EE583 Digital Image Processing Morphological Image Processing The

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EE-583: Digital Image Processing Morphological Image Processing • The word morphology refers to the

EE-583: Digital Image Processing Morphological Image Processing • The word morphology refers to the scientific branch that deals the forms and structures of animals/plants. • Morphology in image processing is a tool for extracting image components that are useful in the representation and description of region shape, such as boundaries and skeletons. • Furthermore, the morphological operations can be used for filtering, thinning and pruning. • The language of the Morphology comes from the set theory, where image objects can be represented by sets. For example an image object containing black pixels can be considered a set of black pixels in 2 D space of Z 2. Prepared By: Dr. Hasan Demirel, Ph. D

EE-583: Digital Image Processing Morphological Image Processing Set Theory Fundamentals • Given that A

EE-583: Digital Image Processing Morphological Image Processing Set Theory Fundamentals • Given that A is a set in Z 2 and a=(a 1, a 2), then a is an element in A: a is not an element in A: • given sets A and B, A is said to be the subset of B: • The union of A and B is denoted by: • The intersection of A and B is denoted by: • Two sets are disjoint/mutually exclusive if • The complement of set A is the set of elements not contained in A, • The difference of two sets: Prepared By: Dr. Hasan Demirel, Ph. D

EE-583: Digital Image Processing Morphological Image Processing Set Theory Fundamentals Given 2 sets A

EE-583: Digital Image Processing Morphological Image Processing Set Theory Fundamentals Given 2 sets A and B Prepared By: Dr. Hasan Demirel, Ph. D

EE-583: Digital Image Processing Morphological Image Processing Set Theory Fundamentals • The reflection of

EE-583: Digital Image Processing Morphological Image Processing Set Theory Fundamentals • The reflection of set B is defined by: • The translation of set A by point z=(z 1, z 2) is defined by: Translation of A by z. Reflection of B Prepared By: Dr. Hasan Demirel, Ph. D

EE-583: Digital Image Processing Morphological Image Processing Logic operation involving Binary Images • Given

EE-583: Digital Image Processing Morphological Image Processing Logic operation involving Binary Images • Given 1 -bit binary images, A and B, the basic logical operations are illustrated: • Note that the black indicates binary 1 and white indicates binary 0 here. Prepared By: Dr. Hasan Demirel, Ph. D

EE-583: Digital Image Processing Morphological Image Processing Dilation and Erosion • Dilation and erosion

EE-583: Digital Image Processing Morphological Image Processing Dilation and Erosion • Dilation and erosion are the two fundamental operations used in morphological image processing. Almost all morphological algorithms depend on these two operations: • Dilation: Given A and B sets in Z 2, the dilation of A by B, is defined by: • The dilation of A and B is a set of all displacements, z , such that ^ B and A overlap by at least one element. The definition can also be written as: • Set B is referred to as the structuring element and used in dilation as well as in other morphological operations. Dilation expands/dilutes a given image. Prepared By: Dr. Hasan Demirel, Ph. D

EE-583: Digital Image Processing Morphological Image Processing Dilation and Erosion • Dilation: Given the

EE-583: Digital Image Processing Morphological Image Processing Dilation and Erosion • Dilation: Given the structuring element B and set A. origin Shaded area is the dilation of A by B • The structuring element B enlarges the size of A at its boundaries. Dilation simply expands a given image. • The structuring element B enlarges the size of A at its boundaries, in relation to the distance from the origin of the structuring element. Prepared By: Dr. Hasan Demirel, Ph. D

EE-583: Digital Image Processing Morphological Image Processing Dilation and Erosion • Dilation: Given the

EE-583: Digital Image Processing Morphological Image Processing Dilation and Erosion • Dilation: Given the following distorted text image where the maximum length of the broken characters are 2 pixels. The image can be enhanced by bridging the gaps by using the structuring element given below: 3 x 3 structuring element • Note that the broken characters are joined. Prepared By: Dr. Hasan Demirel, Ph. D

EE-583: Digital Image Processing Morphological Image Processing Dilation and Erosion • Erosion: Given A

EE-583: Digital Image Processing Morphological Image Processing Dilation and Erosion • Erosion: Given A and B sets in Z 2, the erosion of A by structuring element B, is defined by: • The erosion of A by structuring element B is the set of all points z, such that B, translated by z, is contained in A. Shaded area is the erosion of A by B structuring element • Note that in erosion the structuring element B erodes the input image A at its boundaries. Erosion shrinks a given image. Prepared By: Dr. Hasan Demirel, Ph. D

