Introduction to Digital Image Processing Using MATLAB

Raymond Phan – Ph.D. Candidate
Department of Electrical and Computer Engineering
Distributed Multimedia Computing Research Lab
EPH 408
rphan@ee.ryerson.ca
Some slides were taken from Prof. R. A. Peters PPT slides:
http://www.archive.org/details/Lectures_on_Image_Processing

Topics Covered in this Presentation
 1st Hour: 6:10 p.m. – 7:00 p.m.
Introduction to Digital Images and in MATLAB
 Quick intro to myself
 What is MATLAB?
 Where to get MATLAB and how to run
 Basic I/O  Reading and writing images
 Accessing pixels and groups of pixels
 Resizing Images
 Rotating Images
 …break for 10 minutes!

 2nd Hour: 7:10 p.m. – 8:00 p.m.
Operations on Digital Images
 Simple contrast and brightness enhancing
 Intro to image histograms
 Advanced enhancing using image histograms
 Intro to convolution in images
 Blurring / Smoothing images
 Edge detection
 Sharpening images

 3rd Hour: 8:10 p.m. – 9:00 p.m.
Applications of Image Processing
 Segmenting simple objects
 Noise Filtering
 Simple image stitching using template matching
 NOTE!
 For a more comprehensive MATLAB tutorial, check:
http://www.ee.ryerson.ca/~rphan/ele532/MATLABTutorial.ppt
 You can access the slides, images and code at:
http://www.rnet.ryerson.ca/~rphan/IEEEDIPTalk

 1st Hour: 6:10 p.m. – 7:00 p.m.
Introduction to Digital Images and in MATLAB
 Quick intro to myself
 What is MATLAB and where do I get it / find it?
 Intro to Digital Images
 Basic I/O  Reading and writing images
 Accessing pixels and groups of pixels
 Resizing Images
 Rotating Images

Introduction of Myself
 Started in 2002 in the B.Eng. – Computer Engineering
program
 Program only started at this time  Relatively new
 Graduated in 2006
 Started my M.A.Sc. in 2006 – ELCE
 Finished in 2008
 Winner – Ryerson Gold Medal (2008 – SGS)
 Started my Ph.D. in 2008 – ELCE
 Will finish before my back gives out
 Currently a 4th year Ph.D. Candidate
 2010 NSERC Vanier Canada Graduate Scholar

Introduction of Myself (2)
 Research Interests
 Digital Image Processing, Signal Processing,
Multimedia, Computer Vision, Stereo Vision, 3DTV, etc.
 M.A.Sc. Thesis – Content-Based Image Retrieval
System
 Featured in the Toronto Star (January 4th, 2008)
 Searching for images using actual images, rather than
keywords
 Current Ph.D. Thesis – Faster and more accurate 2D to
3D conversion

What is MATLAB?
 MATLAB  Stands for MATrix LABoratory
 Created by Cleve Moler @ Stanford U. in 1970
 Why? Makes linear algebra, numerical analysis and
optimization a lot easier
 MATLAB is a dynamically typed language
 Means that you do not have to declare any variables
 All you need to do is initialize them and they are created
 MATLAB treats all variables as matrices
 Scalar – 1 x 1 matrix. Vector – 1 x N or N x 1 matrix
 Why? Makes calculations a lot faster (will see later)

What is MATLAB? (2)
 How can I get and/or use MATLAB?  3 ways:
 1) Find it on any of the ELCE departmental computers
 Log in to your account, go to Applications  Math 
MATLAB R2010b
 2) Use any Ryerson computer on to the ACS network
 Log in with your Matrix ID and Password, then go to Start 
MATLAB R2010b
 3) Install it on your own laptop
 Go to http://www.ee.ryerson.ca/matlab for more details
 You must be on the Ryerson network to sign up for an account
 After, you can download MATLAB from anywhere

 MATLAB uses the Image Processing Toolbox (IPT)
 Should already be installed with MATLAB!

