Watershed Segmentation Image Processing

Image segmentation is based on three principal concepts
Detection of discontinuities.
Thresholding
Region Processing
Morphological Watershed Image Segmentation embodies many of the concepts of above three approaches

1. A PRESENTATION ON SEGMENTATION USING MORPHOLOGICAL WATERSHEDS

2. Prepared by: Siddiqui Arshad Hussain A. M.E.(MSA) Part-2 Roll no. 296 Course: Image Processing [email protected] Faculty of Technology And Engineering, Maharaja Sayajirao University Of Baroda Department of Electrical Engineering

3. Contains Image Segmentation Historical Background Introduction Basic Concept Different Levels Of Flooding Dam Construction Watershed Segmentation Algorithm Drawback of Watersheds algorithm Gradient of image Use of Marker Summery References 3 [email protected]

4. 1. Image Segmentation: Let R represent entire spatial image region occupied by an image. We may view image segmentation as a process that partition R into n Sub-region R1,R2,….., Rn . 4 [email protected]

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6. 2. Historical Background of Watershed S egmentation. In 1975 first algorithm was developed, for Topographical digital elevation.(US, and 1984/86 ) In 1978/82/90 first algorithm was developed for digital image processing .(US, and 1982/90) focus on elevation (gradient). N ot accurate, because extreme computational demand , Not efficient In 1991 L. V incent and P. Soile make this idea practical .(Make this concept successful ) Each minima represent one basin .( Flooding ) Fill from bottom. Algorithm based on sorting the pixel in increasing order of their gray values . 1994 modified watershed segmentation. . . 6 [email protected]

7. There are two basic approaches to watershed image segmentation. Flooding. ( C atchment Basin) (Used in Watershed Segmentation) Rainfall (Finding, downstream path from each pixel to local minima)or gradient. 7 [email protected]

8. 3. INTRODUCTION OF WATERSED SEGMENTATION Image segmentation is based on three principal concepts Detection of discontinuities Thresholding Region Processing Morphological Watershed Image Segmentation embodies many of the concepts of above three approaches Often produces more stable segmentation including continuous segmentation boundaries Provides a simple framework for incorporating knowledge based constraints 8 [email protected]

9. 4. BASIC CONCEPT OF WATERSED SEGMENTATION Image is visualized in 3-DIMENSIONS. 2 spatial dimensions grey levels Any grey tone image can be considered as a T OPOLOGICAL SURFACE. 9 [email protected]

10. Based on visualizing an image in 3D 10 [email protected]

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12. CONTINUED…. Topographical interpretation consist of three points Points belonging to regional minimum Catchment Basin or watershed Divide lines or watershed lines (Points at which water would be equally likely to fall to one or more such minima) Main aim of the segmentation algorithm based on this concept is to find watershed lines. 12 [email protected]

13. Punch the regional minimum and flood the entire topography at uniform rate from below A dam is built to prevent the rising water from distinct catchment basins from merging Eventually only the tops of the dams are visible above the water line These dam boundaries correspond to the divide lines of the watersheds DIFFERENT LEVELS OF FLOODING 13 [email protected]

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16. In topographical view shown earlier the height of the mountains was proportional to the grey scale value of the original image Water level is rising in consecutive images shown in the previous slide In order to prevent water from spilling out of the structure we imagine the entire topography to be enclosed by dams of height greater than highest possible mountain The value of the height is determined by the highest possible gray-level value in the input image 16 [email protected]

17. 5. Dam Construction Dam construction is based on binary images, which are members of 2-D integer space The dam must be built to keep water from spilling across the basins . Let M 1 and M 2 be the set of coordinates of the points in the two regional minima . The set of coordinates of the points in the catchment basin associated with the two minima in the flooding level n be C n (M 1 ) and C n (M 2 ) . Let the Union of these sets be C[n]. 17 [email protected]

18. CONTD…. 18 [email protected]

19. CONTD…. Now let q denote the connected component formed in the figure b by dilation from flooding stage n -1 to stage n The dilation of the connected components by the structuring element in figure 3 is subjected to 2 conditions The dilation has to be constrained to q The center of the structuring element can be located only at the points of q during dilation The dilation cannot be performed on the set of points that may cause the sets being dilated to merge 19 [email protected]

20. CONTD…. Condition 1 is satisfied by every point during dilation and condition 2 did not apply to any point during dilation process in the first figure In figure 2 several points fail the condition 1 while meeting condition 2 resulting in broken perimeter shown in the figure In figure 4, 1-pixel cross-hatched path shows the desired separating dam at the n th stage of flooding Construction of dam at this level of flooding is completed by setting all the points in the path just determined to the value greater than maximum gray-level value in the image 20 [email protected]

