BYST Seg-1 DIP - WS2002: Segmentation Digital Image Processing Image Segmentation Bundit Thipakorn, Ph.D. Computer Engineering Department

BYST Seg-2 DIP - WS2002: Segmentation Image Segmentation What picture are they?

BYST Seg-3 DIP - WS2002: Segmentation Aim: partition an image into meaningful regions (or categories) corresponding to part of, or the whole of objects within the image. Complete Segmentation A set of disjoint regions corresponding uniquely with objects in the original image. SegmentationCont’d.

BYST Seg-4 DIP - WS2002: Segmentation Segmentation Partial Segmentation A set of disjoint regions that are homogeneous with respect to selected property such as brightness, colour, reflectivity, texture, etc. Every pixel in an image is assigned to one of a number of the disjoint regions. Cont’d.

BYST Seg-5 DIP - WS2002: Segmentation A good segmentation is typically one in which: SegmentationCont’d. q pixels in the same categories have similar selected property and form a connected region; q neighbouring pixels that are in different categories have dissimilar selected property.

BYST Seg-6 DIP - WS2002: Segmentation SegmentationCont’d. Start Dividing the image 1. All regions of interest are identified. or 2. Reach certain uniformity. Stop No Yes Depends on the problem being solved. Easy : if outcome is known. Easy : if outcome is known. Otherwise, it is very difficult. Otherwise, it is very difficult.

BYST Seg-7 DIP - WS2002: Segmentation SegmentationCont’d. That is, Autonomous segmentation is one of the most difficult tasks in image processing. Two main approaches: q Boundary-Based (Edge) Methods: Object is represented by its outline.

BYST Seg-8 DIP - WS2002: Segmentation SegmentationCont’d. q Region-Based (Area) Methods: Object is represented by its respective 2D region. Boundary-Based Object Representation Region-Based Object Representation

BYST Seg-9 DIP - WS2002: Segmentation Segmentation Input Image 1. Pixels along a boundary. or 2. Pixels contained in a region. SegmentationCont’d.

BYST Seg-10 DIP - WS2002: Segmentation determine a closed boundary such that an inside and an outside can be defined. Edge-Based Segmentation

BYST Seg-11 DIP - WS2002: Segmentation Edge-BasedCont’d. Detection of Discontinuities Point Detection: Detect isolated points. Point Detection: Detect isolated points.

BYST Seg-12 DIP - WS2002: Segmentation Edge-BasedCont’d. Line Detection: Detect part of a image line. Line Detection: Detect part of a image line. = a dark narrow region bounded on both sides by lighter regions, or vice-versa.

BYST Seg-13 DIP - WS2002: Segmentation Edge-BasedCont’d.

BYST Seg-14 DIP - WS2002: Segmentation Edge-BasedCont’d. Edge Detection: (See Image Filtering in Spatial Domain). Edge Detection: (See Image Filtering in Spatial Domain). Edge is: 1. A boundary between two regions having the strong intensity contrast. 2. A boundary having the maximum/minimum of intensity gradient (the 1 st derivative of the gray-level profile). 3. A boundary where the zero-crossing of the 2 nd derivative of the gray-level profile. or or

BYST Seg-15 DIP - WS2002: Segmentation Edge-BasedCont’d.

BYST Seg-16 DIP - WS2002: Segmentation Region = group of pixels sharing common features Region-Based Segmentation

BYST Seg-17 DIP - WS2002: Segmentation Formal Definition Region-BasedCont’d. A segmentation of the array R for a uniformity predicate P is a partition of R into disjoint non-empty subsets R 1, R 2, R 3, …, R t and can be defined mathematically as following: q R i = R q R i is a connected region; i = 1, 2, 3, …, n.  R i R j =  for all i and j; i ≠ j. q P(R i ) = True for i = 1, 2, 3, …, n.

BYST Seg-18 DIP - WS2002: Segmentation Region-BasedCont’d. q P(R i R j ) = False for i ≠ j. Where P(R i ) is the logical predicate over the points in set R and  is the null set. 0 R1R1R1R1 R2R2R2R2 R3R3R3R3 R4R4R4R4 RiRiRiRi RjRjRjRj RnRnRnRn

BYST Seg-19 DIP - WS2002: Segmentation Region-BasedCont’d. Region-Based Methods o Thresholding, o Region growing, o Region merging and splitting, o Clustering, etc.

BYST Seg-20 DIP - WS2002: Segmentation Region-BasedCont’d. RegionGrowing

BYST Seg-21 DIP - WS2002: Segmentation RegionMerging

BYST Seg-22 DIP - WS2002: Segmentation Region-BasedCont’d. Split-and Merge Algorithm (d)(c) (a)(b)

BYST Seg-23 DIP - WS2002: Segmentation Region-BasedCont’d. Clustering = partition a set of vectors (pixels) into groups having similar values. Classical Clustering Algorithms lest squares error measure Let consider a set of K clusters C 1, C 2, …, C K with means m 1, m 2, …, m K. We can use a lest squares error measure to measure how close the data are to their assigned clusters. A least squares error measure can be defined as: