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Digital Image Processing
Lecture # 7
Image Enhancement in Spatial Domain- III
ALI JAVED
Lecturer
SOFTWARE ENGINEERING DEPARTMENT
U.E.T TAXILA
Email:: [email protected]
Office Room #:: 7
Presentation Outline Sharpening Spatial Filtering
Edge Detection
Derivatives
1st Order Derivative
2nd Order Derivative
Laplacian Operator
Unsharp Masking
High Boost Filtering
Gradient Operators
Sobel Operator
Prewitt Operator
Robert Cross Operator
Canny Edge Detection
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Spatial Filtering for Sharpening
Background: To highlight fine detail in an image or to enhance blurred detail
Applications: Medical imaging, industrial inspection etc.
Foundation (Blurring vs Sharpening):
Blurring/smoothing is performed by spatial averaging (equivalent to integration)
Sharpening is performed by noting only the gray level changes in the image that is the differentiation
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Edge Detection
What is an Edge? Edge is a change but every change is not an edge Edge is a noticeable or abrupt change
E.g 2 is not a noticeable change in the range of (0 to 255)
We have to define a threshold if the change is more than a specified threshold then we will define it as an edge point. Here gradual change exists you cannot pinpoint where the edge exists so the change must be abrupt For each pixel we have to look in horizontal, vertical and diagonal direction
dx/ds -> for horizontal direction dy/ds -> for vertical direction dd/ds -> for diagonal direction
5 7
50 55 60 65 70
50 15 35
40 20 30
225 195 230
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Edge Detection
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Spatial Filtering for Sharpening
Operation of Image Differentiation
Enhance edges and discontinuities (magnitude of output gray level >> 0)
De-emphasize areas with slowly varying gray-level values (output gray level: 0)
Mathematical Basis of Filtering for Image Sharpening
First-order derivatives [Gradient]
Second-order derivatives
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Derivatives
First Order Derivative A basic definition of the first-order derivative of a one-dimensional function f(x) is the difference Second Order Derivative Similarly, we define the second-order derivative of a one-dimensional function f(x) is the difference
)()1( xfxfx
f
)(2)1()1(2
2
xfxfxfx
f
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1st & 2nd Order Derivatives
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1st & 2nd Order Derivatives
First Order Derivative Must be zero in area of constant gray levels Non zero along the ramps Non zero at the onset of the gray level step or ramp
Second Order Derivative Zero in flat areas Zero along the ramps of constant slope Non zero at the onset and end of the gray level step or ramp
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Example for Discrete Derivatives
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Steps to Apply Edge Detector Kernel
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Laplacian Mask: 2nd Order Derivative
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Laplacian Mask: 2nd Order Derivative
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Laplacian for Image Enhancement
Image background is removed by Laplacian filtering. Background can be recovered simply by adding original image to Laplacian output
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Laplacian for Image Enhancement
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Image Sharpening Based on Un-sharp Masking
Un-sharp masking Sharpen images consists of subtracting an unsharp (smoothed)
version of an image from the original image
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High Boost Filtering
Principal application:
High Boost filtering is used when input image is darker than desired
High-boost filter makes the image lighter and more natural
A slight further generalization of un-sharp masking is called High Boost filtering A high boost filtered image, fhb, is defined at any point (x, y) as
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High Boost Filtering Masks
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High Boost Filtering Masks
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1st Derivative Filtering- The Gradient
1st derivative filters is Gradient which represents change For a function f (x, y) the gradient of f at coordinates (x, y) is given as the column vector:
y
fx
f
G
G
y
xf
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1st Derivative Filtering- The Gradient
)f( magf
21
22
yx GG
21
22
y
f
x
f
The magnitude of this vector is given by:
The direction of this vector is given by:
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1st Derivative Filtering- The Gradient
Now we want to define digital approximations and their Filter Masks For simplicity we use a 3x3 region For example z5 denotes f(x,y), z1 denotes f(x-1,y-1) A simple approximation for First Derivative is
z1 z2 z3
z4 z5 z6
z7 z8 z9
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1st Derivative Filtering- The Gradient
A simple approximation for First Derivative is
Two other definitions proposed by Roberts use cross- difference
If we use
z1 z2 z3
z4 z5 z6
z7 z8 z9
Roberts Cross-Gradient Operators
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A Simple Edge Detector- The Gradient
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Gradient Operators
Normally the smallest mask used is of size 3 x 3
Based on the concept of approximating the gradient several spatial masks have been proposed
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Gradient Operators
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Gradient Operators
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Gradient Operators
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Sharpening Masks Coefficients
Why the summation of coefficients in all masks of derivate operators equals to zero?