Intro to Digital Images
Color images have 3 values per pixel;
Digital Image monochrome / grayscale images = 1
value/pixel.

a grid of squares,
each of which
contains a single
color

each square is
called a pixel (or
picture element)

Intro to Digital Images – (2)
Pixels
 A digital image, I, is a mapping from a 2D grid of
uniformly spaced discrete points, {p = (r,c)}, into a set
of positive integer values, {I( p)}, or a set of vector
values, e.g., {[R G B]T(p)}.
 Each column location of each row in I has a value
 The pair (p, I(p)) is a “pixel” (for picture element)
 p = (r,c) pixel location indexed by row r & column c
 I(p) = I(r,c)  Value of the pixel at location p
 If I(p) is a single number  I is monochrome (B&W)
 If I(p) is a 3 element vector  I is a colour (RGB) image

 Monochromatic Case:
 We call the values at each pixel intensities
 Smaller intensities denote a darker pixel
 Bigger intensities denote a lighter pixel
 Colour Case:
 Think of a colour image as a 3D matrix  First layer is
red, second layer is green, third layer is blue
 Why RGB? Trichromacy theory  All colours found in
nature can naturally be decomposed into Red, Green
and Blue  This is basically how CCD cameras work!
 The three element vector tells you how much red, green
and blue the pixel is compromised of (i.e. [R G B]T = [0
255 0]  No red, no blue, all green

Pixel : [ p, I(p)]

p = (r, c )  red  12 
Pixel Location: p = (r , c)
= (row # , col # ) I ( p ) = green  = 43
   
Pixel Value: I(p) = I(r , c) = (272, 277)  blue  61
   

 How do digital cameras take images (very basic)?
 Uses sampling and quantization
 What we see now through our eyes is continuous
 There is essentially an infinite amount of points that
comprise our field of view (FoV)
 Not good, because we want to store this information!
 We first need to sample the FoV  Transfer the FoV to
a rectangular grid, and grab the colour in each location
of the grid

Sampling and Quantization
pixel grid column index
row index

real image sampled quantized sampled &
quantized

 We’re not done yet! There are also an infinite number
of possible colours
 We will now need to quantize the colours
 Quantizing will reduce the total number of colours to a
smaller amount
 Key  Quantize accurately so that we can’t tell much
difference between the original image and the quantized
one
 A digital image is essentially taking our FoV and
performing a sampling and quantization
 Values are now discrete and positive

Sampling and Quantization
pixel grid column index
row index

real image sampled quantized sampled &
quantized

 Digital images store their intensities / colour values as
discrete and positive values
 Usually, digital images need 8 bits for B & W and 24-
bits for colour (8 bits for each primary colour)
 B & W – 0 for Black and 255 for White  All integers
 Colour – 0 to 255 for Red, Green and Blue  All integers
 Note: We can consider a colour image as three 2D images
 Without compression, files would be very large!
 Compression algorithms (PNG, JPEG, etc.) eliminate
extra information to reduce the size of the image

R/W Images in MATLAB
 So we have an image file… how do I access the info?
 Open up MATLAB and change working directory to
where image is stored
 Use the imread() function
 im = imread(‘name_of_image.ext’)
 Use single quotes, and type in the full name of the image
with its extension (.bmp, .jpg, etc.)
 im will contain a 2D matrix (rows x cols) of B&W values
or a 3D matrix (rows x cols x 3) of colour values
 Matrix corresponds to each pixel in the digital image for
B & W, or a colour component of a pixel in colour

R/W Images in MATLAB – (2)
 How do I access a pixel in MATLAB  B&W case?
 pix = im(row,col);
 row & col: Row & column of the pixel to access
 pix contains the intensity value
 Access elements in an array by round braces, not square!
 For you C buffs  Indexing starts at 1, not 0!
 How do I access a pixel in MATLAB  Colour case?
 pix = im(row,col,1);  Red colour value
 pix = im(row,col,2);  Green colour value
 pix = im(row,col,3);  Blue colour value
 3rd argument  3rd dimension of matrix
 Only grabs one colour value at a time!