EE-583: Digital Image Processing Morphological Image Processing Dilation and Erosion • Erosion: Given the

EE-583: Digital Image Processing Morphological Image Processing Dilation and Erosion • Erosion: Given the structuring element B and set A. Shaded line is what is left from the erosion of A by B structuring element Prepared By: Dr. Hasan Demirel, Ph. D

EE-583: Digital Image Processing Morphological Image Processing Dilation and Erosion • Erosion: Given the

EE-583: Digital Image Processing Morphological Image Processing Dilation and Erosion • Erosion: Given the following binary image with squares on size 1, 3, 5, 7, 9 and 15. You can get rid of all the squares less than size of 15 by erosion followed by dilation of a structuring element of 13 x 13 structuring element Erosion of A by B Prepared By: Dr. Hasan Demirel, Ph. D

EE-583: Digital Image Processing Morphological Image Processing Dilation and Erosion • Dilation: Cont. from

EE-583: Digital Image Processing Morphological Image Processing Dilation and Erosion • Dilation: Cont. from the previous slide. Note that erosion followed by dilation helps to perform filtering. 13 x 13 structuring element dilation by B Prepared By: Dr. Hasan Demirel, Ph. D

EE-583: Digital Image Processing Morphological Image Processing Opening and closing • Opening: The process

EE-583: Digital Image Processing Morphological Image Processing Opening and closing • Opening: The process of erosion followed by dilation is called opening. It has the effect of eliminating small and thin objects, breaking the objects at thin points and smoothing the boundaries/contours of the objects. • Given set A and the structuring element B. Opening of A by structuring element B is defined by: • Closing: The process of dilation followed by erosion is called closing. It has the effect of filling small and thin holes, connecting nearby objects and smoothing the boundaries/contours of the objects. • Given set A and the structuring element B. Closing of A by structuring element B is defined by: Prepared By: Dr. Hasan Demirel, Ph. D

EE-583: Digital Image Processing Morphological Image Processing Opening and closing • Opening: The opening

EE-583: Digital Image Processing Morphological Image Processing Opening and closing • Opening: The opening of A by the structuring element B is obtained by taking the union of all translates of B that fit into A. • The opening operation can also be expressed by the following formula: Outer boundary of A Origin of B Circular structuring element Possible translations of B in A Shaded area: complete opening Prepared By: Dr. Hasan Demirel, Ph. D

EE-583: Digital Image Processing Morphological Image Processing Opening and closing • Closing: The closing

EE-583: Digital Image Processing Morphological Image Processing Opening and closing • Closing: The closing has a similar geometric interpretation except that we roll B on the outside of the boundary. • The opening operation can also be expressed by the following formula: Outer boundary of A Outer boundaries of closing Possible translations of B on the outer boundaries of A Shaded area: complete closing Prepared By: Dr. Hasan Demirel, Ph. D

EE-583: Digital Image Processing Morphological Image Processing Opening and closing B circular structuring element

EE-583: Digital Image Processing Morphological Image Processing Opening and closing B circular structuring element result of erosion of A by B result of opening of A by B result of dilation of A by B result of closing of A by B Prepared By: Dr. Hasan Demirel, Ph. D

EE-583: Digital Image Processing Morphological Image Processing Opening and closing • Noise Filtering: The

EE-583: Digital Image Processing Morphological Image Processing Opening and closing • Noise Filtering: The morphological operations can be used to remove the noise as in the following example: 3 x 3 square structuring element result of opening followed by closing after opening Note that impulsive noise within the background and the fingerprints is removed. Prepared By: Dr. Hasan Demirel, Ph. D

EE-583: Digital Image Processing Morphological Image Processing Hit-or-Miss Transform (Template Matching) • Hit-or-miss transform

EE-583: Digital Image Processing Morphological Image Processing Hit-or-Miss Transform (Template Matching) • Hit-or-miss transform can be used for shape detection/ Template matching. • Given the shape as the structuring element B 1 the Hit-or-miss transform is defined by: * • Where B 2 =W-X and B 1=X. W is the window enclosing B 1. Windowing is used to isolate the structuring element/object. B 2=W-X, used as the second structuring element. Complement of B 1 Shape that we are searching for Used as the structuring element (B 1=X) Prepared By: Dr. Hasan Demirel, Ph. D

