Intensity Transformation and Spatial filtering

Dr.S.SHAJUN NISHA, MCA.,M.Phil.,M.Tech.,MBA.,Ph.D
Assistant Professor & Head
PG & Research Dept. of Computer Science
Sadakathullah Appa College
shajunnisha_s@yahoo.com
+91 99420 96220
INTENSITY TRANSFORMATION
& SPATIAL FILTERING

Introduction
 Spatial domain
Refers to the image plane itself
Image processing methods are based and directly
applied to image pixels
 Two principle categories of spatial processing:
Intensity transformation
Spatial filtering

=Input image
= Output image
= Operator defined
over a neighbourhood
Spatial domain processes are denoted by
• Process of small window operation are called spatial filtering

Intensity Transformation Functions
 The simplest form of the transformation T is applied on 1x1 (a
single pixel)
 The value of g at (x,y) depends only on the intensity of f at that
point, and T becomes an intensity or gray-level transformation
function.
 Simplified form as
s = T(r)
 where r denotes the intensity of f and s the intensity of g, both
at any corresponding point (x,y) in the images.

Function imadjust
 Function imadjust is the basic IPT tool for intensity
transformations of grayscale images.
Syntax
 g = imadjust(f, [low_in high_in], [low_out high_out],
gamma)

Functions imadjust and stretchlim
Command
 g1 = imadjust(f, [0 1], [1 0]);
Input Output
 g = imcomplement(f) can also be used to obtain the above
output

g2 = imadjust(f, [0.5 0.75], [0 1]);
Result of expanding the intensity range [0.5, 0.75].
g3 = imadjust(f, [ ], [ ], 2);

f=imread('cameraman.tif');
figure,imshow(f);
g1 = imadjust(f, [0 1], [1 0]);
figure,imshow(g1);
g2 = imadjust(f, [0 1], [1 0], 0.5);
figure,imshow(g2);
g3 = imadjust(f, [0 1], [1 0], 1);
figure,imshow(g3);
g4 = imadjust(f, [0 1], [1 0], 2);
figure,imshow(g4);
g5 = imadjust(f, [0.5 0.75], [0 1]);
figure,imshow(g5);
g6 = imadjust(f, [0.5 0.75], [0 1], 0.5);
figure,imshow(g6);
imhist(f);

Logarithmic and Contrast-Stretching Transformations
 Logarithmic and contrast-stretching transformations are basic tools for
dynamic range manipulation.
 Logarithm transformations are implemented using the expression
g = c*log(1 + double(f))
 where c is a constant.
 The shape of this transformation is similar to the gamma curve with the
low values set at 0 and the high values set to 1 on both scales. Note,
however, that the shape of the gamma curve is variable,
 whereas the shape of the log function is fixed.

Intensity Transformation and Spatial filtering

 Contrast-Stretching has the form
 where r represents the intensities of the input image, s the
corresponding intensity values in the output image, and E
controls the slope of the function.
 This equation is implemented in MATLAB for an entire image
as
g = 1./(1 + (m./f).^E)

Example using Log transformation to reduce dynamic range
g = im2uint8(mat2gray(log(1 + double(f))));
imshow(g)

HISTOGRAM PROCESSING & FUNCTION PLOTTING
Intensity transformation functions based on
information extracted from image intensity histograms
play a basic role in image processing, in areas such as
enhancement, compression, segmentation, and
description.
It includes histogram, histogram equalization,
histogram matching, contrast limited adaptive
histogram equalization,
 The focus of this section is on obtaining, plotting, and
using histograms for image enhancement.

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
 where is the k th intensity level in the interval [0, G] and
is the number of pixels in the image whose intensity level is
 it is useful to work with normalized histograms, obtained
simply by dividing all elements of by the total number of
pixels in the image, which we denote by n:

 The core function in the toolbox for dealing with image histograms
is imhist, which has the following basic syntax:
h = imhist(f, b)
 the normalized histogram simply by using the expression
p = imhist(f, b)/numel(f)
 numel(f) gives the number of elements in array f (i.e., the number
of pixels in the image), b is the number of bins used in forming the
histogram (if b is not included in the argument, b = 256 is used by
default). A bin is simply a subdivision of the intensity scale.
 Histograms often are plotted using bar graphs. For this purpose we
can use the function
 bar(horz, v, width)
 imhist(f)

• A stem graph is similar to a bar graph.
•The syntax is
stem(horz, v, 'color_linestyle_marker', 'fill')
where v is row vector containing the points to be plotted, and
horz is as described for bar.