 How can I get the RGB pixel entirely? Use the :
command
 pix = im(row,col,:);
 : means to grab all values of one dimension
 However, this will give you a 1 x 1 x 3 matrix… we just
want an array! Call the squeeze() command
 pix = squeeze(im(row,col,:));
 Now a 3 x 1 vector. To access R, G and B values, do:
 red = pix(1)  Red, gr = pix(2)  Green,
blue = pix(3)  Blue

 So I know how to get pixels; how can I modify them in
the image?
 Easy! Just go backwards
 For a B & W Image do:
im(row,col) = pix;
 For a colour image, do either:
im(row,col,1) = red;
im(row,col,2) = green;
im(row,col,3) = blue; or
im(row,col,:) = [red; green; blue] or
im(row,col,:) = rgb; %rgb - 3 x 1 vector

 How do I access a subset of the image?
 How do I grab a portion of the image and store it into
another variable?
 Do the following for monochromatic images:
im2 = im(row1:row2,col1:col2);
 Do the following for colour images:
im2 = im(row1:row2,col1:col2,:);
 This will grab a rectangular region between rows 1 and
2, and columns 1 and 2
 e.g., if I wanted to get rows 17 – 31, and columns 32 – 45
for colour, do: im2 = im(17:31,32:45,:);

 So I know how to get pixels; how can I display images?
 Use the imshow() command
 imshow(im);  im: Image loaded into MATLAB
 Shows a new window with the image in it
 If you do: imshow(im,[])
 For monochromatic: Smallest intensity becomes 0 and
largest intensity becomes 255 for display
 For colour: Apply the above for each colour channel
 Every time you use imshow, the image you want to
display is put in the same window… so what do you do?

 Use figure command to create a new blank window
 Then, run the imshow command to display the image
on the other window
 We can also do:
 imshow(im(:,:,1));  Shows red channel
 imshow(im(:,:,2));  Shows green channel
 imshow(im(:,:,3));  Shows blue channel
 (:,:,1) means grab all of the rows and columns for the
first layer (i.e. red), etc.

 When showing the red channel:
 Darker pixels mean there isn’t much red in that pixel
 Lighter pixels mean there is a lot of red in that pixel
 Same applies for green and blue!
 How do I save images to disk? Use imwrite()
 imwrite(im, ‘name_of_image.ext’, ‘EXT’);
 im  image to write to disk
 name_of_image.ext  Name of the image
 ‘EXT’  Extension of the file (‘JPG’, ‘BMP’, ‘PNG’, etc.)

Demo Time #1!
Reading in Images
Accessing Pixels
Changing Image Pixels
Obtaining a Subset
Display Images  Monochromatic and Colour
Displaying Colour Channels Separately
Writing Images to File

Resizing Images
 One common thing that many people do is resize
images
 i.e. Make an image bigger from a smaller image, or make
an image smaller from a larger image
 How do we resize images in MATLAB? Use the
imresize command  How do we use it?
out = imresize(im, scale, ‘method’); or
out = imresize(im, [r c], ‘method’);
 For both methods  im is the image we want to resize,
and out is the resized image

Resizing Images – (2)
 Let’s look at the first method:
out = imresize(im, scale, ‘method’);
 scale takes each of the dimensions of the image (# of
rows and columns), and multiplies by this much to
determine the output
 e.g. If we have an image that is 20 rows x 40 columns:
 If scale = 2, the output  40 rows x 80 columns
 If scale = 0.5, the output  10 rows x 20 columns
 method determines the type of interpolation when
resizing  Important when making an image bigger

 When we are making an image bigger, we are trying to
create an image with a lack of information present
 There are three main types of interpolation
 Nearest Neighbour  method = ‘nearest’
 Uses the best pixels that are near the original pixels and fills in
missing information
 Bilinear Interpolation  method = ‘bilinear’
 Uses linear interpolation in 2D to fill in missing information
 Bicubic Interpolation  method = ‘bicubic’
 Uses cubic interpolation in 2D to fill in missing information
 Usually, bicubic is known to have the best accuracy

 Now, let’s take a look at the second method for resizing
out = imresize(im, [r c], ‘method’);
 This routine will resize the image to any desired
dimensions you want
 You can customize how many rows and columns the
final image will have
 Example: To resize a 130 rows x 180 columns image to
65 rows x 90 columns, with bilinear interpolation, do:
out = imresize(im, [65 90], ‘bilinear’);
 We can also do!
out = imresize(im, 0.5, ‘bilinear’);

