The document discusses image smoothing and sharpening techniques in digital image processing. It begins by defining what a digital image is and the goals of digital image processing. Then it discusses various applications of digital image processing like image enhancement, medical visualization, and human-computer interfaces. Key techniques covered include image smoothing using spatial filters to average pixel values in a neighborhood and image sharpening using spatial filters based on spatial differentiation to highlight edges. Examples of the Hubble space telescope and facial recognition are also mentioned.
WEBINAR ON FUNDAMENTALS OF DIGITAL IMAGE PROCESSING DURING COVID LOCK DOWN by by K.Vijay Anand , Associate Professor, Department of Electronics and Instrumentation Engineering , R.M.K Engineering College, Tamil Nadu , India
WEBINAR ON FUNDAMENTALS OF DIGITAL IMAGE PROCESSING DURING COVID LOCK DOWN by by K.Vijay Anand , Associate Professor, Department of Electronics and Instrumentation Engineering , R.M.K Engineering College, Tamil Nadu , India
Image enhancement is the process of adjusting digital images so that the results are more suitable for display or further image analysis. For example, you can remove noise, sharpen, or brighten an image, making it easier to identify key features.
Here are some useful examples and methods of image enhancement:
Filtering with morphological operators, Histogram equalization, Noise removal using a Wiener filter, Linear contrast adjustment, Median filtering, Unsharp mask filtering, Contrast-limited adaptive histogram equalization (CLAHE). Decorrelation stretch
At the end of this lesson, you should be able to;
describe spatial resolution
describe intensity resolution
identify the effect of aliasing
describe image interpolation
describe relationships among the pixels
This slides about brief Introduction to Image Restoration Techniques. How to estimate the degradation function, noise models and its probability density functions.
Image Restoration And Reconstruction
Mean Filters
Order-Statistic Filters
Spatial Filtering: Mean Filters
Adaptive Filters
Adaptive Mean Filters
Adaptive Median Filters
This is the basic introductory presentation for beginners. It gives you the idea about what is image processing means. The presentation consists of introduction to digital image processing, image enhancement, image filtering, finding an image edge, image analysis, tools for image processing and finally some application of digital image processing.
Introduction to digital image processing, image processing, digital image, analog image, formation of digital image, level of digital image processing, components of a digital image processing system, advantages of digital image processing, limitations of digital image processing, fields of digital image processing, ultrasound imaging, x-ray imaging, SEM, PET, TEM
Image enhancement is the process of adjusting digital images so that the results are more suitable for display or further image analysis. For example, you can remove noise, sharpen, or brighten an image, making it easier to identify key features.
Here are some useful examples and methods of image enhancement:
Filtering with morphological operators, Histogram equalization, Noise removal using a Wiener filter, Linear contrast adjustment, Median filtering, Unsharp mask filtering, Contrast-limited adaptive histogram equalization (CLAHE). Decorrelation stretch
At the end of this lesson, you should be able to;
describe spatial resolution
describe intensity resolution
identify the effect of aliasing
describe image interpolation
describe relationships among the pixels
This slides about brief Introduction to Image Restoration Techniques. How to estimate the degradation function, noise models and its probability density functions.
Image Restoration And Reconstruction
Mean Filters
Order-Statistic Filters
Spatial Filtering: Mean Filters
Adaptive Filters
Adaptive Mean Filters
Adaptive Median Filters
This is the basic introductory presentation for beginners. It gives you the idea about what is image processing means. The presentation consists of introduction to digital image processing, image enhancement, image filtering, finding an image edge, image analysis, tools for image processing and finally some application of digital image processing.
Introduction to digital image processing, image processing, digital image, analog image, formation of digital image, level of digital image processing, components of a digital image processing system, advantages of digital image processing, limitations of digital image processing, fields of digital image processing, ultrasound imaging, x-ray imaging, SEM, PET, TEM
low pass filters in detail
Low Pass Filters
RC Low Pass Filter
Critical or cutoff frequency
Response curve
Cutoff frequency of RC LPF
RL Low Pass Filter
Cutoff Frequency of RL LPF
Phase Response in Low Pass Filter
Digital image processing is the use of computer algorithms to perform image processing on digital images. As a subcategory or field of digital signal processing, digital image processing has many advantages over analog image processing.