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Noise in an image
Problem with Edge Localization
High Threshold may suppress meaningful edges
Low Threshold may include unwanted edges
Noise may have high magnitude
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Blurred Edges
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Canny Edge Detection
The Canny edge detection operator was developed by John F. Canny in 1986 and uses a multi-stage algorithm to detect a wide range of edges in images. Algorithm Steps
Image smoothing
Gradient computation
Edge direction computation
Non-maximum suppression
Hysteresis Thresholding
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Image Smoothing
Reduces image noise that can lead to erroneous output Performed by convolution of the input image with a Smoothing filter
2 4 5 4 2
4 9 12 9 4
5 12 15 12 5
4 9 12 9 4
2 4 5 4 2
1 ―
159
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Image Smoothing
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Gradient Computation
Determines intensity changes High intensity changes indicate edges Performed by convolution of smoothed image with masks to determine horizontal and vertical derivatives
-1 0 1
-2 0 2
-1 0 1
-1 -2 -1
0 0 0
1 2 1
x y
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Gradient Computation
Gradient magnitude determined by adding X and Y gradient images
= x + y
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Edge Direction Computation
Edge directions are determined from running a computation on the X and Y gradient images Edge directions are then classified by their nearest 45° angle
x
Θx,y = tan-1 y
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Edge Direction Computation
0 ° 90 ° 45 ° 135 °
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Non-Maximum Suppression
Given estimates of the image gradients, a search is then carried out to determine if the gradient magnitude assumes a local maximum in the gradient direction.
This is worked out by passing a 3x3 grid over the intensity map. From this stage referred to as non-maximum suppression, a set of edge points, in the form of a binary image, is obtained.
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Non-Maximum Suppression
So, for example,
if the rounded angle is zero degrees the point will be considered to be on the edge if its intensity is greater than the intensities in the north and south directions,
if the rounded angle is 90 degrees the point will be considered to be on the edge if its intensity is greater than the intensities in the west and east directions,
if the rounded angle is 135 degrees the point will be considered to be on the edge if its intensity is greater than the intensities in the north east and south west directions,
if the rounded angle is 45 degrees the point will be considered to be on the edge if its intensity is greater than the intensities in the north west and south east directions.
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Non-Maximum Suppression
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Thresholding
Reduce number of false edges by applying a threshold T
all values below T are changed to 0
selecting a good values for T is difficult
some false edges will remain if T is too low
some edges will disappear if T is too high
some edges will disappear due to softening of the edge contrast by shadows
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Hysteresis Thresholding
Thresholding with hysteresis requires two thresholds - high and low. we begin by applying a high threshold. This marks out the edges we can be fairly sure are genuine. Starting from these, using the directional information derived earlier, edges can be traced through the image. While tracing an edge, we apply the lower threshold, allowing us to trace faint sections of edges. Once this process is complete we have a binary image where each pixel is marked as either an edge pixel or a non-edge pixel.
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Hysteresis Thresholding
Apply two thresholds in the suppressed image
T2 = 2T1
two images in the output
Gives Strong Edge pixels
T2 T1
Gives Weak Edge pixels
T2 T1
TH TL
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Hysteresis Thresholding
the image from T2 contains fewer edges but has gaps in the contours
the image from T1 has many false edges
combine the results from T1 and T2
link the edges of T2 into contours until we reach a gap
link the edge from T2 with edge pixels from a T1 contour until a T2 edge is found again
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Hysteresis Thresholding
T2=2 T1=1
02000030
00000030
00000230
00000300
00020200
03020000
30000000
02010030
10100030
00000230
00000300
00021200
03120000
30000000
gaps
filled
from
T1
A T2 contour has pixels along the green arrows
Linking: search in a 3x3 of each pixel and connect the pixel at the center with the one having greater value
Search in the direction of the edge (direction of Gradient)
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Hysteresis Thresholding
Any question