values', 'fontsize', 9)
ylabel('Output intensity values', 'fontsize', 9)
25

C.3.Histogram matching
• The toolbox implements histogram matching using the following syntax in histeq:
g = histeq(f, hspec)
clc,clear
f = imread(‘Fig0323(a)
(mars_moon_phobos).tif');
g = histeq(f,256);
subplot(2,2,1);imshow(f)
subplot(2,2,3);imshow(g)
subplot(2,2,2);imhist(f)
subplot(2,2,4);imhist(g)
26

• Using of two below functions for enhancing the
histogram:
• g = histeq(f,p)
• p=twomodogauss.
• p=manualhist.
27

D.Spatial Filtering
• As have been mentioned before in earlier lectures, some
neighborhood operations work with the values of the image
pixels in the neighborhood and the corresponding values of a
subimage that has the same dimensions as the neighborhood.

• The sub-image is called a filter, mask, kernel, template, or
window. The values in a filter sub-image are referred to as
coefficients rather than pixels.
28

• These neighborhood operations consists of:
A. Deﬁning a center point, (x,y)

B. Performing an operation that involves only the pixels in a predeﬁned
neighborhood about that center point.

C. Letting the result of that operation be the “response” of the process at
that point.

D. Repeating the process for every point in the image.
29

D.1.Two spatial filtering methods
• linear spatial filtering : If the computations performed on the
pixels of the neighborhoods are linear.

• Nonlinear spatial filtering : If the computations performed on the
pixels of the neighborhoods are nonlinear.
30

• The mechanism of linear spatial ﬁltering
31

D.2.Correlation Vs Convolution(1D)
32

D.3.Correlation Vs Convolution(2D)
33

D.4.Implementation on MATLAB
• In image processing toolbox ( IPT ) linear spatial filtering
known by imfilter, which the syntax is:
• Common mode for calling imfilter:
g = imfilter(f,w,filtering_mode,boundary_options,size_options) f = input image
w = mask
g = outputs
filtering_mode = kind of filter
boundary_options = kind of
expanding
size_options = 1-full
2-same
g = imfilter(f,w,’replicate’)
34

• Two ways for ﬁlters that, they aren’t symmetric and
has not 180 degree rotation :
A. Calling by below code:
B. Pre-processing by below code for 180 degree rotation:
g=imfilter(f,w,’conv’,’replicate’)
Rot90(w,z)
35

clc,clear
f = imread('8 copy.jpg');
w = ones(31);
gd = imfilter(f,w);
gr = imfilter(f,w,'replicate');
gs = imfilter(f,w,'symmetric');
gc = imfilter(f,w,'circular');
f8 = im2uint8(f);
g8r = imfilter(f8,w,'replicate');
subplot(2,3,1);imshow(f,[])
subplot(2,3,2);imshow(gd,[])
subplot(2,3,3);imshow(gr,[])
subplot(2,3,4);imshow(gs,[])
subplot(2,3,5);imshow(gc,[])
subplot(2,3,6);imshow(g8r,[])
36

D.5.nonlinear spatial filtering
• There is two kind of nonlinear filtering :

• Colfilt needs more space than nlfilters but the speed of
processing in colfilts is higher than the nlfilters, they
preference against the nlfilters.
1. Colfilt
2. Nlfilter
37

• The syntax is:
• In the nonlinear filtering we must first added the boundary values to the image.So we using
padarray function.
g = colfilt(f,[m n],’sliding’,@fun, parameters)
[m n] = filtering area
Sliding = filtering is pixel by pixel
@fun = reference to a function
Parameters = desired parameters of @fun
fp = padarray(f,[r c],method,direction)
38

D.6.Standard Spatial Filters of IPT
• Linear Spatial Filters:
w = fspecial(‘type’,parameters)
40

fspecial(‘average’,[r c])
A triangle mean filter of sixe
r x c
fspecial(‘disk’,r)
A circular mean filter with
radius of r (defult r = 5)
fspecial(‘gaussian’,[r c],sig)
ABS = r x c ,
standard deviation = sig
fspecial(‘laplacian’,alpha)
Alpha=[0 1] default=0.5
fspecial(‘log’,[r c],sig)
ABS = r x c , “gaussian Laplace”
standard deviation = sig
fspecial(‘motion’,len ,theta)
Its combining with image,
estimating moving of the Cam Len
pixel with horz angle theta
fspecial(‘prewitt’)
3x3 mask, estimate vertical
gradient
fspecial(‘sobel’)
estimate vertical sobel gradient
fspecial(‘unsharp’,alpha)
3x3 mask, alpha for controlling
of shape, alpha > 0 & alpha <= 1
Default = 0.2
41

• Nonlinear spatial ﬁltering:
g = ordfilt2(f,order,domain)
EX:g = ordfilt2(f,1,ones(m,n)) >>Min ﬁlter(order1)
g=ordfilt2(f,median(1:m*n),ones(m,n));
g=medfilt2(f,[m n],padopt);
44

References
• Gonzalez, Rafael.(2009).digital image processing using
MATLAB.

Gonzalez, rafael,c.digitalimageprocessingusing matlab

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