EE 4780

Morphological Image Processing

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Example

Two semiconductor wafer images are given. You are supposed to determine the defects based on these images.

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Example

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Example

Absolute value of the difference

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Example

>> b = zeros(size(a));>> b(a>100) = 1;>> figure; imshow(b,[ ]);

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Example

>> c = imerode(b,ones(3,3));>> figure; imshow(c,[]);

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Example

>> d = imdilate(c,ones(3,3));>> figure; imshow(d,[]);

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Mathematical Morphology We defined an image as a two-dimensional function, f(x,y),

of discrete (or real) coordinate variables, (x,y). An alternative definition of an image can be based on the

notion that an image consists of a set of discrete (or continuous) coordinates.

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Morphology

B = {(0,0), (0,1), (1,0)} A = {(5,0), (3,1), (4,1), (5,1), (3,2), (4,2), (5,2)}

A binary image containing two object sets A and B

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Morphology Sets in morphology represent the shapes of objects in an

image. For example, the set A = {(a1,a2)} represents a point in a

binary image. The set of all black pixels in a binary image is a complete

description of the image.

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Mathematical Morphology Morphology is a tool for extracting and processing image

components based on shapes. Morphological techniques include filtering, thinning,

pruning.

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Basic Set Operations

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Some Basic Definitions Let A and B be sets with components a=(a1,a2) and

b=(b1,b2), respectively. The translation of A by x=(x1,x2) is

A + x = {c | c = a + x, for a A} The reflection of A is

Ar = {x | x = -a for a A} The complement of A is

Ac = {x | x A} The union of A and B is

A B = {x | x A or x B } The intersection of A and B is

A B = {x | x A and x B }

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Some Basic Definitions The difference of A and B is.

A – B = A Bc = {x | x A and x B} A and B are said to be disjoint or mutually exclusive if they

have no common elements. If every element of a set A is also an element of another

set B, then A is said to be a subset of B.

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Some Basic Definitions Dilation

A B = {x | (B + x) A } Dilation expands a region.

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Some Basic Definitions

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Some Basic Definitions

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Some Basic Definitions Erosion

A B = {x | (B + x) A} Erosion shrinks a region.

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Some Basic Definitions

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Some Basic Definitions Opening is erosion followed by dilation:

A B = (A B) B Opening smoothes regions, removes spurs, breaks narrow

lines.

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Some Basic Definitions

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Some Basic Definitions Closing is dilation followed by erosion:

A B = (A B) B Closing fills narrow gaps and holes in a region.

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Some Basic Definitions

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Some Basic Definitions

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Some Morphological Algorithms

Opening followed by closing can eliminate noise:(A B) B

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Some Morphological Algorithms

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Some Morphological Algorithms

Boundary of a set, A, can be found byA - (A B)

B

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Some Morphological Algorithms

A region can be filled iteratively byXk+1 = (Xk B) Ac ,

where k = 0,1,… and X0 is a point inside the region.

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Some Morphological Algorithms

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Morphological Operations

BWMORPH Perform morphological operations on binary image. BW2 = BWMORPH(BW1,OPERATION) applies a specific morphological operation to the binary image BW1. BW2 = BWMORPH(BW1,OPERATION,N) applies the operation N times. N can be Inf, in which case the operation is repeated until the image no longer changes.

OPERATION is a string that can have one of these values: 'skel' With N = Inf, remove pixels on the boundaries of objects without allowing objects to break apart 'spur' Remove end points of lines without removing small objects completely. 'fill' Fill isolated interior pixels (0's surrounded by 1's) ...

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Morphological OperationsBW1 = imread('circbw.tif'); BW2 = bwmorph(BW1,'skel',Inf); imshow(BW1);figure, imshow(BW2);

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Morphological OperationsBW1 = imread('circbw.tif'); BW2 = bwperim(BW1); imshow(BW1); figure, imshow(BW2)

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Morphological OperationsPixel Connectivity Connectivity defines which pixels are connected to other pixels. A set of pixels in a binary image that form a connected group is called an object or a connected component.

4-connected 8-connected

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Morphological Operations

X = bwlabel(BW,4); RGB = label2rgb(X, @jet, 'k'); imshow(RGB,'notruesize')

BW = [0 0 0 0 0 0 0 0; 0 1 1 0 0 1 1 1; 0 1 1 0 0 0 1 1; 0 1 1 0 0 0 0 0; 0 0 0 1 1 0 0 0; 0 0 0 1 1 0 0 0; 0 0 0 1 1 0 0 0; 0 0 0 0 0 0 0 0]; X = bwlabel(BW,4) X = 0 0 0 0 0 0 0 0 0 1 1 0 0 3 3 3 0 1 1 0 0 0 3 3 0 1 1 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 2 2 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0

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Some Morphological Algorithms

Application example: Using connected components to detect foreign objects in packaged food.There are four objects with significant size!

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Some Morphological Algorithms

Thinning: Thin regions iteratively; retain connections and endpoints.

Skeletons: Reduces regions to lines of one pixel thick; preserves shape.

Convex hull: Follows outline of a region except for concavities.

Pruning: Removes small branches.

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Summary

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Summary

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Summary

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Summary

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Extensions to Gray-Scale ImagesDilation

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Extensions to Gray-Scale ImagesDilation

Take the maximum within the window.

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Extensions to Gray-Scale ImagesErosion

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Extensions to Gray-Scale Images

Dilation: Makes image brighter Reduces or eliminates dark details

Erosion: Makes image darker Reduces or eliminates bright details

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Extensions to Gray-Scale Images

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Extensions to Gray-Scale Images

Opening: Narrow bright areas are reduced.Closing: Narrow dark areas are reduced.

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Extensions to Gray-Scale Images

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Application Example

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Application Example-Segmentation

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Application Example-Granulometry