Lecture 4 Decision Trees (2): Entropy, Information Gain, Gain RatioMarina Santini
attribute selection, constructing decision trees, decision trees, divide and conquer, entropy, gain ratio, information gain, machine leaning, pruning, rules, suprisal
Neighbourhood operations
What is spatial filtering?
Smoothing operations
What happens at the edges?
Correlation and convolution
Sharpening filters
Combining filtering techniques
Some simple neighbourhood operations include:
Min: Set the pixel value to the minimum in the neighbourhood
Max: Set the pixel value to the maximum in the neighbourhood
Median: The median value of a set of numbers is the midpoint value in that set (e.g. from the set [1, 7, 15, 18, 24] 15 is the median). Sometimes the median works better than the average
Spatial smoothing may be viewed as a process for estimating the value of a pixel from its neighbours.
What is the value that “best” approximates the intensity of a given pixel given the intensities of its neighbours?
We have to define “best” by establishing a criterion.
A spatial filter is an image operation where each pixel value I(u; v) is changed by a function of the intensities of pixels in a neighborhood of (u; v).
It involves moving the filter mask from point to point in an image.
At each point (x,y), the response of the filter at that point is calculated using a predefined relationship
The area of machine learning has enabled experts to reveal
bits of knowledge from the useful information and past
occasions. One of the familiar histories in the world is Titanic
disaster. The main aim is to anticipate the passengers who have
survived using the machine learning techniques. To make the
correct predictions about the disaster various parameters are
included such as Name, Sex, Age, PassengerID, Embarked etc.
Initially the dataset has collected.
The dataset has been contemplated and deselected utilizing
different machine learning calculations like SVM, Random
forest and so forth. The methods are used in this are decision
tree, linear SVM, and logistic regression. Evaluating the Titanic
disaster to decide a relationship between the survival of
passengers and attributes of the travelers utilizing different
machine learning calculations is the main goal of this project.
Hence, various algorithms can be compared based on the
accuracy of a test dataset [1].
The overall accuracy can be calculated by undergoing
several stages as depicted by the below Fig. 1 using aforesaid
machine learning approaches.
A. Dataset
Kaggle website provides the dataset for this work [10]. The
data comprises of 891 rows in the prepare set which is a
traveller test with their related names. The Passenger class,
Ticket number, Age, Sex, name of the passenger, Decision tree characterization procedure is a standout
amongst the most prevalent systems in the developing field of
information mining. A method of building a decision tree from
the set of samples is the method involved in the implementing
decision tree algorithm. It is the form of flow chart where
every non-terminal node represents the test on a particular
attribute and class labels are held with the terminal node [2].
Here, the chance of survival can be calculated
1 of 6 LAB 5 IMAGE FILTERING ECE180 Introduction to.docxmercysuttle
1 of 6
LAB 5: IMAGE FILTERING
ECE180: Introduction to Signal Processing
OVERVIEW
You have recently learned about the convolution sum that serves as the basis of the FIR filter difference equation. The filter
coefficient sequence {𝑏𝑘} – equivalent to the filter’s impulse response ℎ[𝑛] – may be viewed as a one-dimensional moving
window that slides over the input signal 𝑥[𝑛] to compute the output signal 𝑦[𝑛] at each time step. Extending the moving
window concept to a 2-D array that slides over an image pixel array provides a useful and popular way to filter an image.
In this lab project you will implement two types of moving-window image filters, one based on convolution and the other
based on the median value of the pixel grayscale values spanned by the window. You will also gain experience with the
built-in image convolution filter imfilter.
OUTLINE
1. Develop and test a 33 median filter
2. Develop and test a 33 convolution filter
3. Evaluate the median and convolution filters to reduce noise while preserving edges
4. Study the behavior of various 33 convolution filter kernels for smoothing, edge detection, and sharpening
5. Learn how to use imfilter to convolution-filter color images, and study the various mechanisms offered by
imfilter to deal with boundary effects
PREPARATION – TO BE COMPLETED BEFORE LAB
Study these tutorial videos:
1. Nested “for” loops -- http://youtu.be/q2xfz8mOuSI?t=1m8s (review this part)
2. Functions -- http://youtu.be/0zTmMIh6I8A (review as needed)
Ensure that you have added the ECE180 DFS folders to your MATLAB path, especially the “images” and “matlab” subfolders.
Follow along with the tutorial video http://youtu.be/MEqUd0dJNBA, if necessary.
