Lecture 05 roger s gaborski
Download
1 / 31

Introduction to Computer Vision - PowerPoint PPT Presentation


  • 99 Views
  • Uploaded on

Lecture 05 Roger S. Gaborski. Introduction to Computer Vision. Quiz Review In Class Exercise Correlation – Convolution Filtering. Example. Histogram PDF  CDF Equalized Image Filtering using Correlation continued. Histogram Equalization.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Introduction to Computer Vision' - ronna


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Lecture 05 roger s gaborski

Lecture 05

Roger S. Gaborski

Introduction to Computer Vision

Roger S. Gaborski


  • Quiz Review

  • In Class Exercise

  • Correlation – Convolution

    • Filtering

Roger S. Gaborski


Example
Example

  • Histogram PDF  CDF Equalized Image

  • Filtering using Correlation continued


Histogram equalization
Histogram Equalization

  • Consider an image with the following gray level values:

  • Construct the pdf

  • Construct the cdf

  • Equalize the image using the cdf (not histeq)


Histogram equalization1
Histogram Equalization

  • Consider an image with the following gray level values:

  • Construct the pdf

1/9 2/9 3/9 4/9 5/9

.1 .2 .3 .4 .5


Histogram equalization2

pdf

cdf

1/9 2/9 3/9 4/9 5/9

.1 .2 .3 .4 .5

Histogram Equalization

Look Up Table

1/9 2/9 3/9 4/9 5/9 6/9 7/9 8/9 1

cdf

probability

.1 .2 .3 .4 .5

Gray level value

Gray level value


Histogram equalization3
Histogram Equalization

  • Consider an image with the following gray level values:

  • Construct the pdf

  • Construct the cdf

  • Equalize the image using the cdf (not histeq)


Spatial filtering
Spatial Filtering

  • Neighborhood processing

    • Define center point (x, y)

    • Perform operations involving only pixels in the neighborhood

    • Result of operation is response to process at that point

    • Moving the pixel results in a new neighborhood

    • Repeat process for every point in the image

Roger S. Gaborski


Linear and nonlinear spatial filtering
Linear and Nonlinear Spatial Filtering

  • Linear operation

    • Multiply each pixel in the neighborhood by the corresponding coefficient and sum the results to get the response for each point (x, y)

    • If neighborhood is m x n , then mn coefficients are required

    • Coefficients are arranged in a matrix, called

      • filter / filter mask / kernel / template

    • Mask sizes are typically odd numbers (3x3, 5x5, etc.)

Roger S. Gaborski


Image origin

y

Kernel coefficients

mask

x

Image region under mask

Roger S. Gaborski


Correlation and convolution
Correlation and Convolution

  • Correlation

    • Place mask w on the image array f as previously described

  • Convolution

    • First rotate mask w by 180 degrees

    • Place rotated mask on image as described previously

  • Convolution = 180 degree rotation + correlation

Roger S. Gaborski


Example 1d correlation
Example: 1D Correlation

  • Assume w and f are one dimensional

  • Origin of f is its left most point

  • Place w so that its right most point coincides with the origin of f

  • Pad f with 0s so that there are corresponding f points for each w point (also pad end with 0s)

  • Multiply corresponding points and sum

    • In this case (example on next page) result is 0

    • Move w to the right one value, repeat process

    • Continue process for whole length of f

Roger S. Gaborski


Reminder
Reminder

  • ‘full’ is the result we obtain from the operations on the previous slide. If instead of aligning the left most element of f with the right most element of w we aligned the center element of w with the left most value of f we would obtain the ‘same’ result, same indicating the result is the same length of the original w

Roger S. Gaborski


Chapter 3

www.prenhall.com/gonzalezwoodseddins

Roger S. Gaborski


‘Full’

correlation

Roger S. Gaborski




‘Same’

correlation

etc.

Roger S. Gaborski


Example convolution
Example - Convolution

  • Convolution is the same procedure, but the filter is first rotated 180 degrees.

    • Convolution = 180 degree rotation + correlation

  • If the filter is symmetric, correlation and convolution results are the same

Roger S. Gaborski


Chapter 3

www.prenhall.com/gonzalezwoodseddins

This can be simply extend to images

Roger S. Gaborski







Linear filtering in matlab
Linear Filtering in MATLAB

g = imfilter(f, w, filtering mode, boundary, size)

  • filters the imput image f with the filter mask w.

    • f is input image. It can be of any class (logical/numeric) and dimension.

    • g is output image

  • filter mode:

    - 'corr' : correlation, and default mode

    - 'conv' : convolution

Roger S. Gaborski


Parameters
Parameters

  • g = imfilter(f, w, filtering mode, boundary, size)

    Boundary options

    - X pad boundary with value X. Default X = 0.

    - 'symmetric' symmetric padding

    - 'replicate' replicate padding

    - 'circular' circular padding

    Size options

    - 'same' g is the same size of f (default mode)

    - 'full' g is full filtered by w, so size of g is increased

Roger S. Gaborski


Matlab function for filtering imfilter
MATLAB function for filtering: imfilter

  • g = imfilter(f, w, ‘replicate’)

  • Correlation is the default filtering mode.

  • If filters are pre-rotated 180 degrees, can simply use default(corr) for convolution

  • If filter is symmetric, doesn’t matter

Roger S. Gaborski


Chapter 3

www.prenhall.com/gonzalezwoodseddins

Roger S. Gaborski


Example smoothing
Example:Smoothing

  • w = ones(31); (31x31 filter)

    • % Normally the coefficients (w) are scaled to sum to one

    • % In this example only coefficients are not scaled by 312

    • % Convolution should result in a blurred result

  • gd = imfilter(f, w);

    • % Default mode: correlation filtering

  • imshow(gd, [ ]);

Roger S. Gaborski


Chapter 3

www.prenhall.com/gonzalezwoodseddins

Input Default padding ‘replicate’

‘symmetric’ ‘circular’ ‘replicate’, uint8

Roger S. Gaborski


ad