EE-583: Digital Image Processing Morphological Image Processing Hit-or-Miss Transform * B 1 B 2

EE-583: Digital Image Processing Morphological Image Processing Hit-or-Miss Transform * B 1 B 2 Complement of A Erosion of A by B 1 Erosion of comp of AC by B 2 The location of the matched object/shape, Prepared By: Dr. Hasan Demirel, Ph. D

EE-583: Digital Image Processing Morphological Image Processing Basic Morphological Algorithms • Boundary Extraction: The

EE-583: Digital Image Processing Morphological Image Processing Basic Morphological Algorithms • Boundary Extraction: The boundaries/edges of a region/shape can be extracted by first applying erosion on A by B and subtracting the eroded A from A. Ex 1: 3 x 3 Square structuring element is used for boundary extraction. Ex 2: The same structuring element in Ex 1 is used. Note that thicker boundaries can be obtained by increasing the size of structuring element. Prepared By: Dr. Hasan Demirel, Ph. D

EE-583: Digital Image Processing Morphological Image Processing Basic Morphological Algorithms • Region Filling: Region

EE-583: Digital Image Processing Morphological Image Processing Basic Morphological Algorithms • Region Filling: Region filling can be performed by using the following definition. Given a symmetric structuring element B, one of the non-boundary pixels (Xk) is consecutively diluted and its intersection with the complement of A is taken as follows: • Following consecutive dilations and their intersection with the complement of A, finally resulting set is the filled inner boundary region and its union with A gives the filled region F(A). Prepared By: Dr. Hasan Demirel, Ph. D

EE-583: Digital Image Processing Morphological Image Processing Basic Morphological Algorithms • Region Filling: This

EE-583: Digital Image Processing Morphological Image Processing Basic Morphological Algorithms • Region Filling: This region is filled first. Filling of all the other regions A non-boundary pixel Ex 1: X 0=1 (Assume that the shaded boundary points are 1 and the white pixels are 0) Prepared By: Dr. Hasan Demirel, Ph. D

EE-583: Digital Image Processing Morphological Image Processing Basic Morphological Algorithms • Connected Component Extraction:

EE-583: Digital Image Processing Morphological Image Processing Basic Morphological Algorithms • Connected Component Extraction: The following iterative expression can be used to determine all the pixels in component Y which is in A. Known pixel, p Result of second iteration Result of first iteration Result of last iteration • X 0=1 corresponds to one of the pixels on the component Y. Note that one of the pixel locations on the component must be known. • Consecutive dilations and their intersection with A, yields all elements of component Y. Prepared By: Dr. Hasan Demirel, Ph. D

EE-583: Digital Image Processing Morphological Image Processing Basic Morphological Algorithms • Connected Component Extraction:

EE-583: Digital Image Processing Morphological Image Processing Basic Morphological Algorithms • Connected Component Extraction: Input image (Chicken fillet) Thresholded image 15 connected components with different number of pixels After erosion by 5 x 5 square structuring element of 1’s Prepared By: Dr. Hasan Demirel, Ph. D

EE-583: Digital Image Processing Morphological Image Processing Basic Morphological Algorithms • Thinning: Thinning of

EE-583: Digital Image Processing Morphological Image Processing Basic Morphological Algorithms • Thinning: Thinning of A by the structuring element B is defined by: * hit-or-miss transform/template matching • Note that we are only interested in pattern matching of B in A, so no background operation is required of the hit-miss-transform. • The structuring element B consists of a sequence of structuring elements, where B i is the rotated version of Bi-1. Each structuring elements helps thinning in one direction. If there are 4 structuring elements thinning is performed from 4 directions separated by 90 o. If 8 structuring elements are used the thinning is performed in 8 directions separated by 45 o. • The process is to thin A by one pass with B 1, then the result with one pass of B 2, and continue until A is thinned with one pass of Bn. Prepared By: Dr. Hasan Demirel, Ph. D

EE-583: Digital Image Processing Morphological Image Processing Basic Morphological Algorithms • Thinning: The following

EE-583: Digital Image Processing Morphological Image Processing Basic Morphological Algorithms • Thinning: The following set of structuring elements are used for thinning operation. . If there is no change any more. Declared to be thinned object Prepared By: Dr. Hasan Demirel, Ph. D