LAB ACTIVITIES
1. Develop and test a 33 median filter function:
1.1. Implement the following algorithm as the function med3x3:
TIP: First implement and debug the algorithm as a script and then convert it to a function as a final step. Use any
of the smaller grayscale images from the ECE180 “images” folder as you develop the function, or use the test
image X described in the Step 1.2.
(a) Create the function template and save it to an .m file with the same name as the function,
(b) Accept a grayscale image x as the function input,
http://youtu.be/q2xfz8mOuSI?t=1m8s
http://youtu.be/0zTmMIh6I8A
http://youtu.be/MEqUd0dJNBA
2 of 6
(c) Copy x to the output image y and then initialize y(:) to zero; this technique creates y as the same size and
data type as x,
(d) Determine the number of image rows and columns (see size),
(e) Loop over all pixels in image x (subject to boundary limits):
Extract a 33 neighborhood (subarray) about the current pixel,
Flatten the 2-D array to a 1-D array,
Sort the 1-D array values (see sort),
Assign the middle value of the sorted array to the current output pixel, and
(f) Return the median-filtered image y.
1.2. Enter load lab_5_verify to load the
Gabor filter is a powerful way to enhance biometric images like fingerprint images in order to extract correct features from these images, Gabor filter used in extracting features directly asin iris images, and sometimes Gabor filter has been used for texture analysis. In fingerprint images The even symmetric Gabor filter is contextual filter or multi-resolution filter will be used to enhance fingerprint imageby filling small gaps (low-pass effect) in the direction of the ridge (black regions) and to increase the discrimination between ridge and valley (black and white regions) in the direction, orthogonal to the ridge, the proposed method in applying Gabor filter on fingerprint images depending on translated fingerprint image into binary image after applying some simple enhancing methods to partially overcome time consuming problem of the Gabor filter.
MedicalSpatial filtering is a process by which we can alter properties of an optical image by selectively removing certain spatial frequencies that make up an object, for example, filtering video data received from satellite and space probes, or removal of raster from a television picture or scanned image. Image processing, digital images slides spatial filters. Filters are divided into two types: linear (also called convolution) and nonlinear. A convolution is an algorithm that consists of recalculating the value of a pixel based on its own pixel value and the pixel values of its neighbors weighted by the coefficients of a convolution kernel. Spatial filtering is commonly used to "clean up" the output of lasers, removing aberrations in the beam due to imperfect, dirty, or damaged optics, or due to variations in the laser gain medium itself.
Similar to Digital image processing img smoothning (20)
Accelerate your Kubernetes clusters with Varnish CachingThijs Feryn
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2. What is a Digital Image?
A digital image is a representation of a two-
dimensional image as a finite set of digital values,
called picture elements or pixels.
3. Why Digital Image Processing?
Digital image processing focuses on two major tasks:
Improvement of pictorial information for human
interpretation.
Processing of image data for storage, transmission and
representation for autonomous machine perception
4. Applications:
The use of digital image processing techniques has
exploded and they are now used for all kinds of tasks in
all kinds of areas:
Image enhancement/restoration
Artistic effects
Medical visualisation
Industrial inspection
Law enforcement
Human computer interfaces
5. Examples: The Hubble Telescope
Launched in 1990 the Hubble telescope can take
images of very distant objects
However, an incorrect mirror made many of Hubble’s
images useless.
Image processing techniques were used to fix this
6. Examples: HCI
Try to make human computer
interfaces more natural
Face recognition
Gesture recognition
Does anyone remember the
user interface from “Minority
Report”?
7. Key Stages in Digital Image Processing:
Image Morphological
Restoration Processing
Image
Enhancement Segmentation
Image Object
Acquisition Recognition
Problem Domain Representation
& Description
Colour Image Image
Processing Compression
8. Image Representation
Before we discuss image acquisition
recall that a digital image is
col
composed of M rows
and N columns of pixels
each storing a value
Pixel values are most
often grey levels in the
range 0-255(black-white)
f (row, col)
row
12. What Is Image Enhancement?
Image enhancement is the process of making images
more useful
The reasons for doing this include:
Highlighting interesting detail in images
Removing noise from images
Making images more visually appealing
13. Spatial & Frequency Domains
There are two broad categories of image enhancement
techniques
Spatial domain techniques
Direct manipulation of image pixels
Frequency domain techniques
Manipulation of Fourier transform or wavelet transform of an
image
For the moment we will concentrate on techniques that
operate in the spatial domain
14. Image Histograms
The histogram of an image shows us the distribution of grey
levels in the image
Frequencies
Grey Levels
15. Spatial filtering techniques:
Neighbourhood operations
What is spatial filtering?