>> f=imread('cameraman.tif');
>>h = imhist(f);
>> h1 = h(1:10:256);
>> horz = 1:10:256;
>> stem(horz, h1, 'fill')
>> axis([0 255 0 15000])
>> set(gca, 'xtick', [0:50:255])
>> set(gca, 'ytick', [0:2000:15000])

Histogram Equalization
• Intensity levels are continuous quantities normalized to the range
[0, 1],
•let denote the probability density function (PDF) of the
intensity levels in a given image,
• Suppose that we perform the following transformation on the
input levels to obtain output (processed) intensity levels, s,
where is a dummy variable of integration ,then PDF of intensity levels in
an output image will be

• When dealing with discrete quantities we work with histograms
and call the preceding technique histogram equalization
• Let denote the histogram associated with
the intensity levels of a given image, and recall that the values in
a normalized histogram are approximations to the probability of
occurrence of each intensity level in the image. For discrete
quantities we work with summations, and the equalization
transformation becomes
For k=1,2,…..L where is the intensity value in the output
(processed) image corresponding to value in the input image.

Histogram Equalization
 Histogram equalization is implemented in the toolbox by
function histeq,which has the syntax
 g = histeq(f, nlev)
 where f is the input image and nlev is the number of intensity
levels specified for the output image.
>> imshow(f)
>> figure, imhist(f)
>> g = histeq(f, 256);
>> figure, imshow(g)
>> figure, imhist(g)

Histogram Matching (Specification)
The toolbox implements histogram matching using the following
syntax in
histeq:
g = histeq(f, hspec)
>> f1 = histeq(f, 256);

Spatial Filtering
Neighborhood processing consists of
(1) defining a center point,
(2) performing an operation that involves only the pixels in a
predefined neighborhood about that center point;
(3) letting the result of that operation be the “response” of the
process at that point; and
(4) repeating the process for every point in the image.
The process of moving the center point creates new
neighborhoods, one for each pixel in the input image

• The two principal terms used to identify this operation are
neighborhood processing and spatial filtering, with the second
term being more prevalent.
• If the computations performed on the pixels of the
neighborhoods are linear, the operation is called linear spatial
filtering (the term spatial convolution also used); otherwise it
is called nonlinear spatial filtering.

The toolbox implements linear spatial filtering using function
imfilter,
which has the following syntax:
g = imfilter(f, w, filtering_mode, boundary_options,
size_options)
The most common syntax for imfilter is
g = imfilter(f, w, 'replicate')
f = imread('peppers.png');
figure,imshow(f)
w=[256 256];
g = imfilter(f, w, 'symmetric')
figure, imshow(g)

Standard Linear Spatial Filters:
Syntax:
W=fspecial(‘type’, parameters)
Eg:
originalRGB = imread('peppers.png’);
imshow(originalRGB)
h = fspecial('motion', 50, 45);
filteredRGB = imfilter(originalRGB, h);
figure, imshow(filteredRGB)

Non liner spatial Filtering
Syntax
fp = padarray(f, [r c], method, direction)
Eg 1:
f=imread('peppers.png');
fp=padarray(f, [312 312], 'replicate', 'post')
figure,imshow(f);
figure,imshow(fp);
Eg 2:
>> fp = padarray(f, [3 2], 'replicate', 'post')

Standard Non Linear Spatial Filters:
The syntax of function ordfilt2 is
g = ordfilt2(f, order, domain)
to implement a min filter (order 1) of size mxn we use the syntax
g = ordfilt2(f, 1, ones(m, n))
Eg:
>> fn = imnoise(f, 'salt & pepper', 0.2);
>> gm = medfilt2(fn);
>> gms = medfilt2(fn, 'symmetric');

Intensity Transformation and Spatial filtering

More Related Content

What's hot (20)

Similar to Intensity Transformation and Spatial filtering (20)

More from Shajun Nisha (18)

Recently uploaded (20)

Intensity Transformation and Spatial filtering