Rotating Images
 Suppose we want to rotate an image  How?
out = imrotate(im, angle, ‘method’);
 im: The image we want to rotate
 angle: How much we want to rotate the image
 Angle is in degrees! Positive angle denotes counter-
clockwise rotation, and negative angle is clockwise
 When rotating, there will inevitably be some missing
information  method is like before with resizing
 out: The rotated image
 Example: Let’s rotate CCW by 45 degrees by bilinear:
out = imrotate(im, 45, ‘bilinear’);

Demo Time #2!
Enlarging Images
Shrinking Images
Rotating Images

Cont. & Brig. Enhancement
 First real application  Brightness enhancement
 How do we increase /decrease brightness of an image?
 1 way: Just add or subtract a brightness to every pixel
 How? im2 = im + c; or
im2 = im – c;  c is any constant (0 – 255)
 Takes c and add / subtract to every pixel in the image
 Adding / subtracting makes the image brighter / darker
 Round off occurs if out of range (i.e. set to 255 if > 255/set to 0 if < 0)
 What about another way?
 We can also scale the image by a constant
 Do: im2 = c*im;
 If c > 1, increasing brightness
 If c < 1, decreasing brightness

Cont. & Brig. Enhancement (2)
 So we covered brightness… what about contrast?
 Contrast  How well you can see the objects from the
background
 When performing brightness enhancing, you’ll notice
that it looks “white washed out”  Poor contrast
 We can do a contrast enhancement to make objects
look better, leaving background relatively unaffected
 How? Use the power law  s = rγ
 r is the input pixel intensity / colour and s is the output
intensity / colour

 For each pixel, apply this equation to each of the
intensities / colours
 For colour images,
apply to each channel
separately
 Exponent γ determines
how dark or light the
output is
 γ > 1  Make darker
 γ < 1  Make lighter

 How do we apply the power law in MATLAB?
 Use imadjust
out = imadjust(im, [], [], gamma);
 im: Input image to contrast adjust
 Ignore 2nd and 3rd parameters  Beyond the scope of
our talk
 gamma: The γ exponent that we’ve seen earlier
 out: The contrast adjusted image
 Example use: If γ = 1.4, we do:
out = imadjust(im, [], [], 1.4);

Demo Time #3!
Contrast and Brightness Enhancement

Intro to Image Histograms
 We can perform more advanced image enhancement
using histograms
 Before we cover this… we should probably cover what
histograms are! So, what’s a histogram?
 It measures the frequency, or how often, something
occurs
 Let’s look at a grayscale image for now
 Expressed as H(x) = q, x is an intensity- [0,255] for 8 bits
 This tells us that we see the intensity value of x for a
total of q times

Intro to Image Histograms – (2)
 Example: Let’s take a look at an grayscale image

 There are ~1500 pixels with a gray level of around 10
 There are ~1200 pixels with a gray of around 170, etc.

 How do we create histograms in MATLAB?
 imhist(im); %im is read in by imread
 Assuming im is a grayscale image
 If we want this to work with colour images, we will have
to display the histogram of each colour channel by itself
 imhist(im(:,:,1)); % histogram for red
 imhist(im(:,:,2)); % histogram for green
 imhist(im(:,:,3)); % histogram for blue
 The (:,:,1) means that we should grab every row and
column from the red channel, etc.

 Grabbing all of the pixels in any channel will produce a
grayscale image, which can be used for imhist
 We can also call the histogram function by:
h = imhist(im);
 Will create a 256 element array, where the (i+1)’th element
contains how often we see the grayscale i.
 Histograms give us a good insight on image contrast
 If the histogram has too many values towards the left
 Image is too dark
 If the histogram has too many values towards the right
 Image is too bright
 If the histogram has too many values in the middle
 Image looks very washed out

Advanced Enhancement – (1)
 Above cases are when the image has bad contrast
 A good image should have good contrast
 i.e. The histogram should have an equal number of
pixels over the entire histogram (a flat histogram)
 If an image has bad contrast, we can try to correct it by
doing histogram equalization
 Tries to make the image’s histogram as flat as possible
for good contrast  Stretches the histogram out
 For you probability nerds  If you divide each
histogram entry by the total number of entries, this
forms a Probability Density Function (PDF)

