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Spatial Filtering

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  • 5/19/2018 Spatial Filtering

    1/42

    Image

    Filtering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    2D Spatial Image Filtering

    Some Basics

    Dr Muhammad Sarim

    http://find/
  • 5/19/2018 Spatial Filtering

    2/42

    Image

    Filtering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    2D Spatial image Filtering

    Filter( Mask, Kernel, Window, Template.)

    http://find/
  • 5/19/2018 Spatial Filtering

    3/42

    Image

    Filtering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    2D Spatial image Filtering

    Filter( Mask, Kernel, Window, Template.)A mathematical operation / function.

    http://find/
  • 5/19/2018 Spatial Filtering

    4/42

    Image

    Filtering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    2D Spatial image Filtering

    Filter( Mask, Kernel, Window, Template.)A mathematical operation / function.Applied locally on an image.

    http://find/
  • 5/19/2018 Spatial Filtering

    5/42

    Image

    Filtering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    2D Spatial image Filtering

    Filter( Mask, Kernel, Window, Template.)A mathematical operation / function.Applied locally on an image.A 2D matrix.

    http://find/
  • 5/19/2018 Spatial Filtering

    6/42

    Image

    Filtering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    2D Spatial image Filtering

    Filter( Mask, Kernel, Window, Template.)A mathematical operation / function.Applied locally on an image.A 2D matrix.

    Linear Filter

    http://find/
  • 5/19/2018 Spatial Filtering

    7/42

    Image

    Filtering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    2D Spatial image Filtering

    Filter( Mask, Kernel, Window, Template.)A mathematical operation / function.Applied locally on an image.A 2D matrix.

    Linear Filter

    A filter G is said to be linear if, for any two images f andh and any two scalars a and b,

    G(af +bh) =aG(f) +bG(h). (1)

    http://find/
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    Image

    Filtering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    2D Spatial image Filtering

    Filter( Mask, Kernel, Window, Template.)A mathematical operation / function.Applied locally on an image.A 2D matrix.

    Linear Filter

    A filter G is said to be linear if, for any two images f andh and any two scalars a and b,

    G(af +bh) =aG(f) +bG(h). (1)

    Filter responseIn general, linear filtering of an image f of size M Nwith a filter mask of size m n is given by the expression:

    http://find/
  • 5/19/2018 Spatial Filtering

    9/42

    Image

    Filtering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    2D Spatial image Filtering

    Filter( Mask, Kernel, Window, Template.)A mathematical operation / function.Applied locally on an image.A 2D matrix.

    Linear Filter

    A filter G is said to be linear if, for any two images f andh and any two scalars a and b,

    G(af +bh) =aG(f) +bG(h). (1)

    Filter responseIn general, linear filtering of an image f of size M Nwith a filter mask of size m n is given by the expression:

    h(x, y) =c

    s=c

    d

    t=d

    (s, t)f(x+s, y+t). (2)

    http://find/
  • 5/19/2018 Spatial Filtering

    10/42

    Image

    Filtering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    Filter response

