Spatial Filters (Digital Image Processing)

Unit 3-Image Enhancement
Spatial Filters
Lecture By
Kalyan Acharjya
kalyan5.blogspot.in
Lecture No 14
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Disclaimer
 This PPT contents are copied from various
publicly available sources and all images are
copyright of the respective original owner.
 This is used for academic purpose only.
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Spatial Filtering Methods
(or Mask Processing Methods)
output image
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Spatial Filtering (cont’d)
 Filters are classified as:
 Low-pass (i.e., preserve low frequencies)
 High-pass (i.e., preserve high frequencies)
 Band-pass (i.e., preserve frequencies within a band)
 Band-reject (i.e., reject frequencies within a band)
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Spatial Filtering (cont’d)
 Need to define:
 A neighborhood (or mask)
 An Mask Operation
•Typically, the neighborhood
is rectangular and its size is
much smaller than that of
f(x,y) - e.g., 3x3 or 5x5
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Operation:
Filtered
Image
w(i,j)
f(i,j)
g(i,j)
A filtered image is generated as the center of the mask moves to
every pixel in the input image.
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Spatial filtering - Operation
output image
Example: weighted sum of input pixels.
mask
weights:
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Handling Pixels Close to Boundaries
Pad With Zeroes
or
0 0 0 ……………………….0
000……………………….0
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Linear vs Non-Linear
Spatial Filtering Methods
 A filtering method is linear when the output is a weighted sum
of the input pixels.
 Methods that do not satisfy the above property are called
non-linear.
 e.g.,
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Spatial Filters
 We will mainly focus on two types of filters:
 Smoothing (low-pass)
 Sharpening (high-pass)
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Smoothing Filters (low-pass)
 Useful for reducing noise and eliminating
small details.
 The elements of the mask must be positive.
 Sum of mask elements is 1 (after normalization).
Gaussian
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Smoothing filters – Example
Smoothed ImageInput Image
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Sharpening Filters (high-pass)
 Useful for highlighting fine details.
 The elements of the mask contain both positive
and negative weights.
 Sum of mask elements is 0.
1st derivative
of Gaussian
2nd derivative
of Gaussian
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Sharpening Filters - Example
 Warning: the results of sharpening might contain negative
values (i.e., re-map them to [0, 255])
Sharpened ImageInput Image
(for better visualization, the original
image is added to the sharpened image)
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Common Smoothing Filters
 Averaging
 Gaussian
 Median filtering (non-linear)
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Smoothing Filters: Averaging
Un-weighted
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3 3 0 1 1
4 5 4 0 2
2
3 4 0 1
1
5 6 7 1
1 0 2 3 5
4 5 6 7 0
1 1 1
1 1 1
1 1 1Input Image
Mask

Smoothing Filters: Averaging
(cont’d)
 Mask size determines the degree of smoothing (loss of detail).
3x3 5x5 7x7
15x15 25x25
original
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Smoothing filters: Gaussian
 The weights are samples of a 2D Gaussian
function:
mask size is
a function of σ:
σ = 1.4
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(cont’d)
• σ controls the amount of smoothing
• As σ increases, more samples must be obtained to represent the Gaussian
function accurately.
σ = 3
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(cont’d)
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Averaging vs. Gaussian Smoothing
Averaging
Gaussian
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Smoothing Filters: Median Filtering (cont’d)
 Replace each pixel by the median in a
neighborhood around the pixel.
 The size of the neighborhood controls the
amount of smoothing.
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Smoothing Filters: Median Filtering
(non-linear)
 Very effective for removing “salt and pepper” noise (i.e., random
occurrences of black and white pixels).
Averaging
Median
Filtering
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Original Image Image with Noise

Common Sharpening Filters
 Unsharp masking
 High Boost filter
 Gradient (1st derivative)
 Laplacian (2nd derivative)
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Sharpening Filters: Un sharp Masking
 Obtain a sharp image by subtracting a low
pass filtered (i.e., smoothed) image from the
original image:
- =
(after contrast
enhancement)
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Sharpening Filters: High Boost
 Image sharpening emphasizes edges but
details are lost.
 High boost filter: Amplify input image, then
subtract a Low pass image.
(A-1) + =
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Sharpening Filters: High Boost (cont’d)
 If A=1, we get unsharp masking.
 If A>1, part of the original image is added
back to the high pass filtered image.
One way to implement
high boost filtering is using
the masks below
High boost
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Sharpening Filters: High Boost (cont’d)
A=1.4 A=1.9
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Sharpening Filters: Derivatives
 Taking the derivative of an image results in
sharpening the image.
 The derivative of an image (i.e., 2D function)
can be computed using the gradient.
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How do we choose the mask weights?
 Typically, by sampling certain functions:
Gaussian
1st derivative
of Gaussian
2nd derivative
of Gaussian
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First and Second Derivative
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Gradient (cont’d)
 Gradient magnitude: provides information
about edge strength.
 Gradient direction: perpendicular to the
direction of the edge.
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Derivative Results and Laplacian:
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Reminder: Assignment
Online Submission Due Date 10 Oct 2018
1. Comments on Role of Digital Image Processing in
Modern Imaging Based Medical Treatments.
2. Explain your view on Importance of Image
Understanding in Recent Computer Vision Applications
Assignment Submission link is available at kalyan5.blogspot.in
OR
You can directly visit at http://bit.do/dipr_jnu
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Spatial Filters (Digital Image Processing)

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Spatial Filters (Digital Image Processing)