Advanced Enhancement – (2)
 Histogram equalization seeks to modify the PDF so that
all possible events (pixels) are equally likely to occur
 How do we perform histogram equalization?
out = histeq(im); %im given by imread
 What about for colour images?
 You will have to perform histogram equalization on each
channel individually, then merge together
r = im(:,:,1); g = im(:,:,2); b = im(:,:,3);
out(:,:,1) = histeq(r);
out(:,:,2) = histeq(g);
out(:,:,3) = histeq(b);

Demo Time #4!
Displaying and Calculating Histograms
Contrast and Brightness Enhancement by
Histograms

Intro to Convolution
 Before we proceed, we need to understand what
convolution is for a digital image
 Probably learned in ELE/BME 532, ELE 792, etc…. Bleck!
 But! Actually very simple when dealing with 2D images
 Preliminaries:
 First, we need to create an N x N matrix called a mask
 The numbers inside the mask will help us control the
kind of operation we’re doing
 Different #s allow us to blur, sharpen, find edges, etc.
 We need to master convolution first, and the rest is easy!

Intro to Convolution – (2)
 Steps:
 1) For each pixel (r,c) in our image, extract a N x N subset
of pixels, where the centre is at (r,c)
 Example: 9 x 9 subsets shown below @ various locations

 Another example: Let’s grab a 3 x 3 subset, located at
(r,c) = (6,4)
 Pixels are a, b,
… g, and centre
is e

 2) Take each pixel in the subset, and do a point-by-
point multiplication with the corresponding location
in the mask

 Example: Our 3 x 3 subset has pixels:
a b c
G = d
 e f

g
 h i


 Our mask has the following quantities

z y x
H = w
 v u

t
 s r


 When we do a point by point multiplication, we will
now have 9 numbers:
 a*z, b*y, c*x, d*w, e*v, f*u, g*t, h*s, i*r
 3) Create an output image and:
 a) Add up all of these values
 b) Store the output at (r,c) (i.e. the same row and
column location as the input image) in the output image
 Example:
out = a*z + b*y + c*x + d*w + e*v + f*u + g*t + h*s + i*r,
then store out into (r,c) of the output image

 Essentially, convolution is a weighted sum of pixels
from the input image within the subset
 Weighted by the numbers in your mask
 Each pixel in the output image is this weighted sum
 Do this for each location of the input image and assign
to same location in the output image
 What about for colour!?
 Do convolution on each channel separately
 Note: If the output value is floating point (decimal),
we must round in order to make this an 8-bit number
 Here’s one more example to be sure you understand…

Blur / Smooth Images
 So now what? Let’s try blurring/smoothing images
 Blurring? Think of a camera that is out of focus
 Why should we blur? Minimize sensor noise
 Noise  High Frequency
 When we blur, we are essentially low-pass filtering,
eliminating high frequency content
 High frequency content  Edges
 By getting rid of the edges, we blur the image
 How do we blur an image? Try an averaging filter

Blur / Smooth Images – (2)
 Averaging? 1st, create an output image to store results
 1) For each pixel (r,c) in the image, look at a N x N
neighbourhood / subset of pixels that surround (r,c)
 2) Add up all pixel values in the neighbourhood and
divide by N2 (number of pixels in neighbourhood)
 3) Take this new value and store it into same (r,c)
location
 Notes:
 This works for B & W images
 What about for colour images?

 Remember, colour image can be seen as a 3D matrix
 3D matrix  2D matrices with layers
 1st layer  Red values
 2nd layer  Green values
 3rd layer  Blue values
 So, we can blur each layer independently, and use the
RGB values after the blurring of each colour layer
 The bigger the neighbourhood, the more the blurring
 How can we efficiently implement this?