21. 6. WATERSHED SEGMENTATION ALGORITHM Let M 1 , M 2 , M 3 …. M n be the sets of coordinates of points in the regional minima of the image g( x,y ) C(M i ) be the coordinates of points of the catchment basin associated with regional minima M i T[n] = { ( s,t ) | g( s,t ) < n } T[n] = Set of points in g( x,y ) which are lying below the plane g( x,y ) = n n = Stage of flooding, varies from min+1 to max+1 min = minimum gray level value max = maximum gray level value 21 [email protected]

22. ALGORITHM CONTD …. Let C n (M 1 ) be the set of points in the catchment basin associated with M 1 that are flooded at stage n. C n (M i ) = 1 at location ( x,y ) if ( x,y ) Є C(M i ) AND ( x,y ) Є T[n], otherwise it is 0. C[n] be the union of flooded catchment basin portions at the stage n => => 22 [email protected]

23. ALGORITHM CONTD…. Algorithm keeps on increasing the level of flooding, and during the process Cn (Mi) and T[n] either increase or remain constant. Algorithm initializes C[min +1] = T[min+1], and then proceeds recursively assuming that at step n C[n-1] has been constructed. Let Q be set of connected components in T[n]. For each connected component q Є Q[n], there are three possibilities: 23 [email protected]

24. ALGORITHM CONTD …. Condition (a) occurs when a new minima is encountered, in this case q is added to set C[n-1] to form C[n]. Condition (b) occurs when q lies within a catchment basin of some regional minima, in that case Condition (c) occurs when ridge between two catchment basins is hit and further flooding will cause the waters from two basins will merge, so a dam must be built within q. 24 [email protected]

25. DAM CONSTRUCTION As shown in the previous images, a one pixel thick dam can be constructed when needed by dilating q ∩ C[n-1] with a 3 × 3 Structuring matrix of 1’s and constraining the dilation to q. Algorithm efficiency can be improved by using only values of n that correspond to existing gray level values in g( x,y ). Histogram of g( x,y ) can be used to evaluate min, max and these values. 25 [email protected]

26. 7. Drawback of Watershed Algorithm Drawback of Watershed Algorithm based image segmentation. Over Segmentation Sensitivity to noise Low contrast boundaries Poor detection of thin edge 26 [email protected]

27. 8. GRADIENT OF IMAGE Regions of the image characterized by small variations in gray levels have small gradient values , so watershed segmentation is applied on the gradient of the image rather than the actual image. In this way, the regional minima of catchment basins correlate nicely with the small value of the gradients corresponding to the objects of interest . 27 [email protected]

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29. 9. Use of Marker Direct application of the watershed segmentation algorithm generally lead to over-segmentation of an image due to noise and other local irregularities of the gradient . Solution is to limit the number of allowable regions by incorporating a preprocessing stage designed to bring additional knowledge into the segmentation procedure. A concept of markers is used as a solution , A Marker is a connected component belonging to an image. 29 [email protected]

30. OVER-SEGMENTATION 30 [email protected]

31. MARKERS CONTD…. Selection of markers consists of two principal steps: Preprocessing Definition of a set of criteria There two types of markers : External : associated with the background Internal : associated with the objects of interest In the previous image due to large number of potential minima, image is over-segmented. 31 [email protected]

32. MARKERS CONTD…. An effective measure to minimize the effect of small spatial details is to filter the image with a smoothing filter . i.e. a Preprocessing step. For example, we can define the Internal markers to be : region surrounded by the higher altitude points. every region should be a connected component every point in the region should have same gray level value. External markers can be some regions of particular background color. 32 [email protected]

33. Summery: The watershed algorithm Is extremely power full and faster compare to others. But it is also proved to be more accurate. Furthermore , it turn out to be very flexible, since it can be easily adapted to any kind of digital grid and extended to n-dimensional images and graph. 33 [email protected]

34. References: M. Sonka , V. Halava and Roger B., “ Image Processing Analysis and Machine Vision ” , Second Edition By: PWS Publication, Page no. 590,186. R. C. Gonzalez and R. E. Woods, “ Digital Image Processing ” third edition, Prentice Hall, 2010 . William K. Pratt “ Digital Imag e Processing ”, Third Edition, Page number 563. Sonka , Hlava a nd Boyle, “ Digital Image Processing And Computer Vision ”, Page number-202,549. Vincent L. and Soille P. “ Watersheds in digital Spaces: An efficient Algorithm based on immersion Simulations ”, IEEE Transaction on P attern Analysis and Machine Intelligence , 13(6):583-598-1991. 34 [email protected]

35. Thankyou