International Journal of Advance Engineering and Research Development (IJAERD) Volume 5, Issue 02, February-2018, e-ISSN: 2348 - 4470, print-ISSN: 2348-6406 III.
MATERIAL AND METHODOLOGY
Oil spill detection
K means clustering
Histogram based segmentation
Expectation maximization
Figure2. Methodology A. K-mean clustering: K mean clustering is a vector quantization method used for oil spill detection. Here each element is partition into k clusters which belongs to nearest mean, act as prototypes for the cluster. It works on dividing data cell into voronoi cells. K mean cluster determine comparable spatial extent clusters. It classifies data which is new into existing clusters which called as centroid nearest classifier. Let as consider set observations (đ?‘Ž1 , đ?‘Ž2 , đ?‘Ž3 , ‌ . . đ?‘Žđ?‘› ) with D real vector dimensional. Here ‘c’ means clustering partition number of observation into c ≤ đ?‘› sets which is denoted as S = {đ?‘ đ?‘’đ?‘Ą1 , đ?‘ đ?‘’đ?‘Ą2 , đ?‘ đ?‘’đ?‘Ą3 ‌ . đ?‘ đ?‘’đ?‘Ąđ?‘˜ }, it will minimize sum of squares with cluster. argS đ?‘šđ?‘–đ?‘›đ?‘–đ?‘šđ?‘˘đ?‘š đ?‘?đ?‘ đ?‘’đ?‘Ą =1 đ?‘Žâˆˆđ?‘ đ?‘’đ?‘Ą đ?‘– ||đ?‘Ž − đ?œ‡đ?‘? ||2 = đ?‘Žđ?‘&#x;đ?‘”đ?‘ đ?‘’đ?‘Ą đ?‘šđ?‘–đ?‘›đ?‘–đ?‘šđ?‘˘đ?‘š to squared pairwise deviations in same cluster. đ?‘Žđ?‘&#x;đ?‘”đ?‘ đ?‘’đ?‘Ą minđ?‘–đ?‘šđ?‘˘đ?‘š
1 đ?‘? đ?‘?=1 2 đ?‘ đ?‘’đ?‘Ą đ?‘?
đ?‘Ž,đ?‘Śâˆˆđ?‘ đ?‘’đ?‘Ą đ?‘?
đ?‘? đ?‘?=1 |đ?‘ đ?‘’đ?‘Ąđ?‘?
|đ?‘Łđ?‘Žđ?‘&#x;đ?‘ đ?‘? , đ?œ‡đ?‘– is points mean of đ?‘ đ?‘’đ?‘Ąđ?‘? which is similar
||đ?‘Ľ − đ?‘Ś||2
similar features can be deleted by using formula đ?‘Žâˆˆđ?‘ đ?‘’đ?‘Ą đ?‘– ||đ?‘Ž − đ?œ‡đ?‘? |2 = total variance is constant between points in cluster. (1)
đ?‘Žâ‰ đ?‘Ś ∈đ?‘ đ?‘’đ?‘Ą đ?‘? (đ?‘Ž
− đ?œ‡đ?‘? (đ?œ‡đ?‘? − đ?‘Ś), which shows number of
(1)
Let as consider k mean initial set đ?‘›1 , ‌ ‌ ‌ đ?‘›đ?‘˜ , with assign observation in cluster, where mean has Euclidean distance (đ?‘–)
đ?‘ đ?‘’đ?‘Ąđ?‘? = {đ?‘Žđ?‘? | đ?‘Žđ?‘? − đ?‘›đ?‘?đ?‘Ą |2 ≤ | đ?‘Žđ?‘? − đ?‘›đ?‘— đ?‘Ą |2 ∀đ?‘— , 1 ≤ đ?‘— ≤ đ?‘?}, where đ?‘Žđ?‘? assigned one’s and đ?‘ (đ?‘Ą) can be assigned to three or more cluster. In update step it calculates and observed new mean to be centroid in the new cluster. B. Histogram based method Histogram based analysis required one pass through pixel in satellite image. Histogram is computed according to all pixel and help to locate cluster in images. To measure image it can considered intensity and colour for input data. It helps in multiple frame adaptations in satellite image. Consider histogram based on pixel valuesđ??ť0 , đ??ť1 , ‌ ‌ đ??ťđ?‘ , here HK define number of pixel with gray scale ‘n’ and ‘k’ which is maximum value of pixel. In first step guess has to be made đ??ž đ?‘–=0 đ??ťđ?‘˜
≼
đ?‘›2 2
>
đ?‘˜âˆ’1 đ?‘–=0 đ??ťđ?‘˜ ,
đ?‘›2 is number of pixels in n x n Images
In each category calculate pixel value of mean which is equal to or less than k. Value less then and equal to denoted by đ?œ‡1 =
đ?‘˜ đ?‘–=0 đ??źđ??ť đ?‘– đ?‘˜ đ??ť đ?‘–=0 đ?‘–
Re-assign k between two mean as half way: đ?‘˜ = C. Expectation Maximization @IJAERD-2018, All rights Reserved
, if greater than ‘k’ it is given as đ?œ‡2 =
đ?œ‡ 1 +đ?œ‡ 2 2
đ?‘ đ?‘–=đ?‘˜+1 đ??źđ??ť đ?‘– đ?‘ đ?‘˜ =đ?‘–+1 đ??ť đ?‘–
, Repeat above steps until k stop changing values
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