    http://find/
  • 5/19/2018 Spatial Filtering

    11/42

    Image

    Filtering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    Box Filtering

    http://find/
  • 5/19/2018 Spatial Filtering

    12/42

    Image

    Filtering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    Box Filtering

    http://find/http://goback/
  • 5/19/2018 Spatial Filtering

    13/42

    Image

    Filtering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    Box Filtering

    http://find/
  • 5/19/2018 Spatial Filtering

    14/42

    Image

    Filtering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    Box Filtering

    http://find/
  • 5/19/2018 Spatial Filtering

    15/42

    Image

    Filtering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    Box Filtering

    http://find/http://goback/
  • 5/19/2018 Spatial Filtering

    16/42

    Image

    Filtering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    Box Filtering

    http://find/http://goback/
  • 5/19/2018 Spatial Filtering

    17/42

    Image

    Filtering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    Box Filtering

    http://find/
  • 5/19/2018 Spatial Filtering

    18/42

    Image

    Filtering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    Box Filtering

    http://find/
  • 5/19/2018 Spatial Filtering

    19/42

    Image

    Filtering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    Box Filtering

    http://find/
  • 5/19/2018 Spatial Filtering

    20/42

    Image

    Filtering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    Practice

    http://find/
  • 5/19/2018 Spatial Filtering

    21/42

    ImageFiltering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    Practice

    http://find/
  • 5/19/2018 Spatial Filtering

    22/42

    ImageFiltering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    Practice

    http://find/
  • 5/19/2018 Spatial Filtering

    23/42

    ImageFiltering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    Practice

    http://find/
  • 5/19/2018 Spatial Filtering

    24/42

    ImageFiltering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    Practice

    P i

    http://find/
  • 5/19/2018 Spatial Filtering

    25/42

    ImageFiltering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    Practice

    P i

    http://find/
  • 5/19/2018 Spatial Filtering

    26/42

    ImageFiltering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    Practice

    P i

    http://find/
  • 5/19/2018 Spatial Filtering

    27/42

    ImageFiltering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    Practice

    P ti

    http://find/
  • 5/19/2018 Spatial Filtering

    28/42

    ImageFiltering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    Practice

    G i Filt

    http://find/
  • 5/19/2018 Spatial Filtering

    29/42

    ImageFiltering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    Gaussian Filter

    Weight contributions of neighboring pixels by nearness

    G = 1

    22e

    x2+y2

    22

    (3)

    Gaussian Vs Box Filter

    http://find/
  • 5/19/2018 Spatial Filtering

    30/42

    ImageFiltering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    Gaussian Vs Box Filter

    Gaussian Vs Box Filter

    http://find/
  • 5/19/2018 Spatial Filtering

    31/42

    ImageFiltering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    Gaussian Vs Box Filter

    Important Properties

    http://goforward/http://find/http://goback/
  • 5/19/2018 Spatial Filtering

    32/42

    ImageFiltering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    Important Properties

    Remove high-frequency components from the image(low-pass filter).

    Important Properties

    http://goforward/http://find/http://goback/
  • 5/19/2018 Spatial Filtering

    33/42

    ImageFiltering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    Important Properties

    Remove high-frequency components from the image(low-pass filter).

    Images become more smooth.

    Important Properties

    http://goforward/http://find/http://goback/
  • 5/19/2018 Spatial Filtering

    34/42

    ImageFiltering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    Important Properties

    Remove high-frequency components from the image(low-pass filter).

    Images become more smooth.

    Convolution with self is another Gaussian.

    Important Properties

    http://goforward/http://find/http://goback/
  • 5/19/2018 Spatial Filtering

    35/42

    ImageFiltering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    Important Properties

    Remove high-frequency components from the image(low-pass filter).

    Images become more smooth.

    Convolution with self is another Gaussian.

    So can smooth with small-width kernel, repeat, and get

    same result as larger-width kernel would have.

    Important Properties

    http://find/
  • 5/19/2018 Spatial Filtering

    36/42

    ImageFiltering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    Important Properties

    Remove high-frequency components from the image(low-pass filter).

    Images become more smooth.

    Convolution with self is another Gaussian.

    So can smooth with small-width kernel, repeat, and get

    same result as larger-width kernel would have.Convolving two times with Gaussian kernel of width issame as convolving once with kernel of width

    2

    Important Properties

    http://find/http://goback/
  • 5/19/2018 Spatial Filtering

    37/42

    ImageFiltering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    Important Properties

    Separable kernel.

    Important Properties

    http://find/
  • 5/19/2018 Spatial Filtering

    38/42

    ImageFiltering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    Important Properties

    Separable kernel.

    Factors into product of two 1D Gaussians.

    Important Properties

    http://find/
  • 5/19/2018 Spatial Filtering

    39/42

    ImageFiltering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    po ta t ope t es

    Separable kernel.

    Factors into product of two 1D Gaussians.

    G = 1

    22e

    x2+y2

    22

    (4)

    = 1

    22e

    x2

    22

    +

    1

    22e

    y2

    22

    Separability Examples

    http://find/
  • 5/19/2018 Spatial Filtering

    40/42

    ImageFiltering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    p y p

    Separabilitiy

    http://find/
  • 5/19/2018 Spatial Filtering

    41/42

    ImageFiltering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    p y

    Why separability is useful?

    http://find/
  • 5/19/2018 Spatial Filtering

    42/42

    ImageFiltering

    Dr. Sarim

    2D Spatial

    image

    Filtering

    Box Filtering

    Practice

    Gaussian Filter

    Gaussian Vs BoxFilter

    ImportantProperties

    SeparabilityExamples

    Q & A

    Q & A

    http://find/

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