Smoothing operations
What happens at the edges?
16. Neighbourhood Operations
Neighbourhood operations simply operate on a larger
neighbourhood of pixels than point operations
Origin x
Neighbourhoods are
mostly a rectangle
around a central pixel
Any size rectangle
and any shape filter (x, y)
Neighbourhood
are possible
y Image f (x, y)
17. Simple Neighbourhood Operations
Some simple neighbourhood operations include:
Min:
Set the pixel value to the minimum in the neighbourhood
Max:
Set the pixel value to the maximum in the neighbourhood
Median:
The median value of a set of numbers is the midpoint value
in that set (e.g. from the set [1, 7, 15, 18, 24] 15 is the median).
Sometimes the median works better than the average
18. The Spatial Filtering Process
Origin x
a b c r s t
d
g
e
h
f
i
* u
x
v
y
w
z
Original Image Filter
Simple 3*3 Pixels
e 3*3 Filter
Neighbourhood
eprocessed = v*e +
r*a + s*b + t*c +
u*d + w*f +
y Image f (x, y) x*g + y*h + z*i
The above is repeated for every pixel in the
original image to generate the filtered image
19. Smoothing Spatial Filters
One of the simplest spatial filtering operations we
can perform is a smoothing operation
Simply average all of the pixels in a neighbourhood
around a central value
Especially useful 1/ 1/ 1/
9 9 9
in removing noise
from images
Also useful for
1/
9
1/
9
1/
9 Simple
highlighting gross averaging
detail 1/ 1/ 1/ filter
9 9 9
20. Smoothing Spatial Filtering
Origin x
104 100 108 1/ 1/ 1/
9 9 9
1/ 1/ 1/
99 106 98
95 90 85
* 1/
9
1/
9
1/
9
9 9 9
1/ 1/ 1/
104 100 108
Original Image Filter
9 9 9
Simple 3*3 1/
99 106 198
1/ /9
3*3 Smoothing Pixels
9 9
Neighbourhood 195
/9 1/
90 185
/9
Filter
9
e = 1/9*106 +
1/ *104 + 1/ *100 + 1/ *108 +
9 9 9
1/ *99 + 1/ *98 +
9 9
y Image f (x, y) 1/ *95 + 1/ *90 + 1/ *85
9 9 9
= 98.3333
The above is repeated for every pixel in the
original image to generate the smoothed image
21. Sharpening Spatial Filters
Previously we have looked at smoothing filters which
remove fine detail
Sharpening spatial filters seek to highlight fine detail
Remove blurring from images
Highlight edges
Sharpening filters are based on spatial differentiation
24. 1st Derivative
The formula for the 1st derivative of a function is as
follows:
f
f ( x 1) f ( x)
x
It’s just the difference between subsequent values
and measures the rate of change of the function.
25. 2nd Derivative
The formula for the 2nd derivative of a function is as
follows: 2
f
2
f ( x 1) f ( x 1) 2 f ( x)
x
Simply takes into account the values both before and
after the current value
26. Using Second Derivatives For Image
Enhancement
The 2nd derivative is more useful for image enhancement
than the 1st derivative
Stronger response to fine detail
Simpler implementation
We will come back to the 1st order derivative later on
The first sharpening filter we will look at is the Laplacian
Isotropic
One of the simplest sharpening filters
We will look at a digital implementation
27. The Laplacian
The Laplacian is defined as follows:
2 2
2 f f
f 2 2
x y
where the partial 1st order derivative in the x direction is
defined as follows:
2
f
2
f ( x 1, y ) f ( x 1, y ) 2 f ( x, y )
x
and in the y direction as follows:
2
f
2
f ( x, y 1) f ( x, y 1) 2 f ( x, y )
y
28. The Laplacian (cont…)
So, the Laplacian can be given as follows:
2
f [ f ( x 1, y ) f ( x 1, y )
f ( x, y 1) f ( x, y 1)]
4 f ( x, y)