 Create a mask for convolution to efficiently do this
 Mask: Same size as desired subset / neighbourhood
 Mask will contain numbers used to generate our result
 Examples: 1
1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 
1 1 1 1 1  1 1 1 1 1 1 1 
1 25 1 
1 1 1  1 1 1 1 1 
1 1 1 1 1 1 1 1 1
9 1 1 1 1 1 1 1 1 1 1 1 1
  1
 1 1 1 1
 81 1 1 1 1 1 1 1 1 1
 
1 1 1 1 1 1 1 1 1
3 x 3 Averaging 5 x 5 Averaging 1 1 1 1 1 1 1 1 1
1 1
Mask Mask  
1 1 1 1 1 1 1

9 x 9 Averaging
Mask

 These masks make sense. Why?
 Let’s look at the 3 x 3 case:
 Example: Suppose our 3 x 3 neighbourhood is:
1 2 3
G = 4
 5 6

7
 8 9

Our 3 x 3 averaging mask is:
1 1 1

1 1 1  9 9 9
1
H = 1 1 1 = 
1 1 1

9  9 9 9
1 1 1  1
  1 1
9
 9 9


 The output should be:
out = (1)(1/9) + (2)(1/9) + (3)(1/9) + (4)(1/9) + (5)(1/9) +
(6)(1/9) + (7)(1/9) + (8)(1/9) + (9)(1/9)
out = (1/9)(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9)
out = (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) / 9
 … isn’t this exactly the same thing as averaging!?
 You are essentially adding up all of the pixels in the
neighbourhood, and dividing them by the total
number of pixels (9)
 Note: If we get a decimal number, we round to be sure
that we have an integer number

 Understanding was the hard part!
 In MATLAB, this is very easy!
 First, we need to create the mask
 We do this by calling fspecial()
mask = fspecial(‘average’, N);
 mask contains the averaging mask to use
 First parameter specifies we want an averaging mask
 N specifies the size of the mask  Bigger the N, more
blurring we get

 Next, call a command that will perform this multiply
and sum command for each pixel in the image
 Use the imfilter() command
out = imfilter(im, mask);
 out: output image (this case  averaged output)
 im contains the image we want to blur
 mask: Convolution mask to use (this case  averaging)
 Nice little note  imfilter() works on both
grayscale and colour images
 For colour, this automatically performs convolution on
each channel individually and combines after

 imfilter() performs image filtering using masks
 Essentially convolution
 Filtering  Produce an output image that changes the
frequency content of the image
 Blurring, Sharpening, Detecting Edges, etc.
 Why are masks important?
 You change the size of the mask, and values in the mask
and you get different results!
 Essentially how most filters in Adobe Photoshop and
GIMP work

Demo Time #5!
Blurring / Smoothing Images

Edge Detection
 Next? Edge detection… what is an edge?
 Edges are sudden discontinuities appearing in images
 A.K.A. sudden jumps in intensity or colour in images
 How can we detect edges? Very simple: Think Calc.
 Find the derivative of each point in the image
 When slope is very high, that means you found an edge
 But, derivative is only for 1D signals… what about 2D!?
 You must take the gradient  Derivative in both the x
and y directions
 You combine both of these directions to create your
final derivative function

Edge Detection – (2)
 How do I take the derivative? We perform convolution, but
with a different mask  Corresponds to discrete
approximation of the derivative
 Two possible masks we can use:
1 1 1 1 2 1
0 0 0
0
 0 0 
 
− 1 − 1 − 1 − 1 − 2
 − 1

 
Prewitt 3 x3 Mask Sobel 3 x 3 Mask
 These masks detect changes in the horizontal direction
 If there are no changes, then weighted sum of the pixels in 3
x 3 neighbourhood should have same value  Gradient = 0

 Prewitt Mask  Normal derivative
 Sobel Mask  Puts more weight on the central pixels
 How does this detect horizontal changes?
 When using the mask, if there is a change, there is a
huge change above the zero line, and below the zero line
 So when performing correlation, it can detect horizontal
changes
 How do we detect vertical changes?
 Take the transpose of each mask!
 Tranpose  Interchange rows & columns of the mask

 How do we combine the horizontal and vertical
gradient information?
 Remember from Vector Calculus:
2
 ∂G   ∂G 
2

| ∇G |=   +
 ∂y 

 ∂x   
 So, we take the horizontal gradient image, and square
each term, and do the same for the vertical gradient
image
 Now, add both images, and square root them  This is
our output image

