mask in DIP _ms

7/30/2019 mask in DIP _ms

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Linear Operations Using Masks

Masks are patterns used to define theweights used in averaging the

neighbors of a pixel to compute someresult at that pixel

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Expressing linear operations

on neighborhoods

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Images as functions


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Neighborhood operations Average neighborhood to remove noiseor high frequency patternsDetect boundaries at points of contrastusing gradient computationCan use median filtering to smoothwhile keeping boundaries sharp


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Histogram equalization

Left image does not use all available gray levels. Image is recoded so thatall gray levels are used and such that each gray level occurs in roughly thesame number of pixels of the recoded image.

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Histogram equalization can darken a

bright image, perhaps improving contrast

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Can define mapping of input

gray level to output level (xv)

Gamma correction:boost all gray levels

Boost low levelsand reduce high

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Smoothing an image byaveraging neighbors (boxcar)


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Output pixel is the dot product of the input neighborhood and themask


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Properties of smoothing masks


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Types of ideal edges (in 1D)

These types are also present in 2D and 3D images and arecomplicated by orientation variations.


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Boxcar smoothing filter example

So, reducing noise will also degrade the signal.


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Linear smoothing smoothes

noise and blurs signalBlur: step is now ramp

Input image Row after 5x5 mean filter


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Gaussian smoothing


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Median filter replaces center withneighborhood median, not mean

Noisy row of checkersimage

Mean filteringsmoothes signal andramps the boundary

Median filtersmoothes signal andpreserves sharpboundary


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Median filter is not linear

Algorithm requires comparisons and ismore expensive than using mask Can sort all NxN pixel values and pick middleDo not need totally sorted data: O(N)algorithm exists


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Scratches removed by using amedian filter

Thin artifactremoved, sharpboundariespreserved.


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Finding boundary pixels

Computing derivatives or

gradients to locate region change.


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2 rows of intensity vs difference


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Differencing used to estimate1st and 2 nd derivatives

First differences2nd differences

Masks representthe first and 2 nd differences


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Step edges X mask [-1, 0, +1]

Step edge is detected well, but edge location imprecise.


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Ramp and impulse X mask [-1, 0, +1]

Ramp edge now yields a broad weak response. Impulseresponse is a whip, first up and then down.


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2nd derivative using mask [-1, 2, -1]

Response is zero on constant region and a double whip amplifiesand locates the step edge.


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2nd derivative using mask [-1, 2, -1]

Weak response brackets the ramp edge. Bright impulseyields a double whip with gain of 3X original contrast.


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Estimating 2D image gradient


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Gradient from 3x3 neighborhoodEstimate both magnitude and direction of the edge.


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Prewitt versus Sobel masks

Sobel mask uses weights of 1,2,1 and -1,-2,-1 inorder to give more weight to center estimate.The scaling factor is thus 1/8 and not 1/6.


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Computational short cuts


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Alternative masks for gradient


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Computational shortcuts

Use MAX operation on 1D row andcolumn derivatives.Use OR operation on thresholded rowand column derivatives.


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2 rows of intensity vs difference


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Caption for Prewitt image


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Properties of derivative masks

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