We can easily build a filter based on this
0 1 0
1 -4 1
0 1 0
29. The Laplacian (cont…)
Applying the Laplacian to an image we get a new image
that highlights edges and other discontinuities
Original Laplacian Laplacian
Image Filtered Image Filtered Image
Scaled for Display
30. But That Is Not Very Enhanced!
The result of a Laplacian filtering is not an
enhanced image
We have to do more work in order to get
our final image
Subtract the Laplacian result from the
original image to generate our final
sharpened enhanced image
Laplacian
Filtered Image
2 Scaled for Display
g ( x, y ) f ( x, y ) f
31. Laplacian Image Enhancement
- =
Original Laplacian Sharpened
Image Filtered Image Image
In the final sharpened image edges and fine detail are
much more obvious
33. Simplified Image Enhancement
The entire enhancement can be combined into a single
filtering operation
2
g ( x, y ) f ( x, y ) f
f ( x, y) [ f ( x 1, y) f ( x 1, y)
f ( x, y 1) f ( x, y 1)
4 f ( x, y)]
5 f ( x, y) f ( x 1, y) f ( x 1, y)
f ( x, y 1) f ( x, y 1)
34. Simplified Image Enhancement (cont…)
This gives us a new filter which does the whole job for us
in one step
0 -1 0
-1 5 -1
0 -1 0
35. The Big Idea
=
Any function that periodically repeats itself can
be expressed as a sum of sines and cosines of
different frequencies each multiplied by a
different coefficient – a Fourier series
36. The Discrete Fourier Transform (DFT)
The Discrete Fourier Transform of f(x, y), for x = 0, 1,
2…M-1 and y = 0,1,2…N-1, denoted by F(u, v), is given by
the equation:
M 1N 1
j 2 ( ux / M vy / N )
F (u , v) f ( x, y )e
x 0 y 0
for u = 0, 1, 2…M-1 and v = 0, 1, 2…N-1.
37. DFT & Images
The DFT of a two dimensional image can be visualised
by showing the spectrum of the images component
frequencies
DFT
38. The DFT and Image Processing
To filter an image in the frequency domain:
1. Compute F(u,v) the DFT of the image
2. Multiply F(u,v) by a filter function H(u,v)
3. Compute the inverse DFT of the result
40. Smoothing Frequency Domain Filters
Smoothing is achieved in the frequency domain by
dropping out the high frequency components
The basic model for filtering is:
G(u,v) = H(u,v)F(u,v)
where F(u,v) is the Fourier transform of the image being
filtered and H(u,v) is the filter transform function
Low pass filters – only pass the low frequencies,
drop the high ones.
41. Ideal Low Pass Filter
Simply cut off all high frequency components that are a
specified distance D0 from the origin of the transform
changing the distance changes the behaviour of the filter
42. Ideal Low Pass Filter (cont…)
The transfer function for the ideal low pass filter can be
given as:
1 if D(u, v) D0
H (u, v)
0 if D(u, v) D0
where D(u,v) is given as:
2 2 1/ 2
D(u, v) [(u M / 2) (v N / 2) ]
43. Butterworth Low pass Filters
The transfer function of a Butterworth lowpass filter of
order n with cutoff frequency at distance D0 from the
origin is defined as:
1
H (u , v)
1 [ D(u , v) / D0 ]2 n
44. Gaussian Low pass Filters
The transfer function of a Gaussian lowpass filter is
defined as:
D2 (u ,v ) / 2 D0 2
H (u, v) e
46. Sharpening in the Frequency Domain
Edges and fine detail in images are associated with high
frequency components
High pass filters – only pass the high frequencies,
drop the low ones.
High pass frequencies are precisely the reverse of low
pass filters, so:
Hhp(u, v) = 1 – Hlp(u, v)
47. Ideal High Pass Filters
The ideal high pass filter is given as:
0 if D(u, v) D0
H (u, v)
1 if D(u, v) D0
where D0 is the cut off distance as before
48. Butterworth High Pass Filters
The Butterworth high pass filter is given as:
1
H (u , v) 2n
1 [ D0 / D(u , v)]
where n is the order and D0 is the cut off distance as
before
49. Gaussian High Pass Filters
The Gaussian high pass filter is given as: 2
D2 (u ,v ) / 2 D0
H (u, v) 1 e
where D0 is the cut off distance as before
50. Frequency Domain Filtering & Spatial
Domain Filtering
Similar jobs can be done in the spatial and frequency
domains
Filtering in the spatial domain can be easier to
understand
Filtering in the frequency domain can be much faster –
especially for large images