 How do we do this in MATLAB?
 1) Create our Prewitt or Sobel Horizontal Masks:
mask = fspecial(‘prewitt’); or
mask = fspecial(‘sobel’);
 2) Get the Vertical Mask:
mask2 = mask’;  ‘ transposes a matrix
 3) Convolve with each mask separately
dX = imfilter(im, mask);
dY = imfilter(im, mask2);
 4)Find the overall magnitude
mag = sqrt(double(dX).^(2) +
double(dY).^(2));

 Note: We must cast images to double for sqrt() func.
 Now, we’ve found the overall gradient… how do we find
an actual edge? Threshold the image
 What do we mean by threshold?
 Values greater than a threshold is an edge (white)
 Values less than the threshold are not edges (black)
 How do we detect edges in MATLAB? Very easy!
I = edge(im, ‘sobel’); or
I = edge(im, ‘prewitt’);
 So, we can pretty much ignore the previous slide, but I
put that in there so you can see where it comes from

 You can also call the routines this way:
I = edge(im, ‘sobel’, thresh); or
I = edge(im, ‘prewitt’, thresh);
 I specifies edges found in input (B & W image)
 im is the input image with edges to be found
 Second parameter specifies method of finding edges
 thresh determines threshold for finding edges
 If not specified, threshold will be found automatically
 How do we use the thresh variable?
 Choose an intensity (e.g. 128)
 Any gradient value > 128 will be labeled white

 Any gradient value < 128 is labelled black
 thresh is between [0,1], so take your threshold and
divide by 255 to use
i.e. I = edge(im, ‘prewitt’, 128/255);
 Output image will give you a black and white image 
White is an edge, black is not an edge
 Only works for B & W images. To find edges for colour
images, convert the colour image to a B & W image
 Use gray = rgb2gray(im);
 rgb2gray converts a colour image into B & W by
doing: I = (R + G + B) / 3  Each colour pixel is the
average of the red, green and blue components

 Sidenote: Here’s another way of finding the gradient
 Unsharp Masking
 Probably heard this terminology in CSI? So what’s
unsharp masking?
 Let’s go back to Signals and Systems
 Suppose we perform a low-pass filtering of an image 
Get a blurred version
 If we take the original image, and subtract its blurred
version, what are we doing? Removing all low frequency
components, so what’s left? High frequency!

 High frequencies are essentially edge information
 Edges are sudden jumps  Essentially high frequency
 How do we perform unsharp masking?
 1) Blur the image  Try using the following mask:
mask = fspecial(‘average’, 5); %5x5
 So… we blur! im_blur = imfilter(im,mask);
 2) Subtract the original image from the blurred
im_unsharp = im – im_blur;
 Now, why are edges useful? We can use them to
sharpen images  Will take a look after this demo

Demo Time #6!
Edge Detection in Images
Calculating an Unsharp Mask

Image Sharpening
 Last image enhancing topic  Image Sharpening
 What is image sharpening? Make the image look
“clearer”, “sharper”, make the details “pop out more”
 How do we do this?
 Edges are the “detail” behind the image
 Edges are high frequency
 How do we make images sharper?
 Find overall magnitude of the gradient for the image
 Add these values on top of the original image
 Result? Increase the visibility of the edges  Sharper

Image Sharpening – (2)
 Use imfilter with unsharp masking
 mask = fspecial(‘unsharp’);
 The above syntax creates an unsharp mask in such a way
where when you convolve, it will automatically subtract
the image with a blurred version of itself and add the
original image on top
 Good for both x and y direction changes
 How?
mask = fspecial(‘unsharp’);
sharp = imfilter(im, mask);
 This will perform the detection of abrupt changes, and
adding them on top of the image all in one go.

Demo Time #7!
Image Sharpening in Images

 3rd Hour: 8:10 p.m. – 9:00 p.m.
Applications of Image Processing
 Segmenting simple objects
 Noise Filtering
 Simple image stitching using template matching

Segmentation via Thresholding
 There are times when we want to separate objects (the
things we want) from the background  Segmentation
 To make this easier, we convert to a B & W image first if the
image is in colour. Else just leave it alone
 After conversion, most of the time the intensities of the
objects are distinctly different from background
 We can write code to save the pixels that match these
intensities, and disregard the rest
 Pixels that match  Set to white, else set to black
 Output image will be binary  White belonging to object,
and black belonging to background
 We can use this to mask out the background pixels

Segmentation via Thresholding (2)
 What do we do?
 Take a look at the histogram, and see which pixels are
predominantly belonging to the object, and of the
background
 We threshold the image using this information
 We then use this threshold map to figure out what pixels
we want to keep, and what we want to disregard

Demo Time #8!
Object Segmentation via Thresholding

Noise Filtering
 A common task in image processing is to eliminate or
reduce image noise from an image
 Image Noise: Pixels in an image that are corrupted
undesirably
 Pixels could be corrupted in the acquisition process, or
in transmitting, etc.
 How do we reduce image noise?
 Think in the frequency domain  Noise is essentially
high-frequency information
 If we blur the image, we would eliminate the noise, but
the quality would reduce  blurring details

Noise Filtering – (2)
 We can generate artificial noise and add these to
images
 Purpose is for research  Design good filters by
recreating the noise we would encounter in practice
 How do we generate artificial noise? Use imnoise
 We will be concerned with two ways of generating noise
out = imnoise(im, ‘gaussian’, mean, var);
out = imnoise(im, ‘salt & pepper’, prob);
 First method generates Gaussian-based noise
 Usually encountered in transmitting process

 Second method generates “salt & pepper” based noise
 Also known as impulsive noise
 Called this way, because for monochromatic images, it
literally looks like someone took salt (white pixels) and
pepper (black pixels) and shook it over the image
 For colour images, specks of pure red, green and blue
pixels appear
 We can use blurring to get rid of Gaussian noise, but
for impulsive noise, we need to use median filtering
 What’s median filtering? Like convolution, but we’re not
doing a weighted sum

 For each pixel (r,c) in the image, extract an M x N
subset of pixels centered at (r,c)
 Sort these pixels in ascending order, and grab the
median value
 The output image at (r,c) is this value
 How do we perform median filtering in MATLAB?
out = medfilt2(im, [M N]);

Demo Time #9!
Noise Filtering in Images

Template Matching
 Template matching is using a small test image, which
we’ll call a patch
 Objective is to automatically find the location of where
this patch is in the entire image
 Useful in a variety of applications: Image Retrieval, Eye
Detection, etc.
 What I’ll show you today is to do some basic image
stitching
 We will have two images of the same scene, that have
been taken at slightly different perspectives  Only
horizontal shifting is concentrated on here

Template Matching – (2)
 What’s the best way to do template matching?
 1) For each pixel (r,c) in the image, extract a subset that
is the same size as the template with its centre at (r,c)
 2) Perform a cross-correlation between the patch and
this subset
 3) Take this value and assign it to location (r,c) for the
output
 4) The best location of where the template is, is where
the maximum cross-correlation is
 We can perform (1) to (3) by doing:
C = normxcorr2(template, im);

 Output is a correlation map
 To find the row and column co-ordinates of where the
template best matches, do the following:
[row col] = find(C == max(C(:)));
 So, how do we do image stitching?
 1) Extract a region in either image that is common
between both  Template
 2) Find the co-ordinates of where this template is in
both images
 3) Determine how much vertical and horizontal
displacement there is between the two images

 4) Create an output image with dimensions that
encapsulate both images together
 5) Place one image on the left, then place the other
image by displacing it over by the horizontal and vertical
shift
 OK… let’s do some code!

Demo Time #10!
Simple Image Stitching

Conclusion
 MATLAB is a great tool for digital image processing
 Very easy to use
 This is not an exhaustive tutorial! There are many
more things you can do with MATLAB
 For more image processing demos, check out:
http://www.mathworks.com/products/image/demos.html
 Lots of cool image processing stuff you can find here
 For a more comprehensive MATLAB tutorial, check:
http://www.ee.ryerson.ca/~rphan/ele532/MATLABTutorial.ppt
 You can access the slides, images and code at:
http://www.rnet.ryerson.ca/~rphan/IEEEDIPTalk

Introduction to Digital Image Processing